notebooks/multi_latent_phenos.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Global epistasis models with multiple latent phenotypes\n",
    "\n",
    "In this example, we simulate deep mutational scanning libraries under a global epistasis model with **two** latent phenotypes.\n",
    "We then fit global epistasis models with one and two latent phenotypes to the data, compare them, and examine how well they can predict new *unseen* multiple-mutant variants.\n",
    "\n",
    "The overall conclusion is that using multiple latent phenotypes does not seem to be better than using just one latent phenotype, even if the data are in fact simulated under multiple latent phenotypes.\n",
    "Presumably this is because of issues in the fitting of multiple latent phenotypes.\n",
    "\n",
    "## Setup for analysis\n",
    "\n",
    "Import Python modules / packages:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "attributes": {
     "classes": [],
     "id": "",
     "n": "1"
    }
   },
   "outputs": [],
   "source": [
    "import random\n",
    "import time\n",
    "import warnings\n",
    "\n",
    "import binarymap\n",
    "\n",
    "import pandas as pd\n",
    "\n",
    "from plotnine import *\n",
    "\n",
    "import scipy\n",
    "\n",
    "import dms_variants.codonvarianttable\n",
    "import dms_variants.globalepistasis\n",
    "import dms_variants.plotnine_themes\n",
    "import dms_variants.simulate\n",
    "from dms_variants.constants import CBPALETTE, CODONS_NOSTOP"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we set the parameters that define the simulation.\n",
    "We try to choose parameters typical of a Bloom lab viral deep mutational scanning project.\n",
    "There is a modest rate of errors in the variant calling, and a moderate bottleneck going from pre- to post-selection.\n",
    "We use a short gene (60 residues) in order to ensure that the analysis doesn't take too long.\n",
    "Crucially, we test libraries with a variety of mutation rates (average number of codon substitutions per variant):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "attributes": {
     "classes": [],
     "id": "",
     "n": "2"
    }
   },
   "outputs": [],
   "source": [
    "seed = 1  # random number seed\n",
    "genelength = 60  # gene length in codons\n",
    "variants_per_lib = 500 * genelength  # variants per library\n",
    "avgmuts = 2.5  # average mutations per variant\n",
    "bclen = 16  # length of nucleotide barcode for each variant\n",
    "variant_error_rate = 0.005  # rate at which variant sequence mis-called\n",
    "avgdepth_per_variant = 100  # average per-variant sequencing depth\n",
    "lib_uniformity = 5  # uniformity of library pre-selection\n",
    "noise = 0.02  # random noise in selections\n",
    "bottleneck = (\n",
    "    20  # bottleneck from pre- to post-selection as multiple of variants_per_lib\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Seed random number generator for reproducible output:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "attributes": {
     "classes": [],
     "id": "",
     "n": "3"
    }
   },
   "outputs": [],
   "source": [
    "random.seed(seed)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Set pandas display options to show large chunks of Data Frames in this\n",
    "example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "attributes": {
     "classes": [],
     "id": "",
     "n": "4"
    }
   },
   "outputs": [],
   "source": [
    "pd.set_option(\"display.max_columns\", 20)\n",
    "pd.set_option(\"display.width\", 500)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Hide warnings that clutter output:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "attributes": {
     "classes": [],
     "id": "",
     "n": "5"
    }
   },
   "outputs": [],
   "source": [
    "warnings.simplefilter(\"ignore\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Set the gray grid [plotnine theme](https://plotnine.readthedocs.io/en/stable/generated/plotnine.themes.theme.html?highlight=themes) defined in [dms_variants.plotnine_themes](https://jbloomlab.github.io/dms_variants/dms_variants.plotnine_themes.html) as this gives a nice appearance for the plots:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "theme_set(dms_variants.plotnine_themes.theme_graygrid())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Simulate library of variants\n",
    "Simulate libraries of codon variants with each of the average mutation rates.\n",
    "\n",
    "Simulate wildtype gene sequence:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "attributes": {
     "classes": [],
     "id": "",
     "n": "6"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Wildtype gene of 60 codons:\n",
      "AGATCCGTGATTCTGCGTGCTTACACCAACTCACGGGTGAAACGTGTAATCTTATGCAACAACGACTTACCTATCCGCAACATCCGGCTGATGATGATCCTACACAACTCCGACGCTAGTTTTTCGACTCCAGTAGGTTTACGCTCAGGACAGGATTCTTCCCTGGATAAGATGTACCGC\n"
     ]
    }
   ],
   "source": [
    "geneseq = \"\".join(random.choices(CODONS_NOSTOP, k=genelength))\n",
    "print(f\"Wildtype gene of {genelength} codons:\\n{geneseq}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Generate a\n",
    "[CodonVariantTable](https://jbloomlab.github.io/dms_variants/dms_variants.codonvarianttable.html#dms_variants.codonvarianttable.CodonVariantTable)\n",
    "using\n",
    "[simulate_CodonVariantTable](https://jbloomlab.github.io/dms_variants/dms_variants.simulate.html#dms_variants.simulate.simulate_CodonVariantTable)\n",
    "function, with different libraries for each mutation rate:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "attributes": {
     "classes": [],
     "id": "",
     "n": "7"
    }
   },
   "outputs": [],
   "source": [
    "variants = dms_variants.simulate.simulate_CodonVariantTable(\n",
    "    geneseq=geneseq,\n",
    "    bclen=bclen,\n",
    "    library_specs={\n",
    "        \"lib_1\": {\"avgmuts\": avgmuts, \"nvariants\": variants_per_lib},\n",
    "    },\n",
    "    seed=seed,\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot the number of amino-acid mutations per variant:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "attributes": {
     "classes": [],
     "id": "",
     "n": "15"
    }
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 300x210 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "p = variants.plotNumMutsHistogram(\n",
    "    \"aa\",\n",
    "    samples=None,\n",
    "    widthscale=1.2,\n",
    ")\n",
    "p = p + theme(panel_grid_major_x=element_blank())  # no vertical grid lines\n",
    "_ = p.draw(show=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Average number of codon mutations of each type per variant:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "attributes": {
     "classes": [],
     "id": "",
     "n": "17"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 240x230 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "p = variants.plotNumCodonMutsByType(variant_type=\"all\", samples=None)\n",
    "p = p + theme(panel_grid_major_x=element_blank())  # no vertical grid lines\n",
    "_ = p.draw(show=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Examine how well amino-acid mutations are sampled in the library by looking at the\n",
    "fraction\n",
    "of mutations seen <= some number of times, making separate plots for single mutants and all mutants.\n",
    "Most mutations are samples as single mutants, and all are sampled several times as multiple mutants:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "attributes": {
     "classes": [],
     "id": "",
     "n": "19"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 290x220 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 290x220 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for variant_type in [\"single\", \"all\"]:\n",
    "    p = variants.plotCumulMutCoverage(variant_type, mut_type=\"aa\", samples=None)\n",
    "    _ = p.draw(show=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Simulate variant counts under two-latent phenotype global epistasis model\n",
    "Now we simulate the counts of each variant after selection.\n",
    "These simulations are done under a model of the phenotypic effects of mutations.\n",
    "\n",
    "We define two latent-to-observed phenotype functions using an extension of the \"global epistasis\" concepts of [Otwinoski et\n",
    "al](https://doi.org/10.1073/pnas.1804015115) and [Sailer and\n",
    "Harms](https://doi.org/10.1534/genetics.116.195214).\n",
    "In that concept, there is an \"observed\" phenotype which is a nonlinear function of an underlying \"latent\" phenotype that is affected additively by mutations.\n",
    "\n",
    "Here we instead let the observed phenotype be the sum of **two** nonlinear functions each acting on a different latent phenotype.\n",
    "Each nonlinear function is implemented via a [SigmoidPhenotypeSimulator](https://jbloomlab.github.io/dms_variants/dms_variants.simulate.html#dms_variants.simulate.SigmoidPhenotypeSimulator), and these are then combined in a [MultiLatentSigmoidPhenotypeSimulator](https://jbloomlab.github.io/dms_variants/dms_variants.simulate.html#dms_variants.simulate.MultiLatentSigmoidPhenotypeSimulator) that maps the two latent phenotypes to the observed phenotype.\n",
    "The first latent phenotype is strongly affected by most mutations (you can imagine this is something like protein stability) and the other is strongly affected by only some mutations (you can imagine this is something like protein activity).\n",
    "\n",
    "The counts for variants are then simulated according to their enrichments, which are the exponentials of the observed phenotype:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "attributes": {
     "classes": [],
     "id": "",
     "n": "24"
    }
   },
   "outputs": [],
   "source": [
    "pheno1 = dms_variants.simulate.SigmoidPhenotypeSimulator(\n",
    "    geneseq,\n",
    "    seed=seed,\n",
    "    wt_latent=4,\n",
    "    stop_effect=-10,\n",
    "    norm_weights=[\n",
    "        (0.4, -1.25, 1.25),\n",
    "        (0.6, -5.5, 2.25),\n",
    "    ],\n",
    ")\n",
    "pheno2 = dms_variants.simulate.SigmoidPhenotypeSimulator(\n",
    "    geneseq,\n",
    "    seed=seed,\n",
    "    wt_latent=3,\n",
    "    stop_effect=0,\n",
    "    norm_weights=[\n",
    "        (0.7, 0, 0.1),\n",
    "        (0.2, -8, 3),\n",
    "        (0.1, -1, 2),\n",
    "    ],\n",
    ")\n",
    "\n",
    "phenosimulator = dms_variants.simulate.MultiLatentSigmoidPhenotypeSimulator(\n",
    "    [pheno1, pheno2]\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot the distribution of each latent phenotype, the, observed phenotype, and observed enrichment for all single amino-acid mutants, with a dashed vertical line indicating the wildtype:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "attributes": {
     "classes": [],
     "id": "",
     "n": "26"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 350x250 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 350x250 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 350x250 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 350x250 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for value in [\"latentPhenotype\", \"observedPhenotype\", \"observedEnrichment\"]:\n",
    "    if value == \"latentPhenotype\":\n",
    "        for k in range(1, phenosimulator.n_latent_phenotypes + 1):\n",
    "            p = phenosimulator.plotMutsHistogram(value, k=k)\n",
    "            _ = p.draw(show=True)\n",
    "    else:\n",
    "        p = phenosimulator.plotMutsHistogram(value)\n",
    "        _ = p.draw(show=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Use [simulateSampleCounts](https://jbloomlab.github.io/dms_variants/dms_variants.simulate.html#dms_variants.simulate.simulateSampleCounts) to simulate counts of variants when selection on each variant is proportional to\n",
    "its observed enrichment:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "attributes": {
     "classes": [],
     "id": "",
     "n": "27"
    }
   },
   "outputs": [],
   "source": [
    "counts = dms_variants.simulate.simulateSampleCounts(\n",
    "    variants=variants,\n",
    "    phenotype_func=phenosimulator.observedEnrichment,\n",
    "    variant_error_rate=variant_error_rate,\n",
    "    pre_sample={\n",
    "        \"total_count\": variants_per_lib * avgdepth_per_variant,\n",
    "        \"uniformity\": lib_uniformity,\n",
    "    },\n",
    "    pre_sample_name=\"pre-selection\",\n",
    "    post_samples={\n",
    "        \"post-selection\": {\n",
    "            \"noise\": noise,\n",
    "            \"total_count\": variants_per_lib * avgdepth_per_variant,\n",
    "            \"bottleneck\": variants_per_lib * bottleneck,\n",
    "        }\n",
    "    },\n",
    "    seed=seed,\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Add the simulated counts for each library to the [CodonVariantTable](https://jbloomlab.github.io/dms_variants/dms_variants.codonvarianttable.html#dms_variants.codonvarianttable.CodonVariantTable):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "attributes": {
     "classes": [],
     "id": "",
     "n": "29"
    }
   },
   "outputs": [],
   "source": [
    "variants.add_sample_counts_df(counts)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot the number of counts for each variant. \n",
    "The horizontal dashed line shows the total number of variants. \n",
    "The plot shows that all variants are well-sampled in the pre-selection libraries, but that post-selection some variants are sampled more or less.\n",
    "This is expected since selection will decrease and increase the frequency of variants:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "attributes": {
     "classes": [],
     "id": "",
     "n": "32"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 400x210 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "p = variants.plotCumulVariantCounts(libraries=variants.libraries, orientation=\"v\")\n",
    "_ = p.draw(show=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Distribution of the number of amino-acid mutations per variant.\n",
    "As expected, mutations go down after selection:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "attributes": {
     "classes": [],
     "id": "",
     "n": "33"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 480x210 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "p = variants.plotNumMutsHistogram(\n",
    "    mut_type=\"aa\", libraries=variants.libraries, widthscale=1.2, orientation=\"v\"\n",
    ")\n",
    "p = p + theme(panel_grid_major_x=element_blank())  # no vertical grid lines\n",
    "_ = p.draw(show=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Average number of mutations per variant:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "attributes": {
     "classes": [],
     "id": "",
     "n": "34"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 380x230 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "p = variants.plotNumCodonMutsByType(\n",
    "    variant_type=\"all\", libraries=variants.libraries, orientation=\"v\"\n",
    ")\n",
    "p = p + theme(panel_grid_major_x=element_blank())  # no vertical grid lines\n",
    "_ = p.draw(show=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Functional scores for variants\n",
    "Use\n",
    "[CodonVariantTable.func_scores](https://jbloomlab.github.io/dms_variants/dms_variants.codonvarianttable.html#dms_variants.codonvarianttable.CodonVariantTable.func_scores)\n",
    "to calculates a functional score for each variant based on its change in\n",
    "frequency from pre- to post-selection:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "attributes": {
     "classes": [],
     "id": "",
     "n": "37"
    }
   },
   "outputs": [],
   "source": [
    "func_scores = variants.func_scores(\"pre-selection\", libraries=variants.libraries)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Classify variants\n",
    "by the “types” of mutations they\n",
    "have using the\n",
    "[CodonVariantTable.classifyVariants](https://jbloomlab.github.io/dms_variants/dms_variants.codonvarianttable.html#dms_variants.codonvarianttable.CodonVariantTable.classifyVariants):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "func_scores = dms_variants.codonvarianttable.CodonVariantTable.classifyVariants(\n",
    "    func_scores\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot the distributions of scores, coloring by the variant class:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 225x200 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "p = (\n",
    "    ggplot(func_scores, aes(\"variant_class\", \"func_score\"))\n",
    "    + geom_violin(aes(fill=\"variant_class\"))\n",
    "    + ylab(\"functional score\")\n",
    "    + xlab(\"\")\n",
    "    + facet_wrap(\"~ library\", nrow=1)\n",
    "    + theme(\n",
    "        figure_size=(2.25 * len(variants.libraries), 2),\n",
    "        axis_text_x=element_text(angle=90),\n",
    "        panel_grid_major_x=element_blank(),  # no vertical grid lines\n",
    "    )\n",
    "    + scale_fill_manual(values=CBPALETTE[1:])\n",
    ")\n",
    "_ = p.draw(show=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fit global epistasis models with multiple latent phenotypes\n",
    "Now we will fit global epistasis models with multiple latent phenotypes.\n",
    "More information about these models is provided in the description at the top of the [dms_variants.globalepistasis](https://jbloomlab.github.io/dms_variants/dms_variants.globalepistasis.html) module. \n",
    "\n",
    "We use the [fit_models](https://jbloomlab.github.io/dms_variants/dms_variants.globalepistasis.html#dms_variants.globalepistasis.fit_models) function, which fits a non-epistatic model as well as global epistasis models with multiple latent phenotypes (it keeps adding latent phenotypes until their addition no longer helps).\n",
    "This is the best way to fit multi-latent phenotype models, because the model with $K$ latent phenotypes is fit with parameters initialized by the model with $K - 1$ latent phenotyes.\n",
    "Note [fit_models](https://jbloomlab.github.io/dms_variants/dms_variants.globalepistasis.html#dms_variants.globalepistasis.fit_models) does **not** fit multi-latent phenotype models for the no-epistasis models, since this would not make sense: the sum of two linear models is just another linear model.\n",
    "\n",
    "When calling [fit_models](https://jbloomlab.github.io/dms_variants/dms_variants.globalepistasis.html#dms_variants.globalepistasis.fit_models), we have to decide the maximum number of latent phenotypes we allow.\n",
    "Here we cap it at two, because this is the actual number in the simulated data; also the computational time needed for fitting grows rapidly with more latent phenotypes:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "# make sure we're just fitting one library, if multiple you should fit one-by-one\n",
    "assert func_scores[\"library\"].nunique() == 1\n",
    "\n",
    "# create BinaryMap of variants\n",
    "bmap = binarymap.BinaryMap(func_scores)\n",
    "\n",
    "# fit the models\n",
    "fits_df = dms_variants.globalepistasis.fit_models(\n",
    "    binarymap=bmap, likelihood=\"Gaussian\", max_latent_phenotypes=2\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The returned `fits_df` data frame has columns with lots of relevant information:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['description',\n",
       " 'n_latent_phenotypes',\n",
       " 'AIC',\n",
       " 'nparams',\n",
       " 'log_likelihood',\n",
       " 'model',\n",
       " 'fitting_time']"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fits_df.columns.tolist()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `model` column has the actual fit model, so for now let's look at all the other columns that summarize the model fits.\n",
    "You can see that models are ranked by [AIC](https://en.wikipedia.org/wiki/Akaike_information_criterion), which is an overall measure that compares model fit (log likelihood) after correcting for number of parameters.\n",
    "There is also a column that gives the time (in seconds) required for the fitting:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>description</th>\n",
       "      <th>n_latent_phenotypes</th>\n",
       "      <th>AIC</th>\n",
       "      <th>nparams</th>\n",
       "      <th>log_likelihood</th>\n",
       "      <th>fitting_time</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>global epistasis with 2 latent phenotypes</td>\n",
       "      <td>2</td>\n",
       "      <td>79240.3</td>\n",
       "      <td>2415</td>\n",
       "      <td>-37205.2</td>\n",
       "      <td>105.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>global epistasis with 1 latent phenotypes</td>\n",
       "      <td>1</td>\n",
       "      <td>79540.6</td>\n",
       "      <td>1208</td>\n",
       "      <td>-38562.3</td>\n",
       "      <td>43.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>no epistasis</td>\n",
       "      <td>1</td>\n",
       "      <td>133443.5</td>\n",
       "      <td>1202</td>\n",
       "      <td>-65519.8</td>\n",
       "      <td>0.3</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                 description  n_latent_phenotypes       AIC  nparams  log_likelihood  fitting_time\n",
       "0  global epistasis with 2 latent phenotypes                    2   79240.3     2415        -37205.2         105.2\n",
       "1  global epistasis with 1 latent phenotypes                    1   79540.6     1208        -38562.3          43.6\n",
       "2                               no epistasis                    1  133443.5     1202        -65519.8           0.3"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# NBVAL_IGNORE_OUTPUT\n",
    "\n",
    "fits_df.drop(\"model\", axis=\"columns\").round(1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Above we see that both global epistasis models are much better than the no-epistasis model, and that the model with two latent phenotypes is better than the one with just one: it has a better log likelihood, and the [AIC](https://en.wikipedia.org/wiki/Akaike_information_criterion) shows that this improved log likelihood is enough to justify the additional parameters."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Examine model fits\n",
    "Now let's examine how the model fits the data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Predictions of phenotypes of fit variants\n",
    "First, we see how well the model predictions align with the (simulated) measurements on the variants used to fit the models.\n",
    "\n",
    "To do this, we use the fit models in the `model` column of `fits_df` to get a data frame with each models predicted phenotypes on all variants used to fit the models:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>aa_substitutions</th>\n",
       "      <th>func_score</th>\n",
       "      <th>func_score_var</th>\n",
       "      <th>latent_phenotype_1</th>\n",
       "      <th>latent_phenotype_2</th>\n",
       "      <th>observed_phenotype</th>\n",
       "      <th>model</th>\n",
       "      <th>latent_phenotype</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td></td>\n",
       "      <td>0.198</td>\n",
       "      <td>0.007</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>-0.032</td>\n",
       "      <td>global epistasis with 2 latent phenotypes</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>M32K L34R</td>\n",
       "      <td>-1.919</td>\n",
       "      <td>0.011</td>\n",
       "      <td>-0.609</td>\n",
       "      <td>-0.302</td>\n",
       "      <td>-1.903</td>\n",
       "      <td>global epistasis with 2 latent phenotypes</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>S11A R12K R60S</td>\n",
       "      <td>-11.482</td>\n",
       "      <td>4.168</td>\n",
       "      <td>-2.559</td>\n",
       "      <td>3.550</td>\n",
       "      <td>-3.533</td>\n",
       "      <td>global epistasis with 2 latent phenotypes</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>R12Y V13N</td>\n",
       "      <td>-11.422</td>\n",
       "      <td>4.169</td>\n",
       "      <td>-6.005</td>\n",
       "      <td>-3.337</td>\n",
       "      <td>-9.297</td>\n",
       "      <td>global epistasis with 2 latent phenotypes</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>L5A S54R</td>\n",
       "      <td>-0.125</td>\n",
       "      <td>0.008</td>\n",
       "      <td>-0.193</td>\n",
       "      <td>-0.315</td>\n",
       "      <td>-0.284</td>\n",
       "      <td>global epistasis with 2 latent phenotypes</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>89995</th>\n",
       "      <td></td>\n",
       "      <td>-6.216</td>\n",
       "      <td>4.382</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>-0.890</td>\n",
       "      <td>no epistasis</td>\n",
       "      <td>-0.890</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>89996</th>\n",
       "      <td>L23Q</td>\n",
       "      <td>-4.471</td>\n",
       "      <td>1.632</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>-4.972</td>\n",
       "      <td>no epistasis</td>\n",
       "      <td>-4.972</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>89997</th>\n",
       "      <td>V3K</td>\n",
       "      <td>-2.886</td>\n",
       "      <td>0.707</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>-4.031</td>\n",
       "      <td>no epistasis</td>\n",
       "      <td>-4.031</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>89998</th>\n",
       "      <td>R6Q D22V Y59G</td>\n",
       "      <td>-3.249</td>\n",
       "      <td>0.840</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>-3.198</td>\n",
       "      <td>no epistasis</td>\n",
       "      <td>-3.198</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>89999</th>\n",
       "      <td>K14F N20K</td>\n",
       "      <td>1.201</td>\n",
       "      <td>0.514</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>-1.173</td>\n",
       "      <td>no epistasis</td>\n",
       "      <td>-1.173</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>90000 rows × 8 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      aa_substitutions  func_score  func_score_var  latent_phenotype_1  latent_phenotype_2  observed_phenotype                                      model  latent_phenotype\n",
       "0                            0.198           0.007               0.000               0.000              -0.032  global epistasis with 2 latent phenotypes               NaN\n",
       "1            M32K L34R      -1.919           0.011              -0.609              -0.302              -1.903  global epistasis with 2 latent phenotypes               NaN\n",
       "2       S11A R12K R60S     -11.482           4.168              -2.559               3.550              -3.533  global epistasis with 2 latent phenotypes               NaN\n",
       "3            R12Y V13N     -11.422           4.169              -6.005              -3.337              -9.297  global epistasis with 2 latent phenotypes               NaN\n",
       "4             L5A S54R      -0.125           0.008              -0.193              -0.315              -0.284  global epistasis with 2 latent phenotypes               NaN\n",
       "...                ...         ...             ...                 ...                 ...                 ...                                        ...               ...\n",
       "89995                       -6.216           4.382                 NaN                 NaN              -0.890                               no epistasis            -0.890\n",
       "89996             L23Q      -4.471           1.632                 NaN                 NaN              -4.972                               no epistasis            -4.972\n",
       "89997              V3K      -2.886           0.707                 NaN                 NaN              -4.031                               no epistasis            -4.031\n",
       "89998    R6Q D22V Y59G      -3.249           0.840                 NaN                 NaN              -3.198                               no epistasis            -3.198\n",
       "89999        K14F N20K       1.201           0.514                 NaN                 NaN              -1.173                               no epistasis            -1.173\n",
       "\n",
       "[90000 rows x 8 columns]"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# NBVAL_IGNORE_OUTPUT\n",
    "\n",
    "phenotypes_df = pd.concat(\n",
    "    [\n",
    "        tup.model.phenotypes_df.assign(model=tup.description)\n",
    "        for tup in fits_df.itertuples()\n",
    "    ],\n",
    "    sort=False,\n",
    "    ignore_index=True,\n",
    ")\n",
    "\n",
    "phenotypes_df.round(3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now plot the experimentally measured functional scores versus the observed phenotype predicted by the model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1200x400 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "p = (\n",
    "    ggplot(phenotypes_df, aes(\"observed_phenotype\", \"func_score\"))\n",
    "    + geom_bin2d()\n",
    "    + facet_wrap(\"~ model\", nrow=1, scales=\"free_x\")\n",
    "    + theme(figure_size=(4 * phenotypes_df[\"model\"].nunique(), 4))\n",
    "    + xlab(\"observed phenotype predicted by model\")\n",
    "    + ylab(\"measured functional score\")\n",
    ")\n",
    "_ = p.draw(show=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Distribution of latent effects\n",
    "For the model with two latent phenotypes, look at the distribution of the latent effects for the two latent phenotypes, and the correlation among them.\n",
    "First, get these latent effects:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mutation</th>\n",
       "      <th>latent_effect</th>\n",
       "      <th>latent_phenotype_number</th>\n",
       "      <th>latent_phenotype_name</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>R1*</td>\n",
       "      <td>-1.334</td>\n",
       "      <td>1</td>\n",
       "      <td>latent phenotype 1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>R1A</td>\n",
       "      <td>-0.003</td>\n",
       "      <td>1</td>\n",
       "      <td>latent phenotype 1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>R1C</td>\n",
       "      <td>-0.332</td>\n",
       "      <td>1</td>\n",
       "      <td>latent phenotype 1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>R1D</td>\n",
       "      <td>-1.031</td>\n",
       "      <td>1</td>\n",
       "      <td>latent phenotype 1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>R1E</td>\n",
       "      <td>-0.976</td>\n",
       "      <td>1</td>\n",
       "      <td>latent phenotype 1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2395</th>\n",
       "      <td>R60S</td>\n",
       "      <td>1.606</td>\n",
       "      <td>2</td>\n",
       "      <td>latent phenotype 2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2396</th>\n",
       "      <td>R60T</td>\n",
       "      <td>-0.379</td>\n",
       "      <td>2</td>\n",
       "      <td>latent phenotype 2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2397</th>\n",
       "      <td>R60V</td>\n",
       "      <td>-0.904</td>\n",
       "      <td>2</td>\n",
       "      <td>latent phenotype 2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2398</th>\n",
       "      <td>R60W</td>\n",
       "      <td>-2.811</td>\n",
       "      <td>2</td>\n",
       "      <td>latent phenotype 2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2399</th>\n",
       "      <td>R60Y</td>\n",
       "      <td>0.040</td>\n",
       "      <td>2</td>\n",
       "      <td>latent phenotype 2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>2400 rows × 4 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     mutation  latent_effect  latent_phenotype_number latent_phenotype_name\n",
       "0         R1*         -1.334                        1    latent phenotype 1\n",
       "1         R1A         -0.003                        1    latent phenotype 1\n",
       "2         R1C         -0.332                        1    latent phenotype 1\n",
       "3         R1D         -1.031                        1    latent phenotype 1\n",
       "4         R1E         -0.976                        1    latent phenotype 1\n",
       "...       ...            ...                      ...                   ...\n",
       "2395     R60S          1.606                        2    latent phenotype 2\n",
       "2396     R60T         -0.379                        2    latent phenotype 2\n",
       "2397     R60V         -0.904                        2    latent phenotype 2\n",
       "2398     R60W         -2.811                        2    latent phenotype 2\n",
       "2399     R60Y          0.040                        2    latent phenotype 2\n",
       "\n",
       "[2400 rows x 4 columns]"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# NBVAL_IGNORE_OUTPUT\n",
    "\n",
    "# 2-latent phenotype model should be the first one if `fits_df`\n",
    "# is sorted by descending log likelihood\n",
    "model_2latent = fits_df.sort_values(\"log_likelihood\", ascending=False)[\"model\"].values[\n",
    "    0\n",
    "]\n",
    "assert model_2latent.n_latent_phenotypes == 2\n",
    "\n",
    "latenteffects2 = model_2latent.latent_effects_df.assign(\n",
    "    latent_phenotype_name=lambda x: (\n",
    "        \"latent phenotype \" + x[\"latent_phenotype_number\"].astype(str)\n",
    "    )\n",
    ")\n",
    "latenteffects2.round(3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Distribution of latent effects for the two phenotypes:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x250 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "p = (\n",
    "    ggplot(latenteffects2, aes(\"latent_effect\"))\n",
    "    + geom_histogram()\n",
    "    + facet_wrap(\"~ latent_phenotype_name\", nrow=1)\n",
    "    + theme(figure_size=(2.5 * model_2latent.n_latent_phenotypes, 2.5))\n",
    "    + xlab(\"latent effect of mutation\")\n",
    "    + ylab(\"number of mutations\")\n",
    ")\n",
    "_ = p.draw(show=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Correlation between latent effects of all single mutations for the two phenotypes:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ZoyoXAQcCB5cNysys19aFaqoviNViqrneCIAWay/PPx0nE0mPYHrW5cWSso+5xoGXAF4LvgItJxps0eNprEXvq1qLNcNze3q16GnUSsv14Vtds9Xa5QUmL5wPPfD23Sz/b69Ym7N2ExT+3di0qVjQ4sO82gV8c9pbbi152YHSTc1kBcl7EsD1TcqDmQNtzMwGVq3WKkW0Th/tBi/GnNd0+q+bZLInyTv8U+CVwL2ZsrXATRExVJnWzIZX8XEmswcvzpwmpW7Ym9xn6jiZRMTFAJK2B26J8KIJZjZ/1Qp/2Gv2ulhWaG6umyRtLukNwFPS3b8FvhIRzZbzNTMbOFPReSpo/thKTQurmBxyPioyAn5X4DySScR+ne5+D3C4pBdGxBUVxmdm1hPtHnN13u7RkD0azhuV5FKka/BngO8Dh9QXYEmnTD6VZFoVr3ViZgNvqqYZH/Q9azTPSS4R5E+wNg8VSSa7kkkkABExKel44PLKIhsBeV2Ai3ZpbdUlV2P5fx7ldddttc57q+6urbScfLHANYtO5jgoag8/nFum8RZTpLfqRm0dmaxpUbbxPNHrakQ6Mj65zaN7fLM5VSSZ3A9sC/yhYf/jmaPlIc3MypqK8VXtBitWmVpi9os/VXj5viuSTM4BTpP0XuAX6b7dgU+STP5oZjbwWo8zaa6b9o9RG2tSJJm8lySvfi1z/jrgCyTTrJiZDbxaF7251mvTuD5qCSSrSNfgtcC7JH0QeGK6+4aIyH/4a2Y2YAolk0YjnDwaFV5pMU0e11YYi5nZnKnVuu/EEE1fTSelEekF3FSRcSabkDzO2gvYioZp7CPiCdWEZmbWO53UTFo/tmp//qiMMYFiNZNTgb8HziRZddEVvYrlrXfezvlT5zAxMcGSJUu6u1+rWYor1qy7bpGYh4UWzFoaaFqLGYticl1uWd7v85TrPtZxXKOgWTKpvM0jc71hTyxFksmLgf0i4tKqgzEzmytTU9pQmsO/hhtvFMO1Gm2RZHIfM2cMNjObd2o1tVgwht41gEwnlRU9ukNfFEkmHwaOlvQ69+Ays/kqYqx1paQXVZYgm6Tu68Ed+qZIMvl3ki7Bd0haTjLGZL2I2KWCuMzMeqps+0hexaXtZYe0lblIMjm38ijMzOZYFBgBP+P8iuIYFkUGLR7Vi0Dms6KTDeaVtZqw8SfrvtF5YCW1ir3oz1z1xIzzYTLHVmqt1nlvtf5ci4ke896TiYmJTsMaCVHFoEVbr9DUo+niWG+U9HFJW6T7dpH02GrDKxTbcknRsHmaFzObIUKdb7Uutw6vO0yKDFr8W+ACYCWwHfBlkt5dryCZTfjACuMr6iMkcdV5NmMzm6Flm8mssm4++GP2+cOVN5oq0mZyAnB6RLxfUvZD+ofA2dWEVdoDEXF7v4Mws8FVq2kss1BVhZ/3Ta4UM79N11HZqrJbDoAij7meCXypyf6/AFuXC6cyh0m6R9KVkt6XrgRpZjatpgUxJWJK0O1jrBIbtfX33Ljfb0GVinzIrgEe0WT/DsBd5cKpxOeAK0gevT0H+DiwDck69c2MN2uYjIhKGiyrbvRsd72q4u7kXoNyXj9U+T5XLS+uQY65L9oNWqyrqsoy+7Ha8oquPBCKJJPvAx+R9C/p65C0LfAJ4NuVRZYh6TjgA20Oe0pE/CEiTsjsu0bSWuBLkj4YEWuanDe1ZMmSWeujVjVfVNVzTrW7XpXzXBW9zlyf1w+DPJ9YXlyDHHOe66+/vncX77QBvGj7R8G+w5IOBQ4C/gb4UUS8PFP2COCLwEuBVcDJEXFMp+W9VHTQ4n8CdwKLgItJHm9dBhxeXWgzfBo4vc0xeUtg/ork59wOuK66kKZV3T21VfffopMyFumiXPR63Z43Hz/kKtOq+6/1VtGBItnzlLO/nFuBY4G9gcc1lJ0EbEHS2Wkr4AJJN0XE1zos75ki40xWAvtIei7wt8CmwBURcUHVwWXueRfFH6EtBWokyc/MDCg/aLFXIuI7AJKWkkkmkjYGXg3sHhErgBWSTgLeAHytXXmv4y6zONYlwCUVxlKapN2AvwN+RtIdeDfgM8DXI2Ko5sExs5JK1CR6UyFpa0dgIXBVZt9VwIc6LO+pQslE0l7kL451cAVxFbWGJDMvAzYEbiRJJie0OMfMRlGIb+/ygtziV17x09xM0XECEbn3uHPNqm07vUxqU+ChiJjM7FsBLO6wvKeKDFo8kmRQ4OUM2OJYEXEF8Ox+x2Fm80C75qoqmrNafzp2+5ztQWBjSQsyCWMzpgdltyvvqSI1k7cAB0XEmVUHY2Y2Z6a0qGV5j6c7mYro9vP3OpJZ2ncCfpPuWwpc22F5TxVJJguBX1QdiHWmXS+q+dwzqupJIOeDlpNitli++fypc/LP87K9nQlWvfKXP+v5bXLvEdzy0t2fN2t3Osi6vo1J2gioRcTDks4BjpH0GpJmhneQrDFFu/JeKzIC/lTgtVUHYmY2lxRqs9GjLb0+uYMmjyAZI3I48LL0+5+kZYeSzIv4Z+BS4LSGbr/tynumo5qJpGwD9hjwJkl7A9cwe3GsvJHmZmaDo22bSJvHXM2KK2hBjohlJJ2ImpXdD7ymxbkty3up08dcOze8rnc9e3rD/oFpjDcza0VlP638aTdDR8kkIvbsdSBmZnOqihHwWYM5BnLOlJpNV9LjASLilmrCMTObGx3XTIoeN2LJpesGeEkLJB0jaSXJrJfLJa2UdKykDSqP0MysF0LNt1rDlndcu62TawyRIjWTk0hWVXw/yeSOkExbsgz4K+CtlURmA60X3XiHtftvUS27/7bqNuw14DszxQJEulrVzKKqP+abruoYPL7i2/RVkWTyWuDVEfGjzL5rJN0C/AdOJmY2D6hVb66Ks8msyyXJZaimjC66ONbyJvtvBDpbbMbMrM8UTOYWVt3+0bzd5S8lrzpQigxaPBn4sKQN6zvS7w9Py8zMBl5XAw1r9U3J1m7AY42ZW851h0mRmsnOJDMG/1nS1em+nUimWblQ0nfqB0bEK8qHaGbWA4UeMjVkAKVVlqaNIqOlSDJZwezled012MzmFVXRm2p9DhmunllFFFlp8fW9CMTMbE51W5lorJTkXWZE80qpQYs2utyNt79adRu2zrTszdXNdRp3jOgTLycTMxtJUZtu8kh20PtaRfYeQev1VOYZJxMzG0ljNRatH7Q415KEsk0f7twzTiZmNpIUrOrbI6nkvn/q0917osjcXAdmx5hk9i+UdGA1YZmZ9VitwBZdbu2uN0SKDFr8Kski9Y0Wp2VmZgOv0CqJ7QYjdjhY0YMWE3lPGR9Hslykmdngq+LDfMgSQhkdJxNJVzJdebtQUnZem3Fge+DH1YZnZtYbhWoG7c4Z0TEm0F3N5Nz061LgPODBTNlakskfG0fGm5kNpk6SSeaYTvLEjFlVRiyxdJxMIuIoAEnLgXMiYnWvgjIz67WqBi3OuGb2xYg9AisyncoZkPTeAraioRE/Im6uJjQzs95RjQ37VntIEs32fbp7T3SdTCQtAb4CPKexiOQtGq8gLjOz3qr1ff2l+/t8/0oV6c11OjAJvBS4jZGrzJnZMFCty8+uorWY/LvcU/CKA6lIMlkKPCMi/lB1MGY2bZ+x/XPLPNFmeV335uq0cX1E/7wukkx+Bzyq6kDMzOZSmQb4Gfmiyci7EevIBRRLJh8Ajpf0IeBaYF22MCKG6jmgmQ2pEqsjzqrVjGL2aFAkmVyQfr2wYb8b4M1s3ujqMdesqkiz8i4HpQyZIslkz8qjMDOba10+5prOD62zUGNeGRVFxplc3ItAzMzmkmoof+3dEtft9IAYrrbnIrMGI+l5kr4u6ReSHpvuO0DSc6sNz8ysNzTFQtVAU01m++3lNpVuweJ+vwdVKjJo8ZXAmcBZwC5AfW2TzYAPAS+pLDqzEebuv72lYA1TnRxY0Q1n135ubHo76XTgtTBjUOU+EXFZWr4B8BngX9OrngW8OyIm6aMiNZMjgLdExCHM7Ml1KUlyMTMbeJ3UIqgBUw1bpwtppcevr4k0u36+UyJi08x2WabsCOC5wFOBpwHPI/lDvq+KJJMdgZ832b8S2LxcOGZmc6SDlRLbLpDVwcJYLe9RzMHAsRFxW0TcBnwUeEPhq1WkSDK5HXhSk/3PZcjWNDaz4aWI8lstsxU4v4UDJd0r6beS/l3SGICkR5IsRHhV5tirgG0lNVsBd84U6Rr8ZeCzkg4mya2PkbQb8CngmCqDMzPrFdXg8+/ZI7f87Sdc1O4K6dfWVYy8e9yzcvW2Oad8DngfcC/wTOCbJA/OPgNsmh6zInN8/fvF9HG12yLJ5DiSGs2FwMYkj7zWAJ+KiJMqjM3MrHfaPWZq8ihKsw5oc8kCjfcRcUXm5S8lHQccSJJM6osSbgbcnfke4IHu71adIuNMAviopE+SPO7aFPhdRDzY+kwzs8HRbgR8kbm7ZuWOasavrI8kIu6T9GeSCXdvSHcvBW6JiL7VSqBY1+CvAO+KiAdIJn2s798EOCkiDq4wPjOz3phk0aGfuGhWBlDD17LecfxFQJO8EmzwwhfsPut4Sf8C/JikpvEM4DDg85lDvgocLunS9PWHgFMrCrewIg3wrwMWNdm/iKQqZmY28FSLVZoKNDlzI7tNVbfNutdU7S85oR0K3EySTM4CTgE+nSk/BrgM+H26XQp8rHfvVGc6rplIegRJshawWFJ2DfhxksGKd1YbnplZb4x18giq0zVMOjl/lhmfodOnRDy/5SUj1gFvT7eB0c1jrhVMN0ld36Q8gCOrCMrMrNfadM2dZfbhedkl0uu3OWzIdJNM9iR5W34KvJKk21rdWuCmiLi1wtjMzHqn8KzBdR0moxGZQbjjZFKfLVjS9iQ9B0qsU2Zm1l/FV1rMyw4jUgXJUaRr8E0AkjYGtgUWNpRfU01oZma90/Fjro5rFqO9dm+RrsFbknRNe3HOIV5p0cwGXwc1kzL5oMSqwPNSka7BJ5JM6Ph3wCpgX5LuwhPAP1QXmplZ76gWC5rOsZXZKLHlXXP9PF61eFy/34MqFZlO5QXAP0bE5ZJqJA3v50u6H/gg8N+VRmhm1gOaiv4+ihqymkuRZLIJ0+NJ7gO2JOkqfC1ez8TM5glFTM75B3r92ZcE8Oc5vntPFUkm15GsabIcuBp4s6TlwFuA2yqLzMysl2rdZ5L1Q0fUpkrTrsFkCBtUirSZfBbYJv3+KJKG+JuBd9Lj1b4kHZ6uO/+wpBU5x2wr6b/TY+6U9ElJRZKmmQ2xIuuPjNXXIanVpreG16rVqljPZN4p0jX465nvfyPpr4EnAzdHxN35Z1ZiIfAtknlpZq0sJmmcpM3mduA5JEnvayTLC/d9WUszGyAFx5lM10mGKxmUVfov9oh4GLii7YEViIgjASQdlHPIC0nWRd47Iu4ArpL0YeATkpZFxNq5iNPMBl/XNYNofFFPKzVmtOSP2PiSuo6SiaQTOr1gRLyneDil7QZcmyaSuvOALwBPA67sS1RmNnja1Uwakk3r6VRi1p7pE0cju3RaM9m5w+P6Xe/bGrijYd8dmbJmxicmJmbtjAia7R908zFuxzw35mPMvaSp2swP+ojSH/xNz84mpew9IjYsdbMB01EyiYg9exVAuiTlB9oc9pSI+EOPQphasmTJrFH7ExMTLFmypEe37J35GLdjnhvzMebrr282QXk1VIuN1k/tu/7zfi7+Hl4/vmXkBy1W7dPA6W2O+VOH17odeFbDvkdnyszMElPRdD2RuqDiJ1Sz2lw6/lybF/qeTCLiLuCuii53GclylltFRH1g5T7A/WSWGDYza9cAL5oMB+k2u7Rud+l3s0Cl+p5MuiFpW2ALktmKxyUtTYv+GBEPAj8hSRpnSno/STvJscDnI2JNP2I2swHVwaDFtmuYNCaXIRs70o15lUyAo0kmlayr987aE7goIqYkvZSk99ZlwEPAGcBH5jRKMxt8BUbAzza6yaPRvEomEXEQcFCbY24iWY/ezCxfkWSSqXlkR5oAI9MFOM+8SiZmZlVRJ4vFtsg3s1JH4yOuEcstTiZmNpryaia9enI15MnFycTMRpImawsZU5+aPQJgu37cuVecTMysJ/YZ27/p/vNr39/ZyjoAAAuhSURBVJrjSHJM1dYx1aK8VzWJ6eT1UI/u0BdOJmY2mqJNC3y2tEzjen534arG1w0EJxMzG01d9eZqM75kxqGj2V3YycTMRlOt4IImWSJJLPUEMpp5BHAyMbNRVaYGMasb8JB31eqAk4mZjaZuaiZt885ojzEBJxMzG1Ut20xKPq+adfrwZxcnEzPriYHpApxnakqZhap6/KiqSXKK2KKHN5xzTiZmNpqmphYyNta/3lfSZv25cW84mZjZSIpabU1H7SZV1VhmJ60bq7nwYHAyMbPRVLRrcKfJZcTGmziZmNlIijLjTNKEokxiifVjTUYridQ5mZjZaKpg0GLAzEGLI8zJxMxGU4Fk0i5lDH8H4HxOJmY2kko95sq7ZuVXnD+cTMxsNPUgmYwyJxMzG0lRq60DbgAeAFYAK4EHe3jLMWAxsHm6rezhveack4mZjaTzp765GnhSv+MYFmP9DsDMzOY/JxMzMyvNj7nMrKW8tdxhHkzmaHPGNRMzMyvNycTMzEpzMjEzs9KcTMzMrDQnEzMzK829ucysJffYsk64ZmJmZqU5mZiZWWlOJmZmVpqTiZmZleZkYmZmpTmZmJlZaU4mZmZWmpOJmZmV5mRiZmalOZmYmVlpioh+x9BXExMTt0TENv2Ow8xmk3TbkiVLHt/vOKy9kU8mZmZWnh9zmZlZaU4mZmZWmpOJmZmV5mTSAUk7SPqepLsl3S/pEkl79juudiTtJ+lXklZJuk/Suf2OqROSNpR0laSQtLTf8eSRtJ2k0yTdmL7HN0g6StLCfsfWSNLbJS2XtDr9N/Gsfsdkw8XJpDP/RbKQ2AuAZwBXA/8laeu+RtWCpFcCZwJfBXYCdgfO7mtQnTseuLXfQXTgyST/D70ZeBrwbuAtwMf6GVQjSa8CTgCOAnYh+fd7nqSt+hqYDRX35mpD0qOAu4DnR8T/pPsWA/cD+0TEBf2MrxlJC4DlwJERcVqfw+mKpBeTfPC9EvgtsHNEXNXfqDon6X3AWyPiCf2OpU7Sr4D/jYhD09djwC3ASRFxXF+Ds6Hhmkl79wDXAQdK2iT9oH4zcCfwm75Glm8X4LFATdKVkm6T9CNJT+93YK1IejTwZeAA4OE+h1PUZsC9/Q6iLn3k9gxg/R89EVFLX+/Wr7hs+DiZtBFJ1W1vYGfgAWA18B5g34i4r5+xtVD/q3gZcCzwUuA+4CJJW/QrqFYkCTgd+GJEXN7ncAqR9CTgHcCX+h1LxqOAceCOhv13AAP7mNbmn5FNJpKOSxt4W21PTj/kPk9SE3ke8CzgXOAHkuZ05HynMTP9e/1oRHw7In4DvB4IYP8BjfkdwGLg43MZXzNdxJw957HAj4FvRcSX+xO5Wf+MbJuJpC2Bv2pz2J9IEshPgEdGxP2Z8yeA0+bymXMXMe8O/BR4XkRckjn/V8AFEXF476KcqYuYvwm8jCTh1Y0DU8BZEfG63kQ4W6cxR8Ta9PjHABcBvwQOSh8jDYT0MdfDwD9HxLmZ/WcAm0fEP/YtOBsqC/odQL9ExF0kDestSdo4/bbxA6LGHNfsuoj5N8AaYEfgknTfBsB2wE09DHGWLmJ+J3BEZtdjgPOAVwG/6k10zXUaM6yvkfyMpP3s9YOUSAAiYm3672Evkhp1vQF+L+DkfsZmw2Vkk0kXLiNpbzhD0tHAKuAQYHvgv/sZWJ6IuF/SF4GjJN1CkkDelxZ/q3+R5YuIm7OvJT2YfntDRPy5DyG1lSaSi0je3/cCWyZPRSEibu9fZLOcQPLv93Lg18C/AZuQdBs3q4STSRsRcbekfYGPkjw62oCky+o/RsTVfQ2utfcBkyRjTRaR/HX/ggHuNDAf7QM8Kd0aE57mPpzmIuKc9NHd0SSN7leRdCBpbJQ3K2xk20zMzKw6I9uby8zMquNkYmZmpTmZmJlZaU4mZmZWmpOJmZmV5mRiZmalOZmYmVlpTiZmZlaak4mZmZXmZDKPSbpI0on9jqNqw/pzmQ0zJ5MRImmPdC2OzXtw7WWS5s3yup3o5ftVhKTnS/qBpFvTuF7e75jM6pxMzOaPTYCrgbf3OxCzRk4mQ0TSAZIul/SApNslnS1pq7RsO5J1NwDuS/+yPT0tG5P0QUk3Slol6WpJ/5y5bv0v9L3S6z8s6ReSdkzLDwKOBHbKrER4UE6Mp0s6V9KRku6SdL+kL6aLOGWNSTpe0r3pz7Ks4TqbSzo1c42fStopU75M0lXpe7Jc0kpJ35C0OHPMhpI+J+lOSaslXSLpma3eL0kHSrpH0oYN8Zwr6cyGe79Z0i3p+/VNSZs1nPNGSb9P7/0HSW9r9p7VRcSPIuKIiPhuq+PM+iIivM3TjWQtjRMzrw8GXkyyBvyzgV8AP0zLxoFXkKxkuAPJVOSbpWWHA78HXpSeexDJWvd/n5bvkZ73S+DvgacCPwcuTcsXAZ8C/i+97tbAopyYTwceAL4BPA3Yj2RJ5I82/FwrSRLUEuBAksXI9skccz7wfWDX9JhPAXcDW6Tly9L7fBt4OsmKmbc13OezwF/S9+ypaWz3AlvkvV/pz7oC2D9zna2AdcCemXs/CFwILAWeD0yQrBhZP+dfgVvTe2yffr0HeF2Hv/sAXt7vf4PevNW3vgfgrcQvryGZNCnfNf3Q2TR9XU8Km2eO2RB4CNit4dxTgbMbztsrU/6SdN9G6etlwFUdxHx6+qG5cWbfW9IP/rHMz/U/Def9Gjgu/f65abLZsOGYPwJvysTzELA4U3488Mv0+02AtcBrM+UbpMnlfXnvV7r/FNIknb5+D3AD00s6LCNZS+axmWP2JVmCeOtMrK9puO4RwC86/N07mXgbqM2LYw0RSc8g+SDbCXgk048xtwV+l3Pak4CNgfPrqwSmFgJXNhx7Teb729KvWwE3052rI+LhzOvLgE2BxzO9rPA1Defclt4Lkp9vU+CehpgXAU/MvF4eEQ/kXOOJJMnj0nphRKyT9GvgKW3i/zLwv5IeGxF/IanJnR4R2cWBbk7Lsj/jGLCjpAfS+58m6cuZYxaQJEmzecfJZEhI2oRkzfTzSB6h3EWSRM4jSQx5Nk2/7kfyV3nWmobX6zLf1z84e9Xutq7hdWTutSlJYtijyXkrOrxGYRFxpaSrgQMl/YTpx3Wdqr/nhzB7ffupsvGZ9YOTyfB4MvBXwGERcQuApF0bjlmbfh3P7PsdSdLYNiIuLnH/tQ3XbWUnSYsiYlX6+tkkbQy3dHj+FSRtGJMRsbyrKKfdQBLz7qS1IUkbAM8E6mNcmr1fdaeSrKX+WOCC+nuesa2kx0TErenrZ5O0+1wXEXdIuhV4QkScVTB+s4HiZDI8bib58HuHpC+SNDp/uOGYm0j+On+ppB8CqyLiAUmfAj4jaQy4hKSheXfg/og4o8P7Lwe2l7SUZD30ByKisWZTt5DkEc+xwHbAUcDJEVHr8F4XkDw2OlfS+4HrgceQ1A6+GxGXt7tARDwk6QvAJyXdS/L+vZ/kkd9p6WHN3q8H07KzSRr9DyHpINBoNXCGpPcCjwA+B3wzIm5Py48EPidpJfBjkrarXYFHRsQJzWKWtCnJY8m6+vt9b0R0+6jRrFLuGjwkIuIukmf3+5PUNg4D3ttwzF9IPsSOA+4ATk6LPgwcA3yQpFfXj0k+mG/sIoRvp+f9jOQR22taHHshSe+mnwPnkPTKWtbpjdK2iZek53+VJJl8A/hrkp+rU4elcZ9JUtt5EvCiiLgvvU/e+0VErEzPfRA4t8m1/wh8B/gh8BOSNqC3Zc4/FXgj8HrgWuBikt9fq/d8V5J2rHpb1gnp90d3/BOb9Yhmthma9VY6tmXziJj3o7clXQj8NiLe2bB/GUlPq6V9CcysD/yYy6xLkh5J0vi/B5nahtkoczIx696VJF2vPxAR1/U7GLNB4MdcZmZWmhvgzcysNCcTMzMrzcnEzMxKczIxM7PSnEzMzKw0JxMzMyvNycTMzEpzMjEzs9L+PzmkFBUzO0mUAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 300x300 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "p = (\n",
    "    ggplot(\n",
    "        latenteffects2.pivot_table(\n",
    "            index=\"mutation\", values=\"latent_effect\", columns=\"latent_phenotype_name\"\n",
    "        ),\n",
    "        aes(\"latent phenotype 1\", \"latent phenotype 2\"),\n",
    "    )\n",
    "    + geom_bin2d()\n",
    "    + theme(figure_size=(3, 3))\n",
    ")\n",
    "_ = p.draw(show=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Predicted versus true latent effects\n",
    "Now let's see how the model-predicted latent effects correlate with the true latent effects in the simulation for the two-latent phenotype model.\n",
    "\n",
    "First, get a data frame with the **true** (from simulation) latent effects of each mutation on each latent phenotype number:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mutation</th>\n",
       "      <th>actual_effect</th>\n",
       "      <th>actual_number</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>R1*</td>\n",
       "      <td>-8.152</td>\n",
       "      <td>actual 1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>R1A</td>\n",
       "      <td>-0.001</td>\n",
       "      <td>actual 1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>R1C</td>\n",
       "      <td>-0.421</td>\n",
       "      <td>actual 1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>R1D</td>\n",
       "      <td>-6.496</td>\n",
       "      <td>actual 1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>R1E</td>\n",
       "      <td>-1.359</td>\n",
       "      <td>actual 1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2395</th>\n",
       "      <td>R60S</td>\n",
       "      <td>-0.010</td>\n",
       "      <td>actual 2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2396</th>\n",
       "      <td>R60T</td>\n",
       "      <td>-0.004</td>\n",
       "      <td>actual 2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2397</th>\n",
       "      <td>R60V</td>\n",
       "      <td>-0.009</td>\n",
       "      <td>actual 2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2398</th>\n",
       "      <td>R60W</td>\n",
       "      <td>-0.001</td>\n",
       "      <td>actual 2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2399</th>\n",
       "      <td>R60Y</td>\n",
       "      <td>0.002</td>\n",
       "      <td>actual 2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>2400 rows × 3 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     mutation  actual_effect actual_number\n",
       "0         R1*         -8.152      actual 1\n",
       "1         R1A         -0.001      actual 1\n",
       "2         R1C         -0.421      actual 1\n",
       "3         R1D         -6.496      actual 1\n",
       "4         R1E         -1.359      actual 1\n",
       "...       ...            ...           ...\n",
       "2395     R60S         -0.010      actual 2\n",
       "2396     R60T         -0.004      actual 2\n",
       "2397     R60V         -0.009      actual 2\n",
       "2398     R60W         -0.001      actual 2\n",
       "2399     R60Y          0.002      actual 2\n",
       "\n",
       "[2400 rows x 3 columns]"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# NBVAL_IGNORE_OUTPUT\n",
    "\n",
    "actual_latenteffects2 = pd.concat(\n",
    "    [\n",
    "        latenteffects2[[\"mutation\"]]\n",
    "        .drop_duplicates()\n",
    "        .assign(\n",
    "            actual_effect=lambda x: (\n",
    "                x[\"mutation\"].map(\n",
    "                    lambda m: phenosimulator.latentPhenotype(m, k)\n",
    "                    - phenosimulator.latentPhenotype(\"\", k)\n",
    "                )\n",
    "            ),\n",
    "            actual_number=f\"actual {k}\",\n",
    "        )\n",
    "        for k in range(1, phenosimulator.n_latent_phenotypes + 1)\n",
    "    ],\n",
    "    sort=False,\n",
    "    ignore_index=True,\n",
    ")\n",
    "\n",
    "actual_latenteffects2.round(3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Get a comparable data frame for the model-predicted latent effects:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mutation</th>\n",
       "      <th>predicted_effect</th>\n",
       "      <th>predicted_number</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>R1*</td>\n",
       "      <td>-1.334</td>\n",
       "      <td>predicted 1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>R1A</td>\n",
       "      <td>-0.003</td>\n",
       "      <td>predicted 1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>R1C</td>\n",
       "      <td>-0.332</td>\n",
       "      <td>predicted 1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>R1D</td>\n",
       "      <td>-1.031</td>\n",
       "      <td>predicted 1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>R1E</td>\n",
       "      <td>-0.976</td>\n",
       "      <td>predicted 1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2395</th>\n",
       "      <td>R60S</td>\n",
       "      <td>1.606</td>\n",
       "      <td>predicted 2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2396</th>\n",
       "      <td>R60T</td>\n",
       "      <td>-0.379</td>\n",
       "      <td>predicted 2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2397</th>\n",
       "      <td>R60V</td>\n",
       "      <td>-0.904</td>\n",
       "      <td>predicted 2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2398</th>\n",
       "      <td>R60W</td>\n",
       "      <td>-2.811</td>\n",
       "      <td>predicted 2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2399</th>\n",
       "      <td>R60Y</td>\n",
       "      <td>0.040</td>\n",
       "      <td>predicted 2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>2400 rows × 3 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     mutation  predicted_effect predicted_number\n",
       "0         R1*            -1.334      predicted 1\n",
       "1         R1A            -0.003      predicted 1\n",
       "2         R1C            -0.332      predicted 1\n",
       "3         R1D            -1.031      predicted 1\n",
       "4         R1E            -0.976      predicted 1\n",
       "...       ...               ...              ...\n",
       "2395     R60S             1.606      predicted 2\n",
       "2396     R60T            -0.379      predicted 2\n",
       "2397     R60V            -0.904      predicted 2\n",
       "2398     R60W            -2.811      predicted 2\n",
       "2399     R60Y             0.040      predicted 2\n",
       "\n",
       "[2400 rows x 3 columns]"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# NBVAL_IGNORE_OUTPUT\n",
    "\n",
    "predicted_latenteffects2 = latenteffects2.rename(\n",
    "    columns={\"latent_effect\": \"predicted_effect\"}\n",
    ").assign(\n",
    "    predicted_number=lambda x: \"predicted \" + x[\"latent_phenotype_number\"].astype(str)\n",
    ")[\n",
    "    [\"mutation\", \"predicted_effect\", \"predicted_number\"]\n",
    "]\n",
    "\n",
    "predicted_latenteffects2.round(3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now get a data frame with all combinations of predictions and actual latent effects:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mutation</th>\n",
       "      <th>actual_effect</th>\n",
       "      <th>actual_number</th>\n",
       "      <th>predicted_effect</th>\n",
       "      <th>predicted_number</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>R1*</td>\n",
       "      <td>-8.152</td>\n",
       "      <td>actual 1</td>\n",
       "      <td>-1.334</td>\n",
       "      <td>predicted 1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>R1*</td>\n",
       "      <td>-8.152</td>\n",
       "      <td>actual 1</td>\n",
       "      <td>0.066</td>\n",
       "      <td>predicted 2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>R1*</td>\n",
       "      <td>0.000</td>\n",
       "      <td>actual 2</td>\n",
       "      <td>-1.334</td>\n",
       "      <td>predicted 1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>R1*</td>\n",
       "      <td>0.000</td>\n",
       "      <td>actual 2</td>\n",
       "      <td>0.066</td>\n",
       "      <td>predicted 2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>R1A</td>\n",
       "      <td>-0.001</td>\n",
       "      <td>actual 1</td>\n",
       "      <td>-0.003</td>\n",
       "      <td>predicted 1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4795</th>\n",
       "      <td>R60W</td>\n",
       "      <td>-0.001</td>\n",
       "      <td>actual 2</td>\n",
       "      <td>-2.811</td>\n",
       "      <td>predicted 2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4796</th>\n",
       "      <td>R60Y</td>\n",
       "      <td>-0.033</td>\n",
       "      <td>actual 1</td>\n",
       "      <td>-0.109</td>\n",
       "      <td>predicted 1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4797</th>\n",
       "      <td>R60Y</td>\n",
       "      <td>-0.033</td>\n",
       "      <td>actual 1</td>\n",
       "      <td>0.040</td>\n",
       "      <td>predicted 2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4798</th>\n",
       "      <td>R60Y</td>\n",
       "      <td>0.002</td>\n",
       "      <td>actual 2</td>\n",
       "      <td>-0.109</td>\n",
       "      <td>predicted 1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4799</th>\n",
       "      <td>R60Y</td>\n",
       "      <td>0.002</td>\n",
       "      <td>actual 2</td>\n",
       "      <td>0.040</td>\n",
       "      <td>predicted 2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>4800 rows × 5 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     mutation  actual_effect actual_number  predicted_effect predicted_number\n",
       "0         R1*         -8.152      actual 1            -1.334      predicted 1\n",
       "1         R1*         -8.152      actual 1             0.066      predicted 2\n",
       "2         R1*          0.000      actual 2            -1.334      predicted 1\n",
       "3         R1*          0.000      actual 2             0.066      predicted 2\n",
       "4         R1A         -0.001      actual 1            -0.003      predicted 1\n",
       "...       ...            ...           ...               ...              ...\n",
       "4795     R60W         -0.001      actual 2            -2.811      predicted 2\n",
       "4796     R60Y         -0.033      actual 1            -0.109      predicted 1\n",
       "4797     R60Y         -0.033      actual 1             0.040      predicted 2\n",
       "4798     R60Y          0.002      actual 2            -0.109      predicted 1\n",
       "4799     R60Y          0.002      actual 2             0.040      predicted 2\n",
       "\n",
       "[4800 rows x 5 columns]"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# NBVAL_IGNORE_OUTPUT\n",
    "\n",
    "actual_vs_predicted_latenteffects2 = pd.merge(\n",
    "    actual_latenteffects2, predicted_latenteffects2, on=\"mutation\"\n",
    ")\n",
    "\n",
    "actual_vs_predicted_latenteffects2.round(3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot the correlations between the actual and predicted values:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "p = (\n",
    "    ggplot(actual_vs_predicted_latenteffects2, aes(\"actual_effect\", \"predicted_effect\"))\n",
    "    + geom_bin2d()\n",
    "    + facet_grid(\"actual_number ~ predicted_number\", scales=\"free\")\n",
    ")\n",
    "_ = p.draw(show=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Model predictions on new variants\n",
    "Generate some quadruple codon mutants (almost all of which will correspond to sequences never seen by the model) and predict the experimental enrichments from their observed phenotypes with each model (recall that the observed phenotype is proportional to the log enrichment).\n",
    "Compare these to the true values from the phenotype simulator.\n",
    "\n",
    "First, simulate some variants:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>codon_substitutions</th>\n",
       "      <th>aa_substitutions</th>\n",
       "      <th>true_enrichment</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>ACC9TAC TCC37ACA GAT52CAA CTG55ACT</td>\n",
       "      <td>T9Y S37T D52Q L55T</td>\n",
       "      <td>0.000005</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>CGG29GGG ATG31CGC ATG32TAT TCA49ATC</td>\n",
       "      <td>R29G M31R M32Y S49I</td>\n",
       "      <td>0.000002</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>TCC2TCG GCT7CGA ATG32CTA ATG58GCT</td>\n",
       "      <td>A7R M32L M58A</td>\n",
       "      <td>0.000001</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>AGA1CTC GTA45CAC TCA49GTG GGA50TCA</td>\n",
       "      <td>R1L V45H S49V G50S</td>\n",
       "      <td>0.005773</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>GCT7CCA CGT15AAC GAC38AAC ATG58AAC</td>\n",
       "      <td>A7P R15N D38N M58N</td>\n",
       "      <td>0.000001</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>49995</th>\n",
       "      <td>GTA16ATG CCT24AGA GTA45CAC CTG55TCC</td>\n",
       "      <td>V16M P24R V45H L55S</td>\n",
       "      <td>0.000660</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>49996</th>\n",
       "      <td>GTG3TTT CTG5CGC TCA11GGA TCG42TAC</td>\n",
       "      <td>V3F L5R S11G S42Y</td>\n",
       "      <td>0.005104</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>49997</th>\n",
       "      <td>ATC17TAC CTA34TCG TTT41TGT CCA44CTG</td>\n",
       "      <td>I17Y L34S F41C P44L</td>\n",
       "      <td>0.001696</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>49998</th>\n",
       "      <td>CGG29CGT CCA44TAA CTG55GAC TAC59GCG</td>\n",
       "      <td>P44* L55D Y59A</td>\n",
       "      <td>0.000999</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>49999</th>\n",
       "      <td>GTG3CGA TCA11CTT AAA14CCA AAC27AGG</td>\n",
       "      <td>V3R S11L K14P N27R</td>\n",
       "      <td>0.001014</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>50000 rows × 3 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                       codon_substitutions     aa_substitutions  true_enrichment\n",
       "0       ACC9TAC TCC37ACA GAT52CAA CTG55ACT   T9Y S37T D52Q L55T         0.000005\n",
       "1      CGG29GGG ATG31CGC ATG32TAT TCA49ATC  R29G M31R M32Y S49I         0.000002\n",
       "2        TCC2TCG GCT7CGA ATG32CTA ATG58GCT        A7R M32L M58A         0.000001\n",
       "3       AGA1CTC GTA45CAC TCA49GTG GGA50TCA   R1L V45H S49V G50S         0.005773\n",
       "4       GCT7CCA CGT15AAC GAC38AAC ATG58AAC   A7P R15N D38N M58N         0.000001\n",
       "...                                    ...                  ...              ...\n",
       "49995  GTA16ATG CCT24AGA GTA45CAC CTG55TCC  V16M P24R V45H L55S         0.000660\n",
       "49996    GTG3TTT CTG5CGC TCA11GGA TCG42TAC    V3F L5R S11G S42Y         0.005104\n",
       "49997  ATC17TAC CTA34TCG TTT41TGT CCA44CTG  I17Y L34S F41C P44L         0.001696\n",
       "49998  CGG29CGT CCA44TAA CTG55GAC TAC59GCG       P44* L55D Y59A         0.000999\n",
       "49999   GTG3CGA TCA11CTT AAA14CCA AAC27AGG   V3R S11L K14P N27R         0.001014\n",
       "\n",
       "[50000 rows x 3 columns]"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# NBVAL_IGNORE_OUTPUT\n",
    "\n",
    "random.seed(1)\n",
    "\n",
    "nmuts = 4  # predict variants with this many mutations relative to wildtype\n",
    "npredict = 50000  # make predictions for this many variants\n",
    "\n",
    "rand_variants_df = pd.DataFrame(\n",
    "    {\"codon_substitutions\": dms_variants.simulate.codon_muts(geneseq, nmuts, npredict)}\n",
    ").assign(\n",
    "    aa_substitutions=lambda x: x[\"codon_substitutions\"].map(\n",
    "        dms_variants.codonvarianttable.CodonVariantTable.codonToAAMuts\n",
    "    ),\n",
    "    true_enrichment=lambda x: x[\"aa_substitutions\"].map(\n",
    "        phenosimulator.observedEnrichment\n",
    "    ),\n",
    ")\n",
    "\n",
    "rand_variants_df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now add the model-predicted enrichments:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>aa_substitutions</th>\n",
       "      <th>true_enrichment</th>\n",
       "      <th>model_description</th>\n",
       "      <th>predicted_enrichment</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>T9Y S37T D52Q L55T</td>\n",
       "      <td>0.000005</td>\n",
       "      <td>global epistasis with 2 latent phenotypes</td>\n",
       "      <td>0.002543</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>R29G M31R M32Y S49I</td>\n",
       "      <td>0.000002</td>\n",
       "      <td>global epistasis with 2 latent phenotypes</td>\n",
       "      <td>0.001573</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>A7R M32L M58A</td>\n",
       "      <td>0.000001</td>\n",
       "      <td>global epistasis with 2 latent phenotypes</td>\n",
       "      <td>0.001530</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>R1L V45H S49V G50S</td>\n",
       "      <td>0.005773</td>\n",
       "      <td>global epistasis with 2 latent phenotypes</td>\n",
       "      <td>0.009391</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>A7P R15N D38N M58N</td>\n",
       "      <td>0.000001</td>\n",
       "      <td>global epistasis with 2 latent phenotypes</td>\n",
       "      <td>0.001557</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>149995</th>\n",
       "      <td>V16M P24R V45H L55S</td>\n",
       "      <td>0.000660</td>\n",
       "      <td>no epistasis</td>\n",
       "      <td>0.010272</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>149996</th>\n",
       "      <td>V3F L5R S11G S42Y</td>\n",
       "      <td>0.005104</td>\n",
       "      <td>no epistasis</td>\n",
       "      <td>0.121759</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>149997</th>\n",
       "      <td>I17Y L34S F41C P44L</td>\n",
       "      <td>0.001696</td>\n",
       "      <td>no epistasis</td>\n",
       "      <td>0.081950</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>149998</th>\n",
       "      <td>P44* L55D Y59A</td>\n",
       "      <td>0.000999</td>\n",
       "      <td>no epistasis</td>\n",
       "      <td>0.011766</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>149999</th>\n",
       "      <td>V3R S11L K14P N27R</td>\n",
       "      <td>0.001014</td>\n",
       "      <td>no epistasis</td>\n",
       "      <td>0.009191</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>150000 rows × 4 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "           aa_substitutions  true_enrichment                          model_description  predicted_enrichment\n",
       "0        T9Y S37T D52Q L55T         0.000005  global epistasis with 2 latent phenotypes              0.002543\n",
       "1       R29G M31R M32Y S49I         0.000002  global epistasis with 2 latent phenotypes              0.001573\n",
       "2             A7R M32L M58A         0.000001  global epistasis with 2 latent phenotypes              0.001530\n",
       "3        R1L V45H S49V G50S         0.005773  global epistasis with 2 latent phenotypes              0.009391\n",
       "4        A7P R15N D38N M58N         0.000001  global epistasis with 2 latent phenotypes              0.001557\n",
       "...                     ...              ...                                        ...                   ...\n",
       "149995  V16M P24R V45H L55S         0.000660                               no epistasis              0.010272\n",
       "149996    V3F L5R S11G S42Y         0.005104                               no epistasis              0.121759\n",
       "149997  I17Y L34S F41C P44L         0.001696                               no epistasis              0.081950\n",
       "149998       P44* L55D Y59A         0.000999                               no epistasis              0.011766\n",
       "149999   V3R S11L K14P N27R         0.001014                               no epistasis              0.009191\n",
       "\n",
       "[150000 rows x 4 columns]"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# NBVAL_IGNORE_OUTPUT\n",
    "\n",
    "actual_vs_predicted_enrichments = []\n",
    "for tup in fits_df.itertuples():\n",
    "    actual_vs_predicted_enrichments.append(\n",
    "        tup.model.add_phenotypes_to_df(rand_variants_df, unknown_as_nan=True)\n",
    "        .dropna(axis=\"index\")\n",
    "        .assign(\n",
    "            model_description=tup.description,\n",
    "            predicted_enrichment=lambda x: tup.model.enrichments(\n",
    "                x[\"observed_phenotype\"]\n",
    "            ),\n",
    "        )[\n",
    "            [\n",
    "                \"aa_substitutions\",\n",
    "                \"true_enrichment\",\n",
    "                \"model_description\",\n",
    "                \"predicted_enrichment\",\n",
    "            ]\n",
    "        ]\n",
    "    )\n",
    "actual_vs_predicted_enrichments = pd.concat(\n",
    "    actual_vs_predicted_enrichments, sort=False, ignore_index=True\n",
    ")\n",
    "actual_vs_predicted_enrichments"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot the predictions versus the true enrichments for each model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1200x400 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "p = (\n",
    "    ggplot(\n",
    "        actual_vs_predicted_enrichments, aes(\"predicted_enrichment\", \"true_enrichment\")\n",
    "    )\n",
    "    + geom_bin2d()\n",
    "    + facet_wrap(\"~ model_description\", nrow=1)\n",
    "    + theme(\n",
    "        figure_size=(\n",
    "            4 * actual_vs_predicted_enrichments[\"model_description\"].nunique(),\n",
    "            4,\n",
    "        )\n",
    "    )\n",
    ")\n",
    "_ = p.draw(show=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculate the correlations between predicted and true enrichments:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>correlation</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>model_description</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>global epistasis with 1 latent phenotypes</th>\n",
       "      <td>0.987</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>global epistasis with 2 latent phenotypes</th>\n",
       "      <td>0.978</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>no epistasis</th>\n",
       "      <td>0.871</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                           correlation\n",
       "model_description                                     \n",
       "global epistasis with 1 latent phenotypes        0.987\n",
       "global epistasis with 2 latent phenotypes        0.978\n",
       "no epistasis                                     0.871"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# NBVAL_IGNORE_OUTPUT\n",
    "\n",
    "(\n",
    "    actual_vs_predicted_enrichments.groupby(\"model_description\")\n",
    "    .apply(lambda x: x[\"predicted_enrichment\"].corr(x[\"true_enrichment\"]))\n",
    "    .rename(\"correlation\")\n",
    "    .to_frame()\n",
    "    .round(3)\n",
    ")"
   ]
  }
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