{"id":1829,"date":"2025-03-24T09:27:00","date_gmt":"2025-03-24T06:27:00","guid":{"rendered":"http:\/\/csnotes.ru\/?p=1829"},"modified":"2025-04-15T11:14:13","modified_gmt":"2025-04-15T08:14:13","slug":"%d0%bb%d0%b8%d0%bd%d0%b5%d0%b9%d0%bd%d0%b0%d1%8f-%d1%80%d0%b5%d0%b3%d1%80%d0%b5%d1%81%d1%81%d0%b8%d1%8f","status":"publish","type":"post","link":"https:\/\/csnotes.ru\/?p=1829","title":{"rendered":"\u041b\u0438\u043d\u0435\u0439\u043d\u0430\u044f \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u044f"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">\u0410\u043b\u0433\u043e\u0440\u0438\u0442\u043c \u043f\u0440\u043e\u0433\u043d\u043e\u0437\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u044f \u0447\u0438\u0441\u043b\u043e\u0432\u044b\u0445 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439. \u041e\u0441\u043d\u043e\u0432\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0439 \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u0438 \u0438\u043c\u0435\u0435\u0442 \u0432\u0438\u0434:<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\"><span class=\"wp-katex-eq\" data-display=\"false\">y = w_0 + w_1 \\cdot x_1 + w_2 \\cdot x_2<\/span><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u0415\u0441\u043b\u0438 \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442\u044b \u0438 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0435 \u0441\u0432\u0435\u0440\u043d\u0443\u0442\u044c \u0432 \u0432\u0435\u043a\u0442\u043e\u0440\u044b:<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\"><span class=\"wp-katex-eq\" data-display=\"false\">\\hat{y} = \\mathbf{w}^\\top \\mathbf{x} + b<\/span><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u0423\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043e\u043f\u0438\u0441\u044b\u0432\u0430\u0435\u0442 \u043b\u0438\u043d\u0438\u044e \u0438\u043b\u0438 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044c (\u0438\u043b\u0438 \u0433\u0438\u043f\u0435\u0440\u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044c, \u0435\u0441\u043b\u0438 \u0438\u0437\u043c\u0435\u0440\u0435\u043d\u0438\u0439 \u0431\u043e\u043b\u044c\u0448\u0435 3) &#8211; \u043e\u043f\u0438\u0441\u044b\u0432\u0430\u044e\u0449\u0443\u044e \u0438\u0441\u0445\u043e\u0434\u043d\u0443\u044e \u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u044c. \u041f\u043e\u0437\u0432\u043e\u043b\u044f\u0435\u0442 \u0434\u0430\u0442\u044c \u043e\u0431\u0449\u0435\u0435 \u043e\u043f\u0438\u0441\u0430\u043d\u0438\u0435 \u0434\u0430\u043d\u043d\u044b\u0445 \u0438 \u0441\u043f\u0440\u043e\u0433\u043d\u043e\u0437\u0438\u0440\u043e\u0432\u0430\u0442\u044c \u0447\u0438\u0441\u043b\u0435\u043d\u043d\u043e\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u0434\u0430\u043d\u043d\u044b\u0445 \u0434\u043b\u044f \u0440\u0430\u043d\u0435\u0435 \u043d\u0435\u0438\u0437\u0432\u0435\u0441\u0442\u043d\u044b\u0445 \u0432\u0445\u043e\u0434\u043d\u044b\u0445 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439.<\/p>\n\n\n\n<p class=\"has-text-align-left wp-block-paragraph\">\u041c\u0435\u0442\u043e\u0434 \u043d\u0430\u0438\u043c\u0435\u043d\u044c\u0448\u0438\u0445 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043e\u0432 &#8211; \u043c\u0435\u0445\u0430\u043d\u0438\u0437\u043c \u043d\u0430\u0445\u043e\u0436\u0434\u0435\u043d\u0438\u044f \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442\u043e\u0432 w \u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0439 \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u0438. \u0412 \u0441\u043b\u0443\u0447\u0430\u0435 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438, \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c \u0441\u0442\u0440\u0435\u043c\u0438\u0442\u0441\u044f \u043f\u0440\u043e\u0432\u0435\u0441\u0442\u0438 \u043f\u0440\u044f\u043c\u0443\u044e, \u043f\u0440\u043e\u0445\u043e\u0434\u044f\u0449\u0443\u044e \u043a\u0430\u043a \u043c\u043e\u0436\u043d\u043e \u0431\u043b\u0438\u0436\u0435 \u043a \u0442\u043e\u0447\u043a\u0430\u043c \u0434\u0430\u043d\u043d\u044b\u0445 &#8211; \u0447\u0442\u043e\u0431\u044b \u0441\u0443\u043c\u043c\u0430 \u0432\u0441\u0435\u0445 \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0439 \u043e\u0442 \u043f\u0440\u044f\u043c\u043e\u0439 \u0434\u043e \u0442\u043e\u0447\u0435\u043a \u0432 \u0441\u0443\u043c\u043c\u0435 \u0431\u044b\u043b\u043e \u043c\u0438\u043d\u0438\u043c\u0430\u043b\u044c\u043d\u044b\u043c. \u041a\u0432\u0430\u0434\u0440\u0430\u0442 (\u0432\u0442\u043e\u0440\u0430\u044f \u0441\u0442\u0435\u043f\u0435\u043d\u044c) \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u0442\u0441\u044f \u0434\u043b\u044f \u0442\u043e\u0433\u043e, \u0447\u0442\u043e\u0431\u044b \u043a\u043e\u043c\u043f\u0435\u043d\u0441\u0438\u0440\u043e\u0432\u0430\u0442\u044c \u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u044b\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u044f, \u0432\u043e\u0437\u043d\u0438\u043a\u0430\u044e\u0449\u0438\u0435 \u0434\u043b\u044f \u0442\u043e\u0447\u0435\u043a, \u043d\u0430\u0445\u043e\u0434\u044f\u0449\u0438\u0445\u0441\u044f \u043d\u0438\u0436\u0435 \u043f\u0440\u044f\u043c\u043e\u0439.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"813\" height=\"694\" src=\"http:\/\/csnotes.ru\/wp-content\/uploads\/2025\/03\/dst3-ml2-2_7.png\" alt=\"\" class=\"wp-image-2004\" srcset=\"https:\/\/csnotes.ru\/wp-content\/uploads\/2025\/03\/dst3-ml2-2_7.png 813w, https:\/\/csnotes.ru\/wp-content\/uploads\/2025\/03\/dst3-ml2-2_7-300x256.png 300w, https:\/\/csnotes.ru\/wp-content\/uploads\/2025\/03\/dst3-ml2-2_7-768x656.png 768w\" sizes=\"auto, (max-width: 813px) 100vw, 813px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u041c\u0435\u0442\u0440\u0438\u043a\u0438 \u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0439 \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u0438<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">mae &#8211; \u0441\u0440\u0435\u0434\u043d\u044f\u044f \u0430\u0431\u0441\u043e\u043b\u044e\u0442\u043d\u0430\u044f \u043e\u0448\u0438\u0431\u043a\u0430:<strong> <\/strong><\/p>\n\n\n\n<pre class=\"wp-block-preformatted\"><span class=\"wp-katex-eq\" data-display=\"false\"> mae = \\sum_{i=1}^{n} \\frac {(y_i - y) }{n} <\/span><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">mse &#8211; \u0441\u0440\u0435\u0434\u043d\u0435\u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0438\u0447\u043d\u0430\u044f \u043e\u0448\u0438\u0431\u043a\u0430: <\/p>\n\n\n\n<pre class=\"wp-block-preformatted\"><span class=\"wp-katex-eq\" data-display=\"false\"> mse = \\sum_{i=1}^{n} \\frac {(y_i - y)^2}{n}<\/span><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"wp-katex-eq\" data-display=\"false\">R^2<\/span> &#8211; \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442 \u0434\u0435\u0442\u0435\u0440\u043c\u0438\u043d\u0430\u0446\u0438\u0438 <\/p>\n\n\n\n<pre class=\"wp-block-preformatted\"><span class=\"wp-katex-eq\" data-display=\"false\"> R^2 = 1 - \\frac {mse}{mse(mean)}<\/span> - \u043f\u043e\u043a\u0430\u0437\u044b\u0432\u0430\u0435\u0442, \u043a\u0430\u043a\u0443\u044e \u0434\u043e\u043b\u044e \u0434\u0438\u0441\u043f\u0435\u0440\u0441\u0438\u0438 \u043e\u0431\u044a\u044f\u0441\u043d\u044f\u0435\u0442 \u043c\u043e\u0434\u0435\u043b\u044c<\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u0415\u0441\u0442\u044c \u0438 \u0434\u0440\u0443\u0433\u0438\u0435 \u043c\u0435\u0442\u0440\u0438\u043a\u0438, \u043d\u043e \u0438\u0445 \u0432\u044b\u0431\u043e\u0440 \u0437\u0430\u0432\u0438\u0441\u0438\u0442 \u043e\u0442 \u0434\u0430\u043d\u043d\u044b\u0445. \u0414\u043b\u044f \u043d\u0435\u043a\u043e\u0442\u043e\u0440\u044b\u0445 \u0441\u0438\u0442\u0443\u0430\u0446\u0438\u0439 (\u0441\u0438\u043b\u044c\u043d\u044b\u0439 \u0440\u0430\u0437\u0431\u0440\u043e\u0441 \u0434\u0430\u043d\u043d\u044b\u0445) \u043c\u043e\u0433\u0443\u0442 \u0431\u044b\u0442\u044c<br>\u0443\u0434\u043e\u0431\u043d\u044b \u0434\u0440\u0443\u0433\u0438\u0435 \u043c\u0435\u0442\u0440\u0438\u043a\u0438, \u0442\u0430\u043a \u043a\u0430\u043a \u043e\u043d\u0438 \u0431\u0443\u0434\u0443\u0442 \u0431\u043e\u043b\u0435\u0435 \u0438\u043d\u0442\u0435\u0440\u043f\u0440\u0435\u0442\u0438\u0440\u0443\u0435\u043c\u044b\u043c\u0438.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0421\u0443\u0442\u044c \u043f\u043e\u0434\u0433\u043e\u043d\u043a\u0438 \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442\u043e\u0432 \u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0439 \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u0438 &#8211; \u044d\u0442\u043e \u043c\u0438\u043d\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u044f \u0441\u0440\u0435\u0434\u043d\u0435\u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0438\u0447\u043d\u043e\u0439 \u043e\u0448\u0438\u0431\u043a\u0438.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u041e\u0441\u043d\u043e\u0432\u043d\u044b\u0435 \u043c\u0435\u0442\u043e\u0434\u044b \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u0437\u0430\u0434\u0430\u0447\u0438 \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u0438<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">\u0410\u043d\u0430\u043b\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0439 &#8211; \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u043c\u0430\u0442\u0440\u0438\u0446<\/h3>\n\n\n\n<pre class=\"wp-block-preformatted\"><span class=\"wp-katex-eq\" data-display=\"false\">\\mathbf{w} = \\left( \\mathbf{X}^\\top \\mathbf{X} \\right)^{-1} \\mathbf{X}^\\top \\mathbf{y}<\/span><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>w = (X^T<em>X)^(-1)<\/em>X^T*y<\/strong> &#8211; \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u043c \u043d\u0443\u0436\u043d\u044b\u0439 \u043d\u0430\u043c \u0432\u0435\u043a\u0442\u043e\u0440 \u0432\u0435\u0441\u043e\u0432. \u042d\u0442\u043e\u0442 \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c \u043e\u0447\u0435\u043d\u044c \u0437\u0430\u0442\u0440\u0430\u0442\u043d\u044b\u0439 (\u0441\u043b\u043e\u0436\u043d\u043e\u0441\u0442\u044c \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u0438\u044f \u043e\u0431\u0440\u0430\u0442\u043d\u043e\u0439 \u043c\u0430\u0442\u0440\u0438\u0446\u044b &#8211; \u041e(N^3)). \u0415\u0441\u043b\u0438 \u0435\u0441\u0442\u044c \u043c\u0443\u043b\u044c\u0442\u0438\u043a\u043e\u043b\u043b\u0438\u043d\u0435\u0430\u0440\u043d\u043e\u0441\u0442\u044c &#8211; \u0442\u043e \u043c\u0430\u0442\u0440\u0438\u0446\u0430 \u043e\u043a\u0430\u0436\u0435\u0442\u0441\u044f \u0432\u044b\u0440\u043e\u0436\u0434\u0435\u043d\u043d\u043e\u0439, \u0438 \u0432\u0437\u044f\u0442\u044c \u043e\u0431\u0440\u0430\u0442\u043d\u0443\u044e \u043c\u0430\u0442\u0440\u0438\u0446\u0443 \u043d\u0435 \u043f\u043e\u043b\u0443\u0447\u0438\u0442\u0441\u044f.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u0413\u0440\u0430\u0434\u0438\u0435\u043d\u0442\u043d\u044b\u0439 \u0441\u043f\u0443\u0441\u043a &#8211; \u0447\u0438\u0441\u043b\u0435\u043d\u043d\u044b\u0439 \u043c\u0435\u0442\u043e\u0434 \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438 \u0432\u0435\u0441\u043e\u0432<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u0421\u043d\u0430\u0447\u0430\u043b\u0430 \u0432\u0435\u0441\u0430 \u0431\u0435\u0440\u0443\u0442\u0441\u044f \u0441\u043b\u0443\u0447\u0430\u0439\u043d\u044b\u0435, \u0437\u0430\u0442\u0435\u043c \u043e\u043d\u0438 \u043f\u0440\u0438\u043c\u0435\u043d\u044f\u044e\u0442\u0441\u044f \u0438 \u0441\u0447\u0438\u0442\u0430\u0435\u0442\u0441\u044f MSE.<br>\u0417\u0430\u0442\u0435\u043c \u0431\u0435\u0440\u0435\u0442\u0441\u044f \u0433\u0440\u0430\u0434\u0438\u0435\u043d\u0442 \u043e\u0442 MSE \u0438 \u0434\u0435\u043b\u0430\u0435\u0442\u0441\u044f \u0448\u0430\u0433 \u0432 \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u0438 \u0430\u043d\u0442\u0438\u0433\u0440\u0430\u0434\u0438\u0435\u043d\u0442\u0430 \u043f\u043e \u0444\u043e\u0440\u043c\u0443\u043b\u0435:<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\"><span class=\"wp-katex-eq\" data-display=\"false\">\\theta := \\theta - \\alpha \\cdot \\nabla_\\theta \\mathcal{L}(\\theta)<\/span><\/pre>\n\n\n\n<pre class=\"wp-block-preformatted\">\u03b8 := \u03b8 \u2212 \u03b1 \u2207L(\u03b8)<\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u041f\u043e\u043c\u043d\u0438\u043c, \u0447\u0442\u043e \u0433\u0440\u0430\u0434\u0438\u0435\u043d\u0442 \u043f\u043e\u043a\u0430\u0437\u044b\u0432\u0430\u0435\u0442 \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u0435 \u0432\u043e\u0437\u0440\u0430\u0441\u0442\u0430\u043d\u0438\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u043c\u044b \u0431\u0435\u0440\u0435\u043c \u0435\u0433\u043e \u0441\u043e \u0437\u043d\u0430\u043a\u043e\u043c \u043c\u0438\u043d\u0443\u0441.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u0420\u0435\u0430\u043b\u0438\u0437\u0430\u0446\u0438\u044f \u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0439 \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u0438 \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e Scikit Learn<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u041d\u0430 \u043f\u0440\u0438\u043c\u0435\u0440\u0435 \u0434\u0430\u043d\u043d\u044b\u0445 California Housing \u0440\u0435\u0430\u043b\u0438\u0437\u043e\u0432\u0430\u043d\u0430 \u0441\u0442\u0430\u043d\u0434\u0430\u0440\u0442\u043d\u0430\u044f \u043b\u0438\u043d\u0435\u0439\u043d\u0430\u044f \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u044f, \u043b\u0438\u043d\u0435\u0439\u043d\u0430\u044f \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u044f \u0441 \u0440\u0435\u0433\u0443\u043b\u044f\u0440\u0438\u0437\u0430\u0446\u0438\u0435\u0439 (L1, L2, ElascicNet), \u043b\u0438\u043d\u0435\u0439\u043d\u0430\u044f \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u044f \u0441 \u0434\u043e\u0431\u0430\u0432\u043b\u0435\u043d\u0438\u0435\u043c \u043f\u043e\u043b\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u044b\u0445 \u043f\u0440\u0438\u0437\u043d\u0430\u043a\u043e\u0432.<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>from sklearn.linear_model import LinearRegression, Ridge, Lasso, ElasticNet\nfrom sklearn.datasets import fetch_california_housing\nimport pandas as pd\nfrom sklearn.model_selection import train_test_split\nfrom sklearn.metrics import mean_squared_error, root_mean_squared_error\n\n# Download and view data\nhousing = fetch_california_housing(as_frame=True)  # \u0412\u043e\u0437\u0432\u0440\u0430\u0449\u0430\u0435\u0442 \u0434\u0430\u043d\u043d\u044b\u0435 \u0432 \u0444\u043e\u0440\u043c\u0430\u0442\u0435 pandas df\nprint(housing.data.shape, housing.target.shape)\nprint(housing.feature_names)\ndata = housing.data\ntarget = housing.target\n\n\n# Learn Linear Regression\nX_train, X_test, y_train, y_test = train_test_split(data, target, test_size=0.2)\nlr = LinearRegression()  # \u0420\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c \u043f\u0440\u0438\u043c\u0435\u043d\u0435\u043d\u0438\u0435 fit_intercept=True\/False - \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u0435\u0442, \u043f\u0440\u043e\u0439\u0434\u0435\u0442 \u043b\u0438 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044c \u0447\u0435\u0440\u0435\u0437 \u043d\u0430\u0447\u0430\u043b\u043e \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\n                         # \u0417\u0430\u043e\u0434\u043d\u043e \u043f\u043e\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c, \u0432 \u0447\u0435\u043c \u0441\u0443\u0442\u044c \u0438 \u043a\u0430\u043a \u043c\u0435\u043d\u044f\u0435\u0442\u0441\u044f \u0440\u0430\u0441\u043f\u043e\u043b\u043e\u0436\u0435\u043d\u0438\u0435 \u0434\u0430\u043d\u043d\u044b\u0445 \u043d\u0430 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \u043f\u043e\u0441\u043b\u0435 \u0446\u0435\u043d\u0442\u0440\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u044f (StandardScaler \u0438\u043b\u0438 \u0434\u0440\u0443\u0433\u043e\u0433\u043e)\n                         # \u0434\u043e\u043b\u0436\u043d\u044b \u0441\u0442\u0430\u0442\u044c \u0431\u043b\u0438\u0436\u0435 \u043a \u0446\u0435\u043d\u0442\u0440\u0443 \u043f\u043b\u043ec\u043a\u043e\u0441\u0442\u0438 (\u043a 0).\nlr.fit(X_train, y_train)\ny_pred = lr.predict(X_test)\nmse = mean_squared_error(y_test, y_pred)\nrmse = root_mean_squared_error(y_test, y_pred)\nprint(f\"COEF: {lr.coef_}\")\nprint(f\"MSE:  {mse:.5f} - Linear Regression\")\nprint(f\"RMSE: {rmse:.5f} - Linear Regression\")\nprint()\n\n# Learning Linear Regression with L1\/L2 regularization\n# L2 regularization - Ridge\nridge = Ridge(alpha=100)\nridge.fit(X_train, y_train)\ny_pred = ridge.predict(X_test)\nmse = mean_squared_error(y_test, y_pred)\nrmse = root_mean_squared_error(y_test, y_pred)\nprint(f\"COEF: {ridge.coef_}\")\nprint(f\"MSE:  {mse:.5f} - Ridge\")\nprint(f\"RMSE: {rmse:.5f} - Ridge\")\nprint()\n\n# L1 regularization - Lasso\nlasso = Lasso(alpha=1.0)\nlasso.fit(X_train, y_train)\ny_pred = lasso.predict(X_test)\nmse = mean_squared_error(y_test, y_pred)\nrmse = root_mean_squared_error(y_test, y_pred)\nprint(f\"COEF: {lasso.coef_}\")\nprint(f\"MSE:  {mse:.5f} - Lasso\")\nprint(f\"RMSE: {rmse:.5f} - Lasso\")\nprint()\n\n# L1\/L2 elasticnet regularization\nelastic = ElasticNet(alpha=100, l1_ratio=1.0)\nelastic.fit(X_train, y_train)\ny_pred = elastic.predict(X_test)\nmse = mean_squared_error(y_test, y_pred)\nrmse = root_mean_squared_error(y_test, y_pred)\nprint(f\"COEF: {elastic.coef_}\")\nprint(f\"MSE:  {mse:.5f} - ElasticNet\")\nprint(f\"RMSE: {rmse:.5f} - ElasticNet\")\nprint()\n\n# \u0414\u043e\u0431\u0430\u0432\u043b\u0435\u043d\u0438\u0435 \u043f\u043e\u043b\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u043e\u0441\u0442\u0438 (\u043f\u0440\u0438\u0437\u043d\u0430\u043a\u0438 2 \u0438 \u0431\u043e\u043b\u0435\u0435 \u0441\u0442\u0435\u043f\u0435\u043d\u0438)\nfrom sklearn.preprocessing import PolynomialFeatures\nfrom sklearn.pipeline import make_pipeline    # \u0423\u0434\u043e\u0431\u043d\u043e \u043f\u0440\u0438\u043c\u0435\u043d\u0438\u0442\u044c \u043f\u043e\u043b\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u044b\u0435 \u043f\u0440\u0438\u0437\u043d\u0430\u043a\u0438 \u0447\u0435\u0440\u0435\u0437 \u043f\u0430\u0439\u043f\u043b\u0430\u0439\u043d\n\ndegree = 3\nmodel = make_pipeline(PolynomialFeatures(degree), LinearRegression())\nmodel.fit(X_train, y_train)\ny_pred = model.predict(X_test)\nmse = mean_squared_error(y_test, y_pred)\nrmse = root_mean_squared_error(y_test, y_pred)\nprint(f\"COEF: {lr.coef_} - PolynomialFeatures\")\nprint(f\"MSE:  {mse:.5f} - Linear Regression with PolynomialFeatures\")\nprint(f\"RMSE: {rmse:.5f} - Linear Regression with PolynomialFeatures\")<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0410\u043b\u0433\u043e\u0440\u0438\u0442\u043c \u043f\u0440\u043e\u0433\u043d\u043e\u0437\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u044f \u0447\u0438\u0441\u043b\u043e\u0432\u044b\u0445 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439. \u041e\u0441\u043d\u043e\u0432\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0439 \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u0438 \u0438\u043c\u0435\u0435\u0442 \u0432\u0438\u0434: \u0415\u0441\u043b\u0438 \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442\u044b \u0438 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0435 \u0441\u0432\u0435\u0440\u043d\u0443\u0442\u044c \u0432 \u0432\u0435\u043a\u0442\u043e\u0440\u044b: \u0423\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043e\u043f\u0438\u0441\u044b\u0432\u0430\u0435\u0442 \u043b\u0438\u043d\u0438\u044e \u0438\u043b\u0438 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044c (\u0438\u043b\u0438 \u0433\u0438\u043f\u0435\u0440\u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044c, \u0435\u0441\u043b\u0438 \u0438\u0437\u043c\u0435\u0440\u0435\u043d\u0438\u0439 \u0431\u043e\u043b\u044c\u0448\u0435 3) &#8211; \u043e\u043f\u0438\u0441\u044b\u0432\u0430\u044e\u0449\u0443\u044e \u0438\u0441\u0445\u043e\u0434\u043d\u0443\u044e \u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u044c. \u041f\u043e\u0437\u0432\u043e\u043b\u044f\u0435\u0442 \u0434\u0430\u0442\u044c \u043e\u0431\u0449\u0435\u0435 \u043e\u043f\u0438\u0441\u0430\u043d\u0438\u0435 \u0434\u0430\u043d\u043d\u044b\u0445 \u0438 \u0441\u043f\u0440\u043e\u0433\u043d\u043e\u0437\u0438\u0440\u043e\u0432\u0430\u0442\u044c \u0447\u0438\u0441\u043b\u0435\u043d\u043d\u043e\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u0434\u0430\u043d\u043d\u044b\u0445 \u0434\u043b\u044f \u0440\u0430\u043d\u0435\u0435 \u043d\u0435\u0438\u0437\u0432\u0435\u0441\u0442\u043d\u044b\u0445 \u0432\u0445\u043e\u0434\u043d\u044b\u0445 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439. \u041c\u0435\u0442\u043e\u0434 \u043d\u0430\u0438\u043c\u0435\u043d\u044c\u0448\u0438\u0445 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043e\u0432 &#8211; \u043c\u0435\u0445\u0430\u043d\u0438\u0437\u043c \u043d\u0430\u0445\u043e\u0436\u0434\u0435\u043d\u0438\u044f \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442\u043e\u0432 w [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2],"tags":[18,19],"class_list":["post-1829","post","type-post","status-publish","format-standard","hentry","category-ml","tag-regression","tag-lrmetrics"],"views":54,"_links":{"self":[{"href":"https:\/\/csnotes.ru\/index.php?rest_route=\/wp\/v2\/posts\/1829","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/csnotes.ru\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/csnotes.ru\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/csnotes.ru\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/csnotes.ru\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1829"}],"version-history":[{"count":31,"href":"https:\/\/csnotes.ru\/index.php?rest_route=\/wp\/v2\/posts\/1829\/revisions"}],"predecessor-version":[{"id":2197,"href":"https:\/\/csnotes.ru\/index.php?rest_route=\/wp\/v2\/posts\/1829\/revisions\/2197"}],"wp:attachment":[{"href":"https:\/\/csnotes.ru\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1829"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/csnotes.ru\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1829"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/csnotes.ru\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1829"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}