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children: "\\hat{y}_𝑖" })] }) }) }), _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.8889em", verticalAlign: "-0.1944em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord accent", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsxs(_components.span, { className: "vlist", style: { height: "0.6944em" }, children: [_jsxs(_components.span, { style: { top: "-3em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.03588em" }, children: "y" })] }), _jsxs(_components.span, { style: { top: "-3em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), 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mathnormal mtight", children: "i" }) })] }) }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.15em" }, children: _jsx(_components.span, {}) }) })] }) })] })] }) })] }) }), "は予測値、", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsx(_components.mrow, { children: _jsxs(_components.msub, { children: [_jsx(_components.mi, { children: "β" }), _jsx(_components.mi, { children: "𝑘" })] }) }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "\\beta_𝑘" })] }) }) }), _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.8889em", verticalAlign: "-0.1944em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.05278em" }, children: "β" }), _jsx(_components.span, { className: "msupsub", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsx(_components.span, { className: "vlist", style: { height: "0.3361em" }, children: _jsxs(_components.span, { style: { top: "-2.55em", marginLeft: "-0.0528em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.03148em" }, children: "k" }) })] }) }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.15em" }, children: _jsx(_components.span, {}) }) })] }) })] })] }) })] }) }), "は偏回帰係数を表します。"] }), "\n", _jsxs(_components.p, { children: ["Lasso回帰では", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsx(_components.mrow, { children: _jsx(_components.mi, { children: "λ" }) }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "\\lambda" })] }) }) }), _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.6944em" } }), _jsx(_components.span, { className: "mord mathnormal", children: "λ" })] }) })] }) }), "を大きくすると、影響の少ない偏回帰係数がちょうど0になる性質を持つため、変数選択としても使用されます。"] }), "\n", _jsx(_components.h3, { children: "SASでLasso回帰" }), "\n", _jsx(_components.p, { children: "SASでLasso回帰を行うには、glmselectやhpgenselectなどを使用します。" }), "\n", _jsxs(_components.p, { children: ["デフォルトで使用すると最適な", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsx(_components.mrow, { children: _jsx(_components.mi, { children: "λ" }) }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "\\lambda" })] }) }) }), _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.6944em" } }), _jsx(_components.span, { className: "mord mathnormal", children: "λ" })] }) })] }) }), "を自動で決定してくれます。 しかし今回は", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsx(_components.mrow, { children: _jsx(_components.mi, { children: "λ" }) }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "\\lambda" })] }) }) }), _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.6944em" } }), _jsx(_components.span, { className: "mord mathnormal", children: "λ" })] }) })] }) }), "を指定したいのでhpgenselectでステップ数を1にします。"] }), "\n", _jsx(_components.p, { children: "では、実際にLasso回帰を実行してみましょう。" }), "\n", _jsx(_components.p, { children: "まずはデータを作成し、標準化します" }), "\n", _jsx(_components.pre, { children: _jsxs(_components.code, { className: "hljs language-sas", children: [_jsx(_components.span, { className: "hljs-comment", children: "/*logSalaryの欠損データの除去*/" }), "\n", _jsx(_components.span, { className: "hljs-keyword", children: "data " }), "work.baseball_standard;\n ", _jsx(_components.span, { className: "hljs-keyword", children: "set" }), " sashelp.baseball;\n ", _jsx(_components.span, { className: "hljs-keyword", children: "if" }), " logsalary ", _jsx(_components.span, { className: "hljs-keyword", children: "then" }), " ", _jsx(_components.span, { className: "hljs-keyword", children: "output" }), ";\n", _jsx(_components.span, { className: "hljs-keyword", children: "run;" }), "\n", _jsx(_components.span, { className: "hljs-comment", children: "/*標準化*/" }), "\n", _jsx(_components.span, { className: "hljs-keyword", children: "proc standard " }), "data = work.baseball_standard(", _jsx(_components.span, { className: "hljs-keyword", children: "keep" }), " = natbat--crbb logsalary)\n ", _jsx(_components.span, { className: "hljs-keyword", children: "out" }), " = work.baseball_standard\n mean=0\n std = 1\n vardef=N;\n var natbat--crbb;\n", _jsx(_components.span, { className: "hljs-keyword", children: "run;" }), "\n"] }) }), "\n", _jsx(_components.p, { children: "hpgenselectを使用してLasso回帰を実装します。" }), "\n", _jsx(_components.pre, { children: _jsxs(_components.code, { className: "hljs language-sas", children: [_jsx(_components.span, { className: "hljs-built_in", children: "%let" }), " ", _jsx(_components.span, { className: "hljs-keyword", children: "filename" }), " = ", _jsx(_components.span, { className: "hljs-string", children: "\"＜Lasso回帰の予測コードを出力するパス＞\"" }), ";\n", _jsx(_components.span, { className: "hljs-comment", children: "/*lasso回帰の実行*/" }), "\n", _jsx(_components.span, { className: "hljs-keyword", children: "proc hpgenselect " }), "data=work.baseball_standard \n lassorho=0.1 \n lassosteps=1 \n lassotol=0.0001 \n maxiter=1000\n outest;\n model logsalary = natbat--crbb;\n selection method=lasso;\n code ", _jsx(_components.span, { className: "hljs-keyword", children: "file" }), "=", _jsx(_components.span, { className: "hljs-variable", children: "&filename." }), " residual;\n ods ", _jsx(_components.span, { className: "hljs-keyword", children: "output" }), " ParameterEstimates=coef;\n", _jsx(_components.span, { className: "hljs-keyword", children: "run;" }), "\n"] }) }), "\n", _jsx(_components.p, { children: "主要なパラメータは以下の通りです。" }), "\n", _jsxs(_components.ul, { children: ["\n", _jsxs(_components.li, { children: ["lassorho", _jsx(_components.br, {}), "\n", "Lasso回帰の", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsx(_components.mrow, { children: _jsx(_components.mi, { children: "λ" }) }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "\\lambda" })] }) }) }), _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.6944em" } }), _jsx(_components.span, { className: "mord mathnormal", children: "λ" })] }) })] }) }), "を指定します。ステップごとに変わるそうですが、今回は1stepのみ使用するのでそのまま値が使用されます。 lassorhoに関する詳しい記述は", _jsx(_components.a, { href: "https://documentation.sas.com/doc/en/statcdc/14.2/stathpug/stathpug_hpgenselect_details29.htm", children: "ここ" }), " に書いてあります。* lassosteps", _jsx(_components.br, {}), "\n", "繰り返し回数。今回は1を指定します。* lassotol", _jsx(_components.br, {}), "\n", "収束基準* maxiter", _jsx(_components.br, {}), "\n", "イテレーション回数* outest", _jsx(_components.br, {}), "\n", "ParameterEstimatesを出力します。"] }), "\n"] }), "\n", _jsx(_components.p, { children: "ステートメントは以下の通りです。" }), "\n", _jsxs(_components.ul, { children: ["\n", _jsxs(_components.li, { children: ["model (目的変数)=(説明変数)", _jsx(_components.br, {}), "\n", "モデルの式を入力します。* selection method=lasso", _jsx(_components.br, {}), "\n", "lasso回帰で変数選択します。lassosteps=1を指定することで、PythonのLasso回帰と似た結果になります。* code file=", _jsx(_components.br, {}), "\n", "予測結果を生成するプログラムコードを出力します* ods output", _jsx(_components.br, {}), "\n", "ParameterEstimatesをcoefという名前で出力します。"] }), "\n"] }), "\n", _jsxs(_components.p, { children: ["その他、有用なオプションはいろいろあるので、", _jsx(_components.a, { href: "https://support.sas.com/documentation/onlinedoc/stat/142/hpgenselect.pdf", children: "こちら" }), "を参考にしてください。"] }), "\n", _jsx(_components.p, { children: "結果は以下のようになりました。" }), "\n", _jsx(_components.p, { children: _jsx(_components.img, { src: "/images/blog43/image1.png", alt: "" }) }), "\n", _jsx(_components.p, { children: "たとえばnatbatのように偏回帰係数が表示されていない変数がありますが、これはLasso回帰によって0になり、変数が選択されなかったことを意味します。" }), "\n", _jsx(_components.p, { children: "最後に予測をします。" }), "\n", _jsx(_components.pre, { children: _jsxs(_components.code, { className: "hljs language-sas", children: [_jsx(_components.span, { className: "hljs-comment", children: "/*予測*/" }), "\n", _jsx(_components.span, { className: "hljs-keyword", children: "data " }), "Pred;\n ", _jsx(_components.span, { className: "hljs-keyword", children: "set" }), " work.baseball_standard;\n ", _jsx(_components.span, { className: "hljs-title function_", children: "%include" }), " ", _jsx(_components.span, { className: "hljs-variable", children: "&filename." }), ";\n", _jsx(_components.span, { className: "hljs-keyword", children: "run;" }), "\n"] }) }), "\n", _jsx(_components.p, { children: "codeステートメントで出力したコードを%includeすることにより、予測することができます。" }), "\n", _jsx(_components.h3, { children: "まとめ" }), "\n", _jsx(_components.p, { children: "Lasso回帰をSASで実行する方法を紹介しました。" }), "\n", _jsx(_components.p, { children: "今回はstepを1で指定しましたが、今後stepを複数回実行すると精度が向上するのかも検証していきたいです。" })] }); } function MDXContent(props = {}) { const {wrapper: MDXLayout} = Object.assign({}, _provideComponents(), props.components); return MDXLayout ? _jsx(MDXLayout, Object.assign({}, props, { children: _jsx(_createMdxContent, props) })) : _createMdxContent(props); } return { default: MDXContent }; a:["$","div",null,{"className":"container mx-auto px-4 py-8 max-w-7xl","children":["$","div",null,{"className":"flex flex-col md:flex-row gap-8","children":[["$","article",null,{"className":"w-full md:w-[70%] bg-white shadow-lg rounded-lg p-8","children":[["$","header",null,{"className":"mb-8 border-b pb-4","children":[["$","div",null,{"className":"flex items-center gap-2 mb-2","children":[["$","$L6",null,{"href":"/","className":"text-gray-500 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