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{"documenter":{"julia_version":"1.10.2","generation_timestamp":"2024-04-14T11:38:16","documenter_version":"1.3.0"}}
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<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Example · PartitionedLS.jl</title><meta name="title" content="Example · PartitionedLS.jl"/><meta property="og:title" content="Example · PartitionedLS.jl"/><meta property="twitter:title" content="Example · PartitionedLS.jl"/><meta name="description" content="Documentation for PartitionedLS.jl."/><meta property="og:description" content="Documentation for PartitionedLS.jl."/><meta property="twitter:description" content="Documentation for PartitionedLS.jl."/><script data-outdated-warner src="../../assets/warner.js"></script><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.050/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL="../.."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="../../assets/documenter.js"></script><script src="../../search_index.js"></script><script src="../../siteinfo.js"></script><script src="../../../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../../assets/themes/documenter-dark.css" data-theme-name="documenter-dark" data-theme-primary-dark/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../../assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="../../assets/themeswap.js"></script></head><body><div id="documenter"><nav class="docs-sidebar"><a class="docs-logo" href="../../"><img src="../../assets/logo.png" alt="PartitionedLS.jl logo"/></a><button class="docs-search-query input is-rounded is-small is-clickable my-2 mx-auto py-1 px-2" id="documenter-search-query">Search docs (Ctrl + /)</button><ul class="docs-menu"><li><a class="tocitem" href="../../">Documentation</a></li><li class="is-active"><a class="tocitem" href>Example</a></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><a class="docs-sidebar-button docs-navbar-link fa-solid fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>Example</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Example</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/ml-unito/PartitionedLS.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/ml-unito/PartitionedLS.jl/blob/master/docs/src/examples/example.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><p>We present here an analysis of a solution found by a Partitioned LS algorithm on the Ames House Prices dataset, which is publicly available via Kaggle.</p><p>The Julia notebook used to generate the results is available <a href="https://github.com/ml-unito/PartitionedLS-experiments-2/blob/master/housing/exps.ipynb">here</a>.</p><p>This dataset has a relatively high number of columns (79 in total) each detailing one particular characteristic of housing properties in Ames, Iowa. The task is to predict the selling price of each house. </p><p>We propose a grouping of the features into 10 groups, each one representing a high-level characteristic of the property:</p><table><tr><th style="text-align: right">Group</th><th style="text-align: right">Features</th></tr><tr><td style="text-align: right">LotDescritption</td><td style="text-align: right">MSSubClass, MSZoning, LotFrontage, LotArea, Street, Alley, LotShape, LandContour, LotConfig, LandSlope</td></tr><tr><td style="text-align: right">BuildingPlacement</td><td style="text-align: right">Utilities, Neighborhood, Condition1, Condition2</td></tr><tr><td style="text-align: right">BuildingAge</td><td style="text-align: right">YearBuilt, YearRemodAdd</td></tr><tr><td style="text-align: right">BuildingQuality</td><td style="text-align: right">BldgType, HouseStyle, OverallQual, OverallCond, RoofStyle, RoofMatl, Exterior1st, Exterior2nd, MasVnrType, MasVnrArea, ExterQual, ExterCond, Foundation, Functional</td></tr><tr><td style="text-align: right">Basement</td><td style="text-align: right">BsmtQual, BsmtCond, BsmtExposure, BsmtFinType1, BsmtFinSF1, BsmtFinType2, BsmtFinSF2, BsmtUnfSF, TotalBsmtSF</td></tr><tr><td style="text-align: right">PowerAndTemperature</td><td style="text-align: right">Heating, HeatingQC, CentralAir, Electrical, Fireplaces, FireplaceQu</td></tr><tr><td style="text-align: right">Sizes</td><td style="text-align: right">1stFlrSF, 2ndFlrSF, LowQualFinSF, GrLivArea</td></tr><tr><td style="text-align: right">Rooms</td><td style="text-align: right">BsmtFullBath, BsmtHalfBath, FullBath, HalfBath, BedroomAbvGr, KitchenAbvGr, KitchenQual, TotRmsAbvGrd</td></tr><tr><td style="text-align: right">OutsideFacilities</td><td style="text-align: right">GarageType, GarageYrBlt, GarageFinish, GarageCars, GarageArea, GarageQual, GarageCond, PavedDrive, WoodDeckSF, OpenPorchSF, EnclosedPorch, 3SsnPorch, ScreenPorch, PoolArea, PoolQC, Fence</td></tr><tr><td style="text-align: right">Various</td><td style="text-align: right">MiscFeature, MiscVal, MoSold, YrSold, SaleType, SaleCondition</td></tr></table><p>As an example, we collect 6 columns referring to the availability and quality of air conditioning systems, electrical system, heating and fireplaces in a &quot;Power and Temperature&quot; group. Other feature groups refer to overall quality of the construction work and materials employed (&quot;Building Quality&quot;), external facilities such as garages or swimming pools (&quot;Outside Facilities&quot;). The <span>$\beta$</span> values for the groups are as follows:</p><p><img src="../../assets/PartLS_beta.png" alt="\$\\beta\$ values as found by the `Opt` algorithm on the Ames House Prices dataset"/></p><p>We note that the grouped solution enabled by the partitioned least squares formulation is able to give a high-level summary of the regression result. An analyst is therefore able to communicate easily to, e.g. an individual selling their house, that the price is mostly determined by the building quality and the attractiveness of the lot. A deeper analysis is of course possible by investigating the <span>$\alpha$</span> values found by the algorithm. For instance, let consider the contributions to the ``Outside Facilities&#39;&#39;:</p><p><img src="../../assets/PartLS_alpha_OutsideFacilities.png" alt="\$\\alpha\$ values as found by the `Opt` algorithm on the Ames House Prices dataset for the &quot;OutsideFacilities&quot; group"/></p><p>Here, one is able to notice that garage quality has the biggest impact on the property&#39;s price, which is potentially actionable knowledge. </p><p>We argue that the group- and feature-level analysis made possible by our contributions improves on the interpretability of ungrouped linear regression.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../">« Documentation</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.3.0 on <span class="colophon-date" title="Sunday 14 April 2024 11:38">Sunday 14 April 2024</span>. Using Julia version 1.10.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Example · PartitionedLS.jl</title><meta name="title" content="Example · PartitionedLS.jl"/><meta property="og:title" content="Example · PartitionedLS.jl"/><meta property="twitter:title" content="Example · PartitionedLS.jl"/><meta name="description" content="Documentation for PartitionedLS.jl."/><meta property="og:description" content="Documentation for PartitionedLS.jl."/><meta property="twitter:description" content="Documentation for PartitionedLS.jl."/><script data-outdated-warner src="../../assets/warner.js"></script><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.050/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL="../.."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="../../assets/documenter.js"></script><script src="../../search_index.js"></script><script src="../../siteinfo.js"></script><script src="../../../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../../assets/themes/documenter-dark.css" data-theme-name="documenter-dark" data-theme-primary-dark/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../../assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="../../assets/themeswap.js"></script></head><body><div id="documenter"><nav class="docs-sidebar"><a class="docs-logo" href="../../"><img src="../../assets/logo.png" alt="PartitionedLS.jl logo"/></a><button class="docs-search-query input is-rounded is-small is-clickable my-2 mx-auto py-1 px-2" id="documenter-search-query">Search docs (Ctrl + /)</button><ul class="docs-menu"><li><a class="tocitem" href="../../">Documentation</a></li><li class="is-active"><a class="tocitem" href>Example</a></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><a class="docs-sidebar-button docs-navbar-link fa-solid fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>Example</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Example</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/ml-unito/PartitionedLS.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/ml-unito/PartitionedLS.jl/blob/master/docs/src/examples/example.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><p>We present here an analysis of a solution found by a Partitioned LS algorithm on the Ames House Prices dataset, which is publicly available via Kaggle.</p><p>The Julia notebook used to generate the results is available <a href="https://github.com/ml-unito/PartitionedLS-experiments-2/blob/master/housing/exps.ipynb">here</a>.</p><p>This dataset has a relatively high number of columns (79 in total) each detailing one particular characteristic of housing properties in Ames, Iowa. The task is to predict the selling price of each house. </p><p>We propose a grouping of the features into 10 groups, each one representing a high-level characteristic of the property:</p><table><tr><th style="text-align: right">Group</th><th style="text-align: right">Features</th></tr><tr><td style="text-align: right">LotDescritption</td><td style="text-align: right">MSSubClass, MSZoning, LotFrontage, LotArea, Street, Alley, LotShape, LandContour, LotConfig, LandSlope</td></tr><tr><td style="text-align: right">BuildingPlacement</td><td style="text-align: right">Utilities, Neighborhood, Condition1, Condition2</td></tr><tr><td style="text-align: right">BuildingAge</td><td style="text-align: right">YearBuilt, YearRemodAdd</td></tr><tr><td style="text-align: right">BuildingQuality</td><td style="text-align: right">BldgType, HouseStyle, OverallQual, OverallCond, RoofStyle, RoofMatl, Exterior1st, Exterior2nd, MasVnrType, MasVnrArea, ExterQual, ExterCond, Foundation, Functional</td></tr><tr><td style="text-align: right">Basement</td><td style="text-align: right">BsmtQual, BsmtCond, BsmtExposure, BsmtFinType1, BsmtFinSF1, BsmtFinType2, BsmtFinSF2, BsmtUnfSF, TotalBsmtSF</td></tr><tr><td style="text-align: right">PowerAndTemperature</td><td style="text-align: right">Heating, HeatingQC, CentralAir, Electrical, Fireplaces, FireplaceQu</td></tr><tr><td style="text-align: right">Sizes</td><td style="text-align: right">1stFlrSF, 2ndFlrSF, LowQualFinSF, GrLivArea</td></tr><tr><td style="text-align: right">Rooms</td><td style="text-align: right">BsmtFullBath, BsmtHalfBath, FullBath, HalfBath, BedroomAbvGr, KitchenAbvGr, KitchenQual, TotRmsAbvGrd</td></tr><tr><td style="text-align: right">OutsideFacilities</td><td style="text-align: right">GarageType, GarageYrBlt, GarageFinish, GarageCars, GarageArea, GarageQual, GarageCond, PavedDrive, WoodDeckSF, OpenPorchSF, EnclosedPorch, 3SsnPorch, ScreenPorch, PoolArea, PoolQC, Fence</td></tr><tr><td style="text-align: right">Various</td><td style="text-align: right">MiscFeature, MiscVal, MoSold, YrSold, SaleType, SaleCondition</td></tr></table><p>As an example, we collect 6 columns referring to the availability and quality of air conditioning systems, electrical system, heating and fireplaces in a &quot;Power and Temperature&quot; group. Other feature groups refer to overall quality of the construction work and materials employed (&quot;Building Quality&quot;), external facilities such as garages or swimming pools (&quot;Outside Facilities&quot;). The <span>$\beta$</span> values for the groups are as follows:</p><p><img src="../../assets/PartLS_beta.png" alt="\$\\beta\$ values as found by the `Opt` algorithm on the Ames House Prices dataset"/></p><p>We note that the grouped solution enabled by the partitioned least squares formulation is able to give a high-level summary of the regression result. An analyst is therefore able to communicate easily to, e.g. an individual selling their house, that the price is mostly determined by the building quality and the attractiveness of the lot. A deeper analysis is of course possible by investigating the <span>$\alpha$</span> values found by the algorithm. For instance, let consider the contributions to the ``Outside Facilities&#39;&#39;:</p><p><img src="../../assets/PartLS_alpha_OutsideFacilities.png" alt="\$\\alpha\$ values as found by the `Opt` algorithm on the Ames House Prices dataset for the &quot;OutsideFacilities&quot; group"/></p><p>Here, one is able to notice that garage quality has the biggest impact on the property&#39;s price, which is potentially actionable knowledge. </p><p>We argue that the group- and feature-level analysis made possible by our contributions improves on the interpretability of ungrouped linear regression.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../">« Documentation</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.3.0 on <span class="colophon-date" title="Sunday 14 April 2024 16:54">Sunday 14 April 2024</span>. Using Julia version 1.10.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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