{"id":15737,"date":"2024-01-16T09:03:13","date_gmt":"2024-01-16T05:33:13","guid":{"rendered":"https:\/\/rasanegar.com\/blog\/%d8%aa%d8%ae%d9%85%db%8c%d9%86-%da%86%da%af%d8%a7%d9%84%db%8c-%d9%87%d8%b3%d8%aa%d9%87-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86-%d8%a8%d8%a7-%d8%a7%d8%b3%d8%aa%d9%81%d8%a7%d8%af%d9%87-%d8%a7\/"},"modified":"2024-01-16T09:03:13","modified_gmt":"2024-01-16T05:33:13","slug":"%d8%aa%d8%ae%d9%85%db%8c%d9%86-%da%86%da%af%d8%a7%d9%84%db%8c-%d9%87%d8%b3%d8%aa%d9%87-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86-%d8%a8%d8%a7-%d8%a7%d8%b3%d8%aa%d9%81%d8%a7%d8%af%d9%87-%d8%a7","status":"publish","type":"post","link":"https:\/\/rasanegaar.com\/blog\/%d8%aa%d8%ae%d9%85%db%8c%d9%86-%da%86%da%af%d8%a7%d9%84%db%8c-%d9%87%d8%b3%d8%aa%d9%87-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86-%d8%a8%d8%a7-%d8%a7%d8%b3%d8%aa%d9%81%d8%a7%d8%af%d9%87-%d8%a7\/","title":{"rendered":"\u062a\u062e\u0645\u06cc\u0646 \u0686\u06af\u0627\u0644\u06cc \u0647\u0633\u062a\u0647 \u062f\u0631 \u067e\u0627\u06cc\u062a\u0648\u0646 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 Scikit-Learn"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_85 counter-hierarchy ez-toc-counter ez-toc-custom ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\"><p class=\"ez-toc-title\" style=\"cursor:inherit\">\u0633\u0631\u0641\u0635\u0644\u0647\u0627\u06cc \u0645\u0637\u0644\u0628<\/p>\n<\/div><nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/rasanegaar.com\/blog\/%d8%aa%d8%ae%d9%85%db%8c%d9%86-%da%86%da%af%d8%a7%d9%84%db%8c-%d9%87%d8%b3%d8%aa%d9%87-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86-%d8%a8%d8%a7-%d8%a7%d8%b3%d8%aa%d9%81%d8%a7%d8%af%d9%87-%d8%a7\/#%d9%85%d8%b9%d8%b1%d9%81%db%8c\" >\u0645\u0639\u0631\u0641\u06cc<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/rasanegaar.com\/blog\/%d8%aa%d8%ae%d9%85%db%8c%d9%86-%da%86%da%af%d8%a7%d9%84%db%8c-%d9%87%d8%b3%d8%aa%d9%87-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86-%d8%a8%d8%a7-%d8%a7%d8%b3%d8%aa%d9%81%d8%a7%d8%af%d9%87-%d8%a7\/#%d9%85%d8%ad%d8%a7%d8%b3%d8%a8%d8%a7%d8%aa_%d9%85%d8%ab%d8%a7%d9%84\" >\u0645\u062d\u0627\u0633\u0628\u0627\u062a \u0645\u062b\u0627\u0644<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/rasanegaar.com\/blog\/%d8%aa%d8%ae%d9%85%db%8c%d9%86-%da%86%da%af%d8%a7%d9%84%db%8c-%d9%87%d8%b3%d8%aa%d9%87-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86-%d8%a8%d8%a7-%d8%a7%d8%b3%d8%aa%d9%81%d8%a7%d8%af%d9%87-%d8%a7\/#%d8%aa%d8%ae%d9%85%db%8c%d9%86_%da%86%da%af%d8%a7%d9%84%db%8c_%d9%87%d8%b3%d8%aa%d9%87_%d8%a8%d8%a7_%d8%a7%d8%b3%d8%aa%d9%81%d8%a7%d8%af%d9%87_%d8%a7%d8%b2_%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\" >\u062a\u062e\u0645\u06cc\u0646 \u0686\u06af\u0627\u0644\u06cc \u0647\u0633\u062a\u0647 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u067e\u0627\u06cc\u062a\u0648\u0646<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/rasanegaar.com\/blog\/%d8%aa%d8%ae%d9%85%db%8c%d9%86-%da%86%da%af%d8%a7%d9%84%db%8c-%d9%87%d8%b3%d8%aa%d9%87-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86-%d8%a8%d8%a7-%d8%a7%d8%b3%d8%aa%d9%81%d8%a7%d8%af%d9%87-%d8%a7\/#%d8%af%d8%a7%d8%af%d9%87_%d9%87%d8%a7%db%8c_%d9%85%d8%b5%d9%86%d9%88%d8%b9%db%8c\" >\u062f\u0627\u062f\u0647 \u0647\u0627\u06cc \u0645\u0635\u0646\u0648\u0639\u06cc<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/rasanegaar.com\/blog\/%d8%aa%d8%ae%d9%85%db%8c%d9%86-%da%86%da%af%d8%a7%d9%84%db%8c-%d9%87%d8%b3%d8%aa%d9%87-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86-%d8%a8%d8%a7-%d8%a7%d8%b3%d8%aa%d9%81%d8%a7%d8%af%d9%87-%d8%a7\/#%d8%a7%d8%b3%d8%aa%d9%81%d8%a7%d8%af%d9%87_%d8%a7%d8%b2_scikit-learns_%d8%aa%d8%b1%d8%a7%da%a9%d9%85_%d9%87%d8%b3%d8%aa%d9%87\" >\u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 Scikit-Learn&#8217;s \u062a\u0631\u0627\u06a9\u0645 \u0647\u0633\u062a\u0647<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/rasanegaar.com\/blog\/%d8%aa%d8%ae%d9%85%db%8c%d9%86-%da%86%da%af%d8%a7%d9%84%db%8c-%d9%87%d8%b3%d8%aa%d9%87-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86-%d8%a8%d8%a7-%d8%a7%d8%b3%d8%aa%d9%81%d8%a7%d8%af%d9%87-%d8%a7\/#%d8%a2%d8%b4%d9%86%d8%a7%db%8c%db%8c_%d8%a8%d8%a7_%d9%be%d8%a7%d8%b1%d8%a7%d9%85%d8%aa%d8%b1_%d9%be%d9%87%d9%86%d8%a7%db%8c_%d8%a8%d8%a7%d9%86%d8%af\" >\u0622\u0634\u0646\u0627\u06cc\u06cc \u0628\u0627 \u067e\u0627\u0631\u0627\u0645\u062a\u0631 \u067e\u0647\u0646\u0627\u06cc \u0628\u0627\u0646\u062f<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/rasanegaar.com\/blog\/%d8%aa%d8%ae%d9%85%db%8c%d9%86-%da%86%da%af%d8%a7%d9%84%db%8c-%d9%87%d8%b3%d8%aa%d9%87-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86-%d8%a8%d8%a7-%d8%a7%d8%b3%d8%aa%d9%81%d8%a7%d8%af%d9%87-%d8%a7\/#%d8%aa%d9%86%d8%b8%db%8c%d9%85_%d9%be%d8%a7%d8%b1%d8%a7%d9%85%d8%aa%d8%b1_%d9%be%d9%87%d9%86%d8%a7%db%8c_%d8%a8%d8%a7%d9%86%d8%af\" >\u062a\u0646\u0638\u06cc\u0645 \u067e\u0627\u0631\u0627\u0645\u062a\u0631 \u067e\u0647\u0646\u0627\u06cc \u0628\u0627\u0646\u062f<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/rasanegaar.com\/blog\/%d8%aa%d8%ae%d9%85%db%8c%d9%86-%da%86%da%af%d8%a7%d9%84%db%8c-%d9%87%d8%b3%d8%aa%d9%87-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86-%d8%a8%d8%a7-%d8%a7%d8%b3%d8%aa%d9%81%d8%a7%d8%af%d9%87-%d8%a7\/#%d9%87%d8%b3%d8%aa%d9%87_%d9%87%d8%a7%db%8c_%d9%85%d8%ae%d8%aa%d9%84%d9%81_%d8%a8%d8%b1%d8%a7%db%8c_%d8%aa%d8%ae%d9%85%db%8c%d9%86_%da%86%da%af%d8%a7%d9%84%db%8c\" >\u0647\u0633\u062a\u0647 \u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641 \u0628\u0631\u0627\u06cc \u062a\u062e\u0645\u06cc\u0646 \u0686\u06af\u0627\u0644\u06cc<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/rasanegaar.com\/blog\/%d8%aa%d8%ae%d9%85%db%8c%d9%86-%da%86%da%af%d8%a7%d9%84%db%8c-%d9%87%d8%b3%d8%aa%d9%87-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86-%d8%a8%d8%a7-%d8%a7%d8%b3%d8%aa%d9%81%d8%a7%d8%af%d9%87-%d8%a7\/#%d8%a2%d8%b2%d9%85%d8%a7%db%8c%d8%b4_%d8%a8%d8%a7_%d9%87%d8%b3%d8%aa%d9%87_%d9%87%d8%a7%db%8c_%d9%85%d8%ae%d8%aa%d9%84%d9%81\" >\u0622\u0632\u0645\u0627\u06cc\u0634 \u0628\u0627 \u0647\u0633\u062a\u0647 \u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/rasanegaar.com\/blog\/%d8%aa%d8%ae%d9%85%db%8c%d9%86-%da%86%da%af%d8%a7%d9%84%db%8c-%d9%87%d8%b3%d8%aa%d9%87-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86-%d8%a8%d8%a7-%d8%a7%d8%b3%d8%aa%d9%81%d8%a7%d8%af%d9%87-%d8%a7\/#%d9%85%d8%af%d9%84_%d9%86%d9%87%d8%a7%db%8c%db%8c_%d8%a8%d9%87%db%8c%d9%86%d9%87_%d8%b4%d8%af%d9%87\" >\u0645\u062f\u0644 \u0646\u0647\u0627\u06cc\u06cc \u0628\u0647\u06cc\u0646\u0647 \u0634\u062f\u0647<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/rasanegaar.com\/blog\/%d8%aa%d8%ae%d9%85%db%8c%d9%86-%da%86%da%af%d8%a7%d9%84%db%8c-%d9%87%d8%b3%d8%aa%d9%87-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86-%d8%a8%d8%a7-%d8%a7%d8%b3%d8%aa%d9%81%d8%a7%d8%af%d9%87-%d8%a7\/#%d9%86%d8%aa%db%8c%d8%ac%d9%87\" >\u0646\u062a\u06cc\u062c\u0647<\/a><\/li><\/ul><\/nav><\/div>\n<span class=\"span-reading-time rt-reading-time\" style=\"display: block;\"><span class=\"rt-label rt-prefix\">\u0632\u0645\u0627\u0646 \u0644\u0627\u0632\u0645 \u0628\u0631\u0627\u06cc \u0645\u0637\u0627\u0644\u0639\u0647: <\/span> <span class=\"rt-time\"> 3<\/span> <span class=\"rt-label rt-postfix\">\u062f\u0642\u06cc\u0642\u0647<\/span><\/span><p> <br \/>\n<\/p>\n<div><noscript><\/noscript><\/p>\n<h2 id=\"introduction\"><span class=\"ez-toc-section\" id=\"%d9%85%d8%b9%d8%b1%d9%81%db%8c\"><\/span>\u0645\u0639\u0631\u0641\u06cc<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u0627\u06cc\u0646 \u0645\u0642\u0627\u0644\u0647 \u0645\u0642\u062f\u0645\u0647\u200c\u0627\u06cc \u0628\u0631 \u062a\u062e\u0645\u06cc\u0646 \u0686\u06af\u0627\u0644\u06cc \u0647\u0633\u062a\u0647 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u06a9\u062a\u0627\u0628\u062e\u0627\u0646\u0647 \u06cc\u0627\u062f\u06af\u06cc\u0631\u06cc \u0645\u0627\u0634\u06cc\u0646 \u067e\u0627\u06cc\u062a\u0648\u0646 \u0627\u0633\u062a. <code>scikit-learn<\/code>.<\/p>\n<p>\u062a\u062e\u0645\u06cc\u0646 \u0686\u06af\u0627\u0644\u06cc \u0647\u0633\u062a\u0647 (KDE) \u06cc\u06a9 \u0631\u0648\u0634 \u0646\u0627\u067e\u0627\u0631\u0627\u0645\u062a\u0631\u06cc\u06a9 \u0628\u0631\u0627\u06cc \u062a\u062e\u0645\u06cc\u0646 \u062a\u0627\u0628\u0639 \u0686\u06af\u0627\u0644\u06cc \u0627\u062d\u062a\u0645\u0627\u0644 \u06cc\u06a9 \u0645\u062a\u063a\u06cc\u0631 \u062a\u0635\u0627\u062f\u0641\u06cc \u0645\u0639\u06cc\u0646 \u0627\u0633\u062a.  \u0627\u0632 \u0622\u0646 \u0628\u0627 \u0646\u0627\u0645 \u0633\u0646\u062a\u06cc \u0622\u0646 \u0646\u06cc\u0632 \u06cc\u0627\u062f \u0645\u06cc \u0634\u0648\u062f <em>\u067e\u0646\u062c\u0631\u0647 Parzen-Rosenblatt<\/em> \u0631\u0648\u0634\u060c \u067e\u0633 \u0627\u0632 \u06a9\u0627\u0634\u0641\u0627\u0646 \u0622\u0646.<\/p>\n<p>\u0628\u0627 \u062a\u0648\u062c\u0647 \u0628\u0647 \u0646\u0645\u0648\u0646\u0647\u200c\u0627\u06cc \u0627\u0632 \u0645\u0634\u0627\u0647\u062f\u0627\u062a \u0645\u0633\u062a\u0642\u0644\u060c \u062a\u0648\u0632\u06cc\u0639 \u0634\u062f\u0647 \u06cc\u06a9\u0633\u0627\u0646 (iid) \\((x_1,x_2,\\ldots,x_n)\\) \u0627\u0632 \u06cc\u06a9 \u0645\u062a\u063a\u06cc\u0631 \u062a\u0635\u0627\u062f\u0641\u06cc \u0627\u0632 \u06cc\u06a9 \u062a\u0648\u0632\u06cc\u0639 \u0645\u0646\u0628\u0639 \u0646\u0627\u0634\u0646\u0627\u062e\u062a\u0647\u060c \u062a\u062e\u0645\u06cc\u0646 \u0686\u06af\u0627\u0644\u06cc \u0647\u0633\u062a\u0647 \u0628\u0647 \u0635\u0648\u0631\u062a \u0632\u06cc\u0631 \u0627\u0631\u0627\u0626\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f:<\/p>\n<p>$$<br \/>p(x) = \\frac{1}{nh} \\Sigma_{j=1}^{n}K(\\frac{x-x_j}{h})<br \/>$$<\/p>\n<p>\u06a9\u0647 \u062f\u0631 \u0622\u0646 \\(K(a)\\) \u062a\u0627\u0628\u0639 \u0647\u0633\u062a\u0647 \u0648 \\(h\\) \u067e\u0627\u0631\u0627\u0645\u062a\u0631 \u0647\u0645\u0648\u0627\u0631\u0633\u0627\u0632\u06cc \u0627\u0633\u062a \u06a9\u0647 \u067e\u0647\u0646\u0627\u06cc \u0628\u0627\u0646\u062f \u0646\u06cc\u0632 \u0646\u0627\u0645\u06cc\u062f\u0647 \u0645\u06cc \u0634\u0648\u062f.  \u0647\u0633\u062a\u0647\u200c\u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641 \u062f\u0631 \u0627\u062f\u0627\u0645\u0647 \u0627\u06cc\u0646 \u0645\u0642\u0627\u0644\u0647 \u0645\u0648\u0631\u062f \u0628\u062d\u062b \u0642\u0631\u0627\u0631 \u0645\u06cc\u200c\u06af\u06cc\u0631\u0646\u062f\u060c \u0627\u0645\u0627 \u0641\u0642\u0637 \u0628\u0631\u0627\u06cc \u062f\u0631\u06a9 \u0631\u06cc\u0627\u0636\u06cc\u0627\u062a\u060c \u0627\u062c\u0627\u0632\u0647 \u062f\u0647\u06cc\u062f \u0628\u0647 \u06cc\u06a9 \u0645\u062b\u0627\u0644 \u0633\u0627\u062f\u0647 \u0646\u06af\u0627\u0647\u06cc \u0628\u06cc\u0646\u062f\u0627\u0632\u06cc\u0645.<\/p>\n<h3 id=\"examplecomputation\"><span class=\"ez-toc-section\" id=\"%d9%85%d8%ad%d8%a7%d8%b3%d8%a8%d8%a7%d8%aa_%d9%85%d8%ab%d8%a7%d9%84\"><\/span>\u0645\u062d\u0627\u0633\u0628\u0627\u062a \u0645\u062b\u0627\u0644<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u0641\u0631\u0636 \u06a9\u0646\u06cc\u062f \u0646\u0642\u0627\u0637 \u0646\u0645\u0648\u0646\u0647 \u0631\u0627 \u062f\u0627\u0631\u06cc\u0645 <em>(-2\u060c-1\u060c0\u060c1\u060c2)<\/em>\u060c \u0628\u0627 \u06cc\u06a9 \u0647\u0633\u062a\u0647 \u062e\u0637\u06cc \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u062a\u0648\u0633\u0637: \\(K(a)= 1-\\frac{|a|}{h}\\) \u0648 \\(h=10\\).<\/p>\n<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n  <mtable columnalign=\"left center center center center center center center center\" rowspacing=\"4pt\" columnspacing=\"1em\">\n    <mtr>\n      <mtd>\n        <msub>\n          <mi>\u0627\u06cc\u06a9\u0633<\/mi>\n          <mi>j<\/mi>\n        <\/msub>\n      <\/mtd>\n      <mtd>\n        <mo>=<\/mo>\n      <\/mtd>\n      <mtd>\n        <mo stretchy=\"false\">(<\/mo>\n      <\/mtd>\n      <mtd>\n        <mo>&#8211;<\/mo>\n        <mn>2<\/mn>\n      <\/mtd>\n      <mtd>\n        <mo>&#8211;<\/mo>\n        <mn>1<\/mn>\n      <\/mtd>\n      <mtd>\n        <mn>0<\/mn>\n      <\/mtd>\n      <mtd>\n        <mn>1<\/mn>\n      <\/mtd>\n      <mtd>\n        <mn>2<\/mn>\n      <\/mtd>\n      <mtd>\n        <mo stretchy=\"false\">)<\/mo>\n      <\/mtd>\n    <\/mtr>\n    <mtr>\n      <mtd>\n        <mrow class=\"MJX-TeXAtom-ORD\">\n          <mo stretchy=\"false\">|<\/mo>\n        <\/mrow>\n        <mn>0<\/mn>\n        <mo>&#8211;<\/mo>\n        <msub>\n          <mi>\u0627\u06cc\u06a9\u0633<\/mi>\n          <mi>j<\/mi>\n        <\/msub>\n        <mrow class=\"MJX-TeXAtom-ORD\">\n          <mo stretchy=\"false\">|<\/mo>\n        <\/mrow>\n      <\/mtd>\n      <mtd>\n        <mo>=<\/mo>\n      <\/mtd>\n      <mtd>\n        <mo stretchy=\"false\">(<\/mo>\n      <\/mtd>\n      <mtd>\n        <mn>2<\/mn>\n      <\/mtd>\n      <mtd>\n        <mn>1<\/mn>\n      <\/mtd>\n      <mtd>\n        <mn>0<\/mn>\n      <\/mtd>\n      <mtd>\n        <mn>1<\/mn>\n      <\/mtd>\n      <mtd>\n        <mn>2<\/mn>\n      <\/mtd>\n      <mtd>\n        <mo stretchy=\"false\">)<\/mo>\n      <\/mtd>\n    <\/mtr>\n    <mtr>\n      <mtd>\n        <mrow class=\"MJX-TeXAtom-ORD\">\n          <mo stretchy=\"false\">|<\/mo>\n        <\/mrow>\n        <mfrac>\n          <mrow>\n            <mn>0<\/mn>\n            <mo>&#8211;<\/mo>\n            <msub>\n              <mi>\u0627\u06cc\u06a9\u0633<\/mi>\n              <mi>j<\/mi>\n            <\/msub>\n          <\/mrow>\n          <mi>\u0633\u0627\u0639\u062a<\/mi>\n        <\/mfrac>\n        <mrow class=\"MJX-TeXAtom-ORD\">\n          <mo stretchy=\"false\">|<\/mo>\n        <\/mrow>\n      <\/mtd>\n      <mtd>\n        <mo>=<\/mo>\n      <\/mtd>\n      <mtd>\n        <mo stretchy=\"false\">(<\/mo>\n      <\/mtd>\n      <mtd>\n        <mn>0.2<\/mn>\n      <\/mtd>\n      <mtd>\n        <mn>0.1<\/mn>\n      <\/mtd>\n      <mtd>\n        <mn>0<\/mn>\n      <\/mtd>\n      <mtd>\n        <mn>0.1<\/mn>\n      <\/mtd>\n      <mtd>\n        <mn>0.2<\/mn>\n      <\/mtd>\n      <mtd>\n        <mo stretchy=\"false\">)<\/mo>\n      <\/mtd>\n    <\/mtr>\n    <mtr>\n      <mtd>\n        <mi>\u06a9<\/mi>\n        <mo stretchy=\"false\">(<\/mo>\n        <mrow class=\"MJX-TeXAtom-ORD\">\n          <mo stretchy=\"false\">|<\/mo>\n        <\/mrow>\n        <mfrac>\n          <mrow>\n            <mn>0<\/mn>\n            <mo>&#8211;<\/mo>\n            <msub>\n              <mi>\u0627\u06cc\u06a9\u0633<\/mi>\n              <mi>j<\/mi>\n            <\/msub>\n          <\/mrow>\n          <mi>\u0633\u0627\u0639\u062a<\/mi>\n        <\/mfrac>\n        <mrow class=\"MJX-TeXAtom-ORD\">\n          <mo stretchy=\"false\">|<\/mo>\n        <\/mrow>\n        <mo stretchy=\"false\">)<\/mo>\n      <\/mtd>\n      <mtd>\n        <mo>=<\/mo>\n      <\/mtd>\n      <mtd>\n        <mo stretchy=\"false\">(<\/mo>\n      <\/mtd>\n      <mtd>\n        <mn>0.8<\/mn>\n      <\/mtd>\n      <mtd>\n        <mn>0.9<\/mn>\n      <\/mtd>\n      <mtd>\n        <mn>1<\/mn>\n      <\/mtd>\n      <mtd>\n        <mn>0.9<\/mn>\n      <\/mtd>\n      <mtd>\n        <mn>0.8<\/mn>\n      <\/mtd>\n      <mtd>\n        <mo stretchy=\"false\">)<\/mo>\n      <\/mtd>\n    <\/mtr>\n  <\/mtable>\n<\/math><\/p>\n<p>\u0645\u0648\u0627\u0631\u062f \u0628\u0627\u0644\u0627 \u0631\u0627 \u062f\u0631 \u0641\u0631\u0645\u0648\u0644 \\(p(x)\\) \u0648\u0635\u0644 \u06a9\u0646\u06cc\u062f:<\/p>\n<p>$$<br \/>p(0) = \\frac{1}{(5)(10)} (0.8+0.9+1+0.9+0.8) = 0.088<br \/>$$<\/p>\n<h2 id=\"kerneldensityestimationusingpython\"><span class=\"ez-toc-section\" id=\"%d8%aa%d8%ae%d9%85%db%8c%d9%86_%da%86%da%af%d8%a7%d9%84%db%8c_%d9%87%d8%b3%d8%aa%d9%87_%d8%a8%d8%a7_%d8%a7%d8%b3%d8%aa%d9%81%d8%a7%d8%af%d9%87_%d8%a7%d8%b2_%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\"><\/span>\u062a\u062e\u0645\u06cc\u0646 \u0686\u06af\u0627\u0644\u06cc \u0647\u0633\u062a\u0647 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u067e\u0627\u06cc\u062a\u0648\u0646<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u062f\u0631 \u062d\u0627\u0644\u06cc \u06a9\u0647 \u0686\u0646\u062f\u06cc\u0646 \u0631\u0648\u0634 \u0628\u0631\u0627\u06cc \u0645\u062d\u0627\u0633\u0628\u0647 \u062a\u062e\u0645\u06cc\u0646 \u0686\u06af\u0627\u0644\u06cc \u0647\u0633\u062a\u0647 \u062f\u0631 \u067e\u0627\u06cc\u062a\u0648\u0646 \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f\u060c \u0645\u0627 \u0627\u0632 \u06a9\u062a\u0627\u0628\u062e\u0627\u0646\u0647 \u0645\u062d\u0628\u0648\u0628 \u06cc\u0627\u062f\u06af\u06cc\u0631\u06cc \u0645\u0627\u0634\u06cc\u0646 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u062e\u0648\u0627\u0647\u06cc\u0645 \u06a9\u0631\u062f. <code>scikit-learn<\/code> \u0628\u0647 \u0627\u06cc\u0646 \u0645\u0646\u0638\u0648\u0631.  \u06a9\u062a\u0627\u0628\u062e\u0627\u0646\u0647 \u0647\u0627\u06cc \u0632\u06cc\u0631 \u0631\u0627 \u062f\u0631 \u06a9\u062f \u062e\u0648\u062f \u0648\u0627\u0631\u062f \u06a9\u0646\u06cc\u062f:<\/p>\n<pre><code class=\"hljs\"><span class=\"hljs-keyword\">import<\/span> numpy <span class=\"hljs-keyword\">as<\/span> np\n<span class=\"hljs-keyword\">import<\/span> matplotlib.pyplot <span class=\"hljs-keyword\">as<\/span> plt\n<span class=\"hljs-keyword\">from<\/span> sklearn.neighbors <span class=\"hljs-keyword\">import<\/span> KernelDensity\n<span class=\"hljs-keyword\">from<\/span> sklearn.model_selection <span class=\"hljs-keyword\">import<\/span> GridSearchCV\n<\/code><\/pre>\n<h2 id=\"syntheticdata\"><span class=\"ez-toc-section\" id=\"%d8%af%d8%a7%d8%af%d9%87_%d9%87%d8%a7%db%8c_%d9%85%d8%b5%d9%86%d9%88%d8%b9%db%8c\"><\/span>\u062f\u0627\u062f\u0647 \u0647\u0627\u06cc \u0645\u0635\u0646\u0648\u0639\u06cc<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u0628\u0631\u0627\u06cc \u0646\u0634\u0627\u0646 \u062f\u0627\u062f\u0646 \u062a\u062e\u0645\u06cc\u0646 \u0686\u06af\u0627\u0644\u06cc \u0647\u0633\u062a\u0647\u060c \u062f\u0627\u062f\u0647 \u0647\u0627\u06cc \u0645\u0635\u0646\u0648\u0639\u06cc \u0627\u0632 \u062f\u0648 \u0646\u0648\u0639 \u0645\u062e\u062a\u0644\u0641 \u062a\u0648\u0632\u06cc\u0639 \u062a\u0648\u0644\u06cc\u062f \u0645\u06cc \u0634\u0648\u062f.  \u06cc\u06a9\u06cc \u062a\u0648\u0632\u06cc\u0639 \u0644\u06af \u0646\u0631\u0645\u0627\u0644 \u0646\u0627\u0645\u062a\u0642\u0627\u0631\u0646 \u0648 \u062f\u06cc\u06af\u0631\u06cc \u062a\u0648\u0632\u06cc\u0639 \u06af\u0627\u0648\u0633\u06cc \u0627\u0633\u062a.  \u062a\u0627\u0628\u0639 \u0632\u06cc\u0631 2000 \u0646\u0642\u0637\u0647 \u062f\u0627\u062f\u0647 \u0631\u0627 \u0628\u0631\u0645\u06cc \u06af\u0631\u062f\u0627\u0646\u062f:<\/p>\n<pre><code class=\"hljs\"><span class=\"hljs-function\"><span class=\"hljs-keyword\">def<\/span> <span class=\"hljs-title\">generate_data<\/span>(<span class=\"hljs-params\">seed=<span class=\"hljs-number\">17<\/span><\/span>):<\/span>\n    \n    rand = np.random.RandomState(seed)\n    x = ()\n    dat = rand.lognormal(<span class=\"hljs-number\">0<\/span>, <span class=\"hljs-number\">0.3<\/span>, <span class=\"hljs-number\">1000<\/span>)\n    x = np.concatenate((x, dat))\n    dat = rand.normal(<span class=\"hljs-number\">3<\/span>, <span class=\"hljs-number\">1<\/span>, <span class=\"hljs-number\">1000<\/span>)\n    x = np.concatenate((x, dat))\n    <span class=\"hljs-keyword\">return<\/span> x\n<\/code><\/pre>\n<p>\u06a9\u062f \u0632\u06cc\u0631 \u0646\u0642\u0627\u0637 \u0631\u0627 \u062f\u0631 \u0622\u0646 \u0630\u062e\u06cc\u0631\u0647 \u0645\u06cc \u06a9\u0646\u062f <code>x_train<\/code>.  \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u06cc\u0645 \u0646\u0645\u0648\u062f\u0627\u0631 \u067e\u0631\u0627\u06a9\u0646\u062f\u06af\u06cc \u0627\u06cc\u0646 \u0646\u0642\u0627\u0637 \u0631\u0627 \u062f\u0631 \u0627\u0645\u062a\u062f\u0627\u062f \u0645\u062d\u0648\u0631 y \u0628\u0633\u0627\u0632\u06cc\u0645 \u06cc\u0627 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u06cc\u0645 \u0647\u06cc\u0633\u062a\u0648\u06af\u0631\u0627\u0645 \u0627\u06cc\u0646 \u0646\u0642\u0627\u0637 \u0631\u0627 \u0627\u06cc\u062c\u0627\u062f \u06a9\u0646\u06cc\u0645.<\/p>\n<pre><code class=\"hljs\">x_train = generate_data()(:, np.newaxis)\nfig, ax = plt.subplots(nrows=<span class=\"hljs-number\">1<\/span>, ncols=<span class=\"hljs-number\">2<\/span>, figsize=(<span class=\"hljs-number\">10<\/span>, <span class=\"hljs-number\">5<\/span>))\nplt.subplot(<span class=\"hljs-number\">121<\/span>)\nplt.scatter(np.arange(<span class=\"hljs-built_in\">len<\/span>(x_train)), x_train, c=<span class=\"hljs-string\">'red'<\/span>)\nplt.xlabel(<span class=\"hljs-string\">'Sample no.'<\/span>)\nplt.ylabel(<span class=\"hljs-string\">'Value'<\/span>)\nplt.title(<span class=\"hljs-string\">'Scatter plot'<\/span>)\nplt.subplot(<span class=\"hljs-number\">122<\/span>)\nplt.hist(x_train, bins=<span class=\"hljs-number\">50<\/span>)\nplt.title(<span class=\"hljs-string\">'Histogram'<\/span>)\nfig.subplots_adjust(wspace=<span class=\"hljs-number\">.3<\/span>)\nplt.show()\n<\/code><\/pre>\n<p><img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2024\/01\/kernel-density-estimation-in-python-using-scikit-learn-1.png\" alt=\"\u0646\u0645\u0648\u062f\u0627\u0631 \u067e\u0631\u0627\u06a9\u0646\u062f\u06af\u06cc \u0648 \u062a\u062e\u0645\u06cc\u0646 \u0647\u06cc\u0633\u062a\u0648\u06af\u0631\u0627\u0645\" title=\"\"><\/p>\n<h2 id=\"usingscikitlearnskerneldensity\"><span class=\"ez-toc-section\" id=\"%d8%a7%d8%b3%d8%aa%d9%81%d8%a7%d8%af%d9%87_%d8%a7%d8%b2_scikit-learns_%d8%aa%d8%b1%d8%a7%da%a9%d9%85_%d9%87%d8%b3%d8%aa%d9%87\"><\/span>\u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 Scikit-Learn&#8217;s <em>\u062a\u0631\u0627\u06a9\u0645 \u0647\u0633\u062a\u0647<\/em><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u0628\u0631\u0627\u06cc \u06cc\u0627\u0641\u062a\u0646 \u0634\u06a9\u0644 \u062a\u0627\u0628\u0639 \u0686\u06af\u0627\u0644\u06cc \u062a\u062e\u0645\u06cc\u0646 \u0632\u062f\u0647 \u0634\u062f\u0647\u060c \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0645\u062c\u0645\u0648\u0639\u0647\u200c\u0627\u06cc \u0627\u0632 \u0646\u0642\u0627\u0637 \u0631\u0627 \u0628\u0627 \u0641\u0627\u0635\u0644\u0647 \u0645\u0633\u0627\u0648\u06cc \u0627\u0632 \u06cc\u06a9\u062f\u06cc\u06af\u0631 \u062a\u0648\u0644\u06cc\u062f \u06a9\u0631\u062f \u0648 \u0686\u06af\u0627\u0644\u06cc \u0647\u0633\u062a\u0647 \u0631\u0627 \u062f\u0631 \u0647\u0631 \u0646\u0642\u0637\u0647 \u062a\u062e\u0645\u06cc\u0646 \u0632\u062f.  \u0627\u0645\u062a\u06cc\u0627\u0632 \u0622\u0632\u0645\u0648\u0646 \u062a\u0648\u0633\u0637:<\/p>\n<pre><code class=\"hljs\">x_test = np.linspace(-<span class=\"hljs-number\">1<\/span>, <span class=\"hljs-number\">7<\/span>, <span class=\"hljs-number\">2000<\/span>)(:, np.newaxis)\n<\/code><\/pre>\n<p>\u062d\u0627\u0644\u0627 \u06cc\u06a9 \u0631\u0627 \u0627\u06cc\u062c\u0627\u062f \u0645\u06cc \u06a9\u0646\u06cc\u0645 <code>KernelDensity<\/code> \u0634\u06cc\u0621 \u0648 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0646\u06cc\u062f <code>fit()<\/code> \u0631\u0648\u0634 \u0628\u0631\u0627\u06cc \u06cc\u0627\u0641\u062a\u0646 \u0627\u0645\u062a\u06cc\u0627\u0632 \u0647\u0631 \u0646\u0645\u0648\u0646\u0647 \u0647\u0645\u0627\u0646\u0637\u0648\u0631 \u06a9\u0647 \u062f\u0631 \u06a9\u062f \u0632\u06cc\u0631 \u0646\u0634\u0627\u0646 \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a.  \u0631\u0627 <code>KernelDensity()<\/code> \u0631\u0648\u0634 \u0627\u0632 \u062f\u0648 \u067e\u0627\u0631\u0627\u0645\u062a\u0631 \u067e\u06cc\u0634 \u0641\u0631\u0636 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc \u06a9\u0646\u062f <code>kernel=gaussian<\/code> \u0648 <code>bandwidth=1<\/code>.<\/p>\n<pre><code class=\"hljs\">model = KernelDensity()\nmodel.fit(x_train)\nlog_dens = model.score_samples(x_test)\n<\/code><\/pre>\n<p>\u0634\u06a9\u0644 \u062a\u0648\u0632\u06cc\u0639 \u0631\u0627 \u0645\u06cc \u062a\u0648\u0627\u0646 \u0628\u0627 \u062a\u0631\u0633\u06cc\u0645 \u0627\u0645\u062a\u06cc\u0627\u0632 \u0686\u06af\u0627\u0644\u06cc \u0628\u0631\u0627\u06cc \u0647\u0631 \u0646\u0642\u0637\u0647\u060c \u0628\u0647 \u0634\u0631\u062d \u0632\u06cc\u0631 \u0645\u0634\u0627\u0647\u062f\u0647 \u06a9\u0631\u062f:<\/p>\n<pre><code class=\"hljs\">plt.fill(x_test, np.exp(log_dens), c=<span class=\"hljs-string\">'cyan'<\/span>)\nplt.show()\n<\/code><\/pre>\n<p><img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2024\/01\/kernel-density-estimation-in-python-using-scikit-learn-2.png\" alt=\"\u0627\u0645\u062a\u06cc\u0627\u0632 \u0686\u06af\u0627\u0644\u06cc\" title=\"\"><\/p>\n<h3 id=\"understandingthebandwidthparameter\"><span class=\"ez-toc-section\" id=\"%d8%a2%d8%b4%d9%86%d8%a7%db%8c%db%8c_%d8%a8%d8%a7_%d9%be%d8%a7%d8%b1%d8%a7%d9%85%d8%aa%d8%b1_%d9%be%d9%87%d9%86%d8%a7%db%8c_%d8%a8%d8%a7%d9%86%d8%af\"><\/span>\u0622\u0634\u0646\u0627\u06cc\u06cc \u0628\u0627 \u067e\u0627\u0631\u0627\u0645\u062a\u0631 \u067e\u0647\u0646\u0627\u06cc \u0628\u0627\u0646\u062f<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u0645\u062b\u0627\u0644 \u0642\u0628\u0644\u06cc \u062a\u062e\u0645\u06cc\u0646 \u0686\u0634\u0645\u06af\u06cc\u0631\u06cc \u0627\u0632 \u062a\u0627\u0628\u0639 \u0686\u06af\u0627\u0644\u06cc \u0646\u06cc\u0633\u062a \u06a9\u0647 \u0639\u0645\u062f\u062a\u0627\u064b \u0628\u0647 \u067e\u0627\u0631\u0627\u0645\u062a\u0631\u0647\u0627\u06cc \u067e\u06cc\u0634 \u0641\u0631\u0636 \u0646\u0633\u0628\u062a \u062f\u0627\u062f\u0647 \u0645\u06cc \u0634\u0648\u062f.  \u0628\u06cc\u0627\u06cc\u06cc\u062f \u0628\u0627 \u0645\u0642\u0627\u062f\u06cc\u0631 \u0645\u062e\u062a\u0644\u0641 \u067e\u0647\u0646\u0627\u06cc \u0628\u0627\u0646\u062f \u0622\u0632\u0645\u0627\u06cc\u0634 \u06a9\u0646\u06cc\u0645 \u062a\u0627 \u0628\u0628\u06cc\u0646\u06cc\u0645 \u0686\u06af\u0648\u0646\u0647 \u0628\u0631 \u062a\u062e\u0645\u06cc\u0646 \u0686\u06af\u0627\u0644\u06cc \u062a\u0623\u062b\u06cc\u0631 \u0645\u06cc \u06af\u0630\u0627\u0631\u062f.<\/p>\n<pre><code class=\"hljs\">bandwidths = (<span class=\"hljs-number\">0.01<\/span>, <span class=\"hljs-number\">0.05<\/span>, <span class=\"hljs-number\">0.1<\/span>, <span class=\"hljs-number\">0.5<\/span>, <span class=\"hljs-number\">1<\/span>, <span class=\"hljs-number\">4<\/span>)\nfig, ax = plt.subplots(nrows=<span class=\"hljs-number\">2<\/span>, ncols=<span class=\"hljs-number\">3<\/span>, figsize=(<span class=\"hljs-number\">10<\/span>, <span class=\"hljs-number\">7<\/span>))\nplt_ind = np.arange(<span class=\"hljs-number\">6<\/span>) + <span class=\"hljs-number\">231<\/span>\n\n<span class=\"hljs-keyword\">for<\/span> b, ind <span class=\"hljs-keyword\">in<\/span> <span class=\"hljs-built_in\">zip<\/span>(bandwidths, plt_ind):\n    kde_model = KernelDensity(kernel=<span class=\"hljs-string\">'gaussian'<\/span>, bandwidth=b)\n    kde_model.fit(x_train)\n    score = kde_model.score_samples(x_test)\n    plt.subplot(ind)\n    plt.fill(x_test, np.exp(score), c=<span class=\"hljs-string\">'cyan'<\/span>)\n    plt.title(<span class=\"hljs-string\">\"h=\"<\/span>+<span class=\"hljs-built_in\">str<\/span>(b))\n\nfig.subplots_adjust(hspace=<span class=\"hljs-number\">0.5<\/span>, wspace=<span class=\"hljs-number\">.3<\/span>)\nplt.show()\n<\/code><\/pre>\n<p><img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2024\/01\/kernel-density-estimation-in-python-using-scikit-learn-3.png\" alt=\"\u062a\u062e\u0645\u06cc\u0646 \u067e\u0647\u0646\u0627\u06cc \u0628\u0627\u0646\u062f \u0645\u062e\u062a\u0644\u0641\" title=\"\"><\/p>\n<p>\u0645\u0627 \u0628\u0647 \u0648\u0636\u0648\u062d \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u0645 \u0628\u0628\u06cc\u0646\u06cc\u0645 \u06a9\u0647 \u0627\u0641\u0632\u0627\u06cc\u0634 \u067e\u0647\u0646\u0627\u06cc \u0628\u0627\u0646\u062f \u0645\u0646\u062c\u0631 \u0628\u0647 \u062a\u062e\u0645\u06cc\u0646 \u0635\u0627\u0641 \u062a\u0631\u06cc \u0645\u06cc \u0634\u0648\u062f.  \u0645\u0642\u0627\u062f\u06cc\u0631 \u067e\u0647\u0646\u0627\u06cc \u0628\u0627\u0646\u062f \u0628\u0633\u06cc\u0627\u0631 \u06a9\u0648\u0686\u06a9 \u0645\u0646\u062c\u0631 \u0628\u0647 \u0645\u0646\u062d\u0646\u06cc\u200c\u0647\u0627\u06cc \u0646\u0648\u06a9 \u062a\u06cc\u0632 \u0648 \u0644\u0631\u0632\u0627\u0646 \u0645\u06cc\u200c\u0634\u0648\u062f\u060c \u062f\u0631 \u062d\u0627\u0644\u06cc \u06a9\u0647 \u0645\u0642\u0627\u062f\u06cc\u0631 \u0628\u0633\u06cc\u0627\u0631 \u0628\u0627\u0644\u0627 \u0645\u0646\u062c\u0631 \u0628\u0647 \u06cc\u06a9 \u0645\u0646\u062d\u0646\u06cc \u0635\u0627\u0641 \u0628\u0633\u06cc\u0627\u0631 \u062a\u0639\u0645\u06cc\u0645\u200c\u06cc\u0627\u0641\u062a\u0647 \u0645\u06cc\u200c\u0634\u0648\u0646\u062f \u06a9\u0647 \u0627\u0632 \u062f\u0633\u062a \u0645\u06cc\u200c\u0631\u0648\u062f. \u0631\u0648\u06cc \u062c\u0632\u0626\u06cc\u0627\u062a \u0645\u0647\u0645  \u0627\u0646\u062a\u062e\u0627\u0628 \u06cc\u06a9 \u0645\u0642\u062f\u0627\u0631 \u0645\u062a\u0639\u0627\u062f\u0644 \u0628\u0631\u0627\u06cc \u0627\u06cc\u0646 \u067e\u0627\u0631\u0627\u0645\u062a\u0631 \u0645\u0647\u0645 \u0627\u0633\u062a.<\/p>\n<h3 id=\"tuningthebandwidthparameter\"><span class=\"ez-toc-section\" id=\"%d8%aa%d9%86%d8%b8%db%8c%d9%85_%d9%be%d8%a7%d8%b1%d8%a7%d9%85%d8%aa%d8%b1_%d9%be%d9%87%d9%86%d8%a7%db%8c_%d8%a8%d8%a7%d9%86%d8%af\"><\/span>\u062a\u0646\u0638\u06cc\u0645 \u067e\u0627\u0631\u0627\u0645\u062a\u0631 \u067e\u0647\u0646\u0627\u06cc \u0628\u0627\u0646\u062f<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u0631\u0627 <code>scikit-learn<\/code> \u06a9\u062a\u0627\u0628\u062e\u0627\u0646\u0647 \u0627\u062c\u0627\u0632\u0647 \u0645\u06cc \u062f\u0647\u062f \u062a\u0627 \u062a\u0646\u0638\u06cc\u0645 <code>bandwidth<\/code> \u067e\u0627\u0631\u0627\u0645\u062a\u0631 \u0627\u0632 \u0637\u0631\u06cc\u0642 \u0627\u0639\u062a\u0628\u0627\u0631\u0633\u0646\u062c\u06cc \u0645\u062a\u0642\u0627\u0628\u0644 \u0648 \u0645\u0642\u062f\u0627\u0631 \u067e\u0627\u0631\u0627\u0645\u062a\u0631\u06cc \u0631\u0627 \u0628\u0631\u0645\u06cc\u200c\u06af\u0631\u062f\u0627\u0646\u062f \u06a9\u0647 \u0627\u062d\u062a\u0645\u0627\u0644 \u062b\u0628\u062a \u062f\u0627\u062f\u0647\u200c\u0647\u0627 \u0631\u0627 \u0628\u0647 \u062d\u062f\u0627\u06a9\u062b\u0631 \u0645\u06cc\u200c\u0631\u0633\u0627\u0646\u062f.  \u062a\u0627\u0628\u0639\u06cc \u06a9\u0647 \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u0645 \u0628\u0631\u0627\u06cc \u0631\u0633\u06cc\u062f\u0646 \u0628\u0647 \u0627\u06cc\u0646 \u0645\u0648\u0631\u062f \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0646\u06cc\u0645 \u0627\u06cc\u0646 \u0627\u0633\u062a <code>GridSearchCV()<\/code>\u060c \u06a9\u0647 \u0628\u0647 \u0645\u0642\u0627\u062f\u06cc\u0631 \u0645\u062a\u0641\u0627\u0648\u062a\u06cc \u0646\u06cc\u0627\u0632 \u062f\u0627\u0631\u062f <code>bandwidth<\/code> \u067e\u0627\u0631\u0627\u0645\u062a\u0631.<\/p>\n<pre><code class=\"hljs\">bandwidth = np.arange(<span class=\"hljs-number\">0.05<\/span>, <span class=\"hljs-number\">2<\/span>, <span class=\"hljs-number\">.05<\/span>)\nkde = KernelDensity(kernel=<span class=\"hljs-string\">'gaussian'<\/span>)\ngrid = GridSearchCV(kde, {<span class=\"hljs-string\">'bandwidth'<\/span>: bandwidth})\ngrid.fit(x_train)\n<\/code><\/pre>\n<p>\u0628\u0647\u062a\u0631\u06cc\u0646 \u0645\u062f\u0644 \u0631\u0627 \u0645\u06cc \u062a\u0648\u0627\u0646 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 <code>best_estimator_<\/code> \u0632\u0645\u06cc\u0646\u0647 \u0627\u0632 <code>GridSearchCV<\/code> \u0647\u062f\u0641 &#8211; \u0634\u06cc.<\/p>\n<p>\u0628\u06cc\u0627\u06cc\u06cc\u062f \u0628\u0647 \u062a\u062e\u0645\u06cc\u0646 \u0628\u0647\u06cc\u0646\u0647 \u062a\u0631\u0627\u06a9\u0645 \u0647\u0633\u062a\u0647 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0647\u0633\u062a\u0647 \u06af\u0627\u0648\u0633\u06cc \u0648 print \u0645\u0642\u062f\u0627\u0631 \u067e\u0647\u0646\u0627\u06cc \u0628\u0627\u0646\u062f \u0646\u06cc\u0632:<\/p>\n<pre><code class=\"hljs\">kde = grid.best_estimator_\nlog_dens = kde.score_samples(x_test)\nplt.fill(x_test, np.exp(log_dens), c=<span class=\"hljs-string\">'green'<\/span>)\nplt.title(<span class=\"hljs-string\">'Optimal estimate with Gaussian kernel'<\/span>)\nplt.show()\n<span class=\"hljs-built_in\">print<\/span>(<span class=\"hljs-string\">\"optimal bandwidth: \"<\/span> + <span class=\"hljs-string\">\"{:.2f}\"<\/span>.<span class=\"hljs-built_in\">format<\/span>(kde.bandwidth))\n<\/code><\/pre>\n<p><img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2024\/01\/kernel-density-estimation-in-python-using-scikit-learn-4.png\" alt=\"\u0628\u0647\u062a\u0631\u06cc\u0646 \u0628\u0631\u0622\u0648\u0631\u062f\u06af\u0631 \u06af\u0627\u0648\u0633\u06cc\" title=\"\"><\/p>\n<pre><code class=\"hljs\">optimal bandwidth: 0.15\n<\/code><\/pre>\n<p>\u0627\u06a9\u0646\u0648\u0646\u060c \u0628\u0647 \u0646\u0638\u0631 \u0645\u06cc \u0631\u0633\u062f \u06a9\u0647 \u0627\u06cc\u0646 \u062a\u062e\u0645\u06cc\u0646 \u0686\u06af\u0627\u0644\u06cc \u062f\u0627\u062f\u0647 \u0647\u0627 \u0631\u0627 \u0628\u0647 \u062e\u0648\u0628\u06cc \u0645\u062f\u0644 \u0645\u06cc \u06a9\u0646\u062f.  \u0646\u06cc\u0645\u0647 \u0627\u0648\u0644 \u0646\u0645\u0648\u062f\u0627\u0631 \u0628\u0627 \u062a\u0648\u0632\u06cc\u0639 \u0644\u06af \u0646\u0631\u0645\u0627\u0644 \u0645\u0637\u0627\u0628\u0642\u062a \u062f\u0627\u0631\u062f \u0648 \u0646\u06cc\u0645\u0647 \u062f\u0648\u0645 \u0646\u0645\u0648\u062f\u0627\u0631 \u062a\u0648\u0632\u06cc\u0639 \u0646\u0631\u0645\u0627\u0644 \u0631\u0627 \u0628\u0647 \u062e\u0648\u0628\u06cc \u0645\u062f\u0644 \u0645\u06cc \u06a9\u0646\u062f.<\/p>\n<h2 id=\"differentkernelsfordensityestimation\"><span class=\"ez-toc-section\" id=\"%d9%87%d8%b3%d8%aa%d9%87_%d9%87%d8%a7%db%8c_%d9%85%d8%ae%d8%aa%d9%84%d9%81_%d8%a8%d8%b1%d8%a7%db%8c_%d8%aa%d8%ae%d9%85%db%8c%d9%86_%da%86%da%af%d8%a7%d9%84%db%8c\"><\/span>\u0647\u0633\u062a\u0647 \u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641 \u0628\u0631\u0627\u06cc \u062a\u062e\u0645\u06cc\u0646 \u0686\u06af\u0627\u0644\u06cc<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><code>scikit-learn<\/code>  \u062a\u062e\u0645\u06cc\u0646 \u0686\u06af\u0627\u0644\u06cc \u0647\u0633\u062a\u0647 \u0631\u0627 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u062a\u0648\u0627\u0628\u0639 \u0645\u062e\u062a\u0644\u0641 \u0647\u0633\u062a\u0647 \u0627\u0645\u06a9\u0627\u0646 \u067e\u0630\u06cc\u0631 \u0645\u06cc \u06a9\u0646\u062f:<\/p>\n<ol>\n<li><code>kernel ='cosine'<\/code>: \\(K(a;h) \\propto \\cos (\\frac{\\pi a}{2h}) \\text { if } |a| <h \\)<\/li>\n<li><code>kernel = 'epanechnikov'<\/code>: \\(K(a;h) \\propto 1 &#8211; \\frac{a^2}{h^2}\\)<\/li>\n<li><code>kernel = 'exponential'<\/code>: \\(K(a;h) \\propto \\exp (-\\frac{|a|}{h})\\)<\/li>\n<li><code>kernel = 'gaussian'<\/code>: \\(K(a;h) \\propto \\exp(-\\frac{a^2}{2h^2})\\)<\/li>\n<li><code>kernel = 'linear'<\/code>: \\(K(a;h) \\propto 1 &#8211; \\frac{|a|}{h} \\text { if } |a| <h \\)<\/li>\n<li><code>kernel = 'tophat'<\/code>: \\(K(a;h) \\propto 1 \\text { if } |a| <h \\)<\/li>\n<\/ol>\n<p>\u06cc\u06a9 \u0631\u0627\u0647 \u0633\u0627\u062f\u0647 \u0628\u0631\u0627\u06cc \u062f\u0631\u06a9 \u0631\u0648\u0634 \u06a9\u0627\u0631 \u0627\u06cc\u0646 \u0647\u0633\u062a\u0647 \u0647\u0627 \u062a\u0631\u0633\u06cc\u0645 \u0622\u0646\u0647\u0627\u0633\u062a.  \u0627\u06cc\u0646 \u0628\u0647 \u0645\u0639\u0646\u06cc \u0633\u0627\u062e\u062a\u0646 \u06cc\u06a9 \u0645\u062f\u0644 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0646\u0645\u0648\u0646\u0647 \u0627\u06cc \u0628\u0627 \u06cc\u06a9 \u0645\u0642\u062f\u0627\u0631\u060c \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u0645\u062b\u0627\u0644\u060c 0 \u0627\u0633\u062a. \u0633\u067e\u0633\u060c \u0686\u06af\u0627\u0644\u06cc \u062a\u0645\u0627\u0645 \u0646\u0642\u0627\u0637 \u0631\u0627 \u062d\u0648\u0644 \u0635\u0641\u0631 \u062a\u062e\u0645\u06cc\u0646 \u0628\u0632\u0646\u06cc\u062f \u0648 \u0686\u06af\u0627\u0644\u06cc \u0631\u0627 \u062f\u0631 \u0627\u0645\u062a\u062f\u0627\u062f \u0645\u062d\u0648\u0631 y \u0631\u0633\u0645 \u06a9\u0646\u06cc\u062f.  \u06a9\u062f \u0632\u06cc\u0631 \u06a9\u0644 \u0631\u0627 \u0646\u0634\u0627\u0646 \u0645\u06cc \u062f\u0647\u062f process:<\/p>\n<pre><code class=\"hljs\">kernels = (<span class=\"hljs-string\">'cosine'<\/span>, <span class=\"hljs-string\">'epanechnikov'<\/span>, <span class=\"hljs-string\">'exponential'<\/span>, <span class=\"hljs-string\">'gaussian'<\/span>, <span class=\"hljs-string\">'linear'<\/span>, <span class=\"hljs-string\">'tophat'<\/span>)\nfig, ax = plt.subplots(nrows=<span class=\"hljs-number\">2<\/span>, ncols=<span class=\"hljs-number\">3<\/span>, figsize=(<span class=\"hljs-number\">10<\/span>, <span class=\"hljs-number\">7<\/span>))\nplt_ind = np.arange(<span class=\"hljs-number\">6<\/span>) + <span class=\"hljs-number\">231<\/span>\n\n<span class=\"hljs-keyword\">for<\/span> k, ind <span class=\"hljs-keyword\">in<\/span> <span class=\"hljs-built_in\">zip<\/span>(kernels, plt_ind):\n    kde_model = KernelDensity(kernel=k)\n    kde_model.fit(((<span class=\"hljs-number\">0<\/span>)))\n    score = kde_model.score_samples(np.arange(-<span class=\"hljs-number\">2<\/span>, <span class=\"hljs-number\">2<\/span>, <span class=\"hljs-number\">0.1<\/span>)(:, <span class=\"hljs-literal\">None<\/span>))\n    plt.subplot(ind)\n    plt.fill(np.arange(-<span class=\"hljs-number\">2<\/span>, <span class=\"hljs-number\">2<\/span>, <span class=\"hljs-number\">0.1<\/span>)(:, <span class=\"hljs-literal\">None<\/span>), np.exp(score), c=<span class=\"hljs-string\">'blue'<\/span>)\n    plt.title(k)\n\nfig.subplots_adjust(hspace=<span class=\"hljs-number\">0.5<\/span>, wspace=<span class=\"hljs-number\">.3<\/span>)\nplt.show()\n<\/code><\/pre>\n<p><img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2024\/01\/kernel-density-estimation-in-python-using-scikit-learn-5.png\" alt=\"\u0647\u0633\u062a\u0647 \u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641\" title=\"\"><\/p>\n<h3 id=\"experimentingwithdifferentkernels\"><span class=\"ez-toc-section\" id=\"%d8%a2%d8%b2%d9%85%d8%a7%db%8c%d8%b4_%d8%a8%d8%a7_%d9%87%d8%b3%d8%aa%d9%87_%d9%87%d8%a7%db%8c_%d9%85%d8%ae%d8%aa%d9%84%d9%81\"><\/span>\u0622\u0632\u0645\u0627\u06cc\u0634 \u0628\u0627 \u0647\u0633\u062a\u0647 \u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u0628\u06cc\u0627\u06cc\u06cc\u062f \u0628\u0627 \u0647\u0633\u062a\u0647 \u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641 \u0622\u0632\u0645\u0627\u06cc\u0634 \u06a9\u0646\u06cc\u0645 \u0648 \u0628\u0628\u06cc\u0646\u06cc\u0645 \u0686\u06af\u0648\u0646\u0647 \u0622\u0646\u0647\u0627 \u062a\u0627\u0628\u0639 \u0686\u06af\u0627\u0644\u06cc \u0627\u062d\u062a\u0645\u0627\u0644 \u0631\u0627 \u0628\u0631\u0627\u06cc \u062f\u0627\u062f\u0647 \u0647\u0627\u06cc \u0645\u0635\u0646\u0648\u0639\u06cc \u0645\u0627 \u062a\u062e\u0645\u06cc\u0646 \u0645\u06cc \u0632\u0646\u0646\u062f.<\/p>\n<p>\u0645\u0627 \u0645\u06cc\u062a\u0648\u0627\u0646\u06cc\u0645 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0646\u06cc\u0645 <code>GridSearchCV()<\/code>\u060c \u0645\u0627\u0646\u0646\u062f \u0642\u0628\u0644\u060c \u0628\u0631\u0627\u06cc \u06cc\u0627\u0641\u062a\u0646 \u0628\u0647\u06cc\u0646\u0647 <code>bandwidth<\/code> \u0627\u0631\u0632\u0634.  \u0628\u0627 \u0627\u06cc\u0646 \u062d\u0627\u0644\u060c \u0628\u0631\u0627\u06cc <code>cosine<\/code>\u060c <code>linear<\/code>\u060c \u0648 <code>tophat<\/code> \u0647\u0633\u062a\u0647 \u0647\u0627 <code>GridSearchCV()<\/code> \u0645\u0645\u06a9\u0646 \u0627\u0633\u062a \u0628\u0647 \u062f\u0644\u06cc\u0644 \u0628\u0631\u062e\u06cc \u0627\u0645\u062a\u06cc\u0627\u0632\u0627\u062a \u0645\u0646\u062c\u0631 \u0628\u0647 \u0627\u062e\u0637\u0627\u0631 \u0632\u0645\u0627\u0646 \u0627\u062c\u0631\u0627 \u0634\u0648\u062f <code>-inf<\/code> \u0627\u0631\u0632\u0634 \u0647\u0627\u06cc.  \u06cc\u06a9\u06cc \u0627\u0632 \u0631\u0627\u0647 \u0647\u0627\u06cc \u0645\u0645\u06a9\u0646 \u0628\u0631\u0627\u06cc \u0631\u0641\u0639 \u0627\u06cc\u0646 \u0645\u0634\u06a9\u0644\u060c \u0646\u0648\u0634\u062a\u0646 \u06cc\u06a9 \u062a\u0627\u0628\u0639 \u0627\u0645\u062a\u06cc\u0627\u0632\u062f\u0647\u06cc \u0633\u0641\u0627\u0631\u0634\u06cc \u0628\u0631\u0627\u06cc \u0622\u0646 \u0627\u0633\u062a <code>GridSearchCV()<\/code>.<\/p>\n<p>\u062f\u0631 \u06a9\u062f \u0632\u06cc\u0631\u060c <code>-inf<\/code> \u0646\u0645\u0631\u0627\u062a \u0627\u0645\u062a\u06cc\u0627\u0632\u0627\u062a \u0622\u0632\u0645\u0648\u0646 \u062f\u0631 \u0628\u062e\u0634 \u062d\u0630\u0641 \u0634\u062f\u0647 \u0627\u0633\u062a <code>my_scores()<\/code> \u062a\u0627\u0628\u0639 \u0627\u0645\u062a\u06cc\u0627\u0632 \u062f\u0647\u06cc \u0633\u0641\u0627\u0631\u0634\u06cc \u0648 \u06cc\u06a9 \u0645\u0642\u062f\u0627\u0631 \u0645\u06cc\u0627\u0646\u06af\u06cc\u0646 \u0628\u0631\u06af\u0631\u062f\u0627\u0646\u062f\u0647 \u0645\u06cc \u0634\u0648\u062f.  \u0627\u06cc\u0646 \u0644\u0632\u0648\u0645\u0627 \u0628\u0647\u062a\u0631\u06cc\u0646 \u0637\u0631\u062d \u0628\u0631\u0627\u06cc \u0631\u0633\u06cc\u062f\u06af\u06cc \u0646\u06cc\u0633\u062a <code>-inf<\/code> \u0628\u0633\u062a\u0647 \u0628\u0647 \u062f\u0627\u062f\u0647 \u0647\u0627\u06cc \u0645\u0648\u0631\u062f \u0646\u0638\u0631\u060c \u0645\u06cc \u062a\u0648\u0627\u0646 \u0645\u0642\u0627\u062f\u06cc\u0631 \u0627\u0645\u062a\u06cc\u0627\u0632 \u0648 \u0628\u0631\u062e\u06cc \u0627\u0633\u062a\u0631\u0627\u062a\u0698\u06cc \u0647\u0627\u06cc \u062f\u06cc\u06af\u0631 \u0631\u0627 \u0627\u062a\u062e\u0627\u0630 \u06a9\u0631\u062f.<\/p>\n<pre><code class=\"hljs\"><span class=\"hljs-function\"><span class=\"hljs-keyword\">def<\/span> <span class=\"hljs-title\">my_scores<\/span>(<span class=\"hljs-params\">estimator, X<\/span>):<\/span>\n    scores = estimator.score_samples(X)\n    \n    scores = scores(scores != <span class=\"hljs-built_in\">float<\/span>(<span class=\"hljs-string\">'-inf'<\/span>))\n    \n    <span class=\"hljs-keyword\">return<\/span> np.mean(scores)\n\nkernels = (<span class=\"hljs-string\">'cosine'<\/span>, <span class=\"hljs-string\">'epanechnikov'<\/span>, <span class=\"hljs-string\">'exponential'<\/span>, <span class=\"hljs-string\">'gaussian'<\/span>, <span class=\"hljs-string\">'linear'<\/span>, <span class=\"hljs-string\">'tophat'<\/span>)\nfig, ax = plt.subplots(nrows=<span class=\"hljs-number\">2<\/span>, ncols=<span class=\"hljs-number\">3<\/span>, figsize=(<span class=\"hljs-number\">10<\/span>, <span class=\"hljs-number\">7<\/span>))\nplt_ind = np.arange(<span class=\"hljs-number\">6<\/span>) + <span class=\"hljs-number\">231<\/span>\nh_vals = np.arange(<span class=\"hljs-number\">0.05<\/span>, <span class=\"hljs-number\">1<\/span>, <span class=\"hljs-number\">.1<\/span>)\n\n<span class=\"hljs-keyword\">for<\/span> k, ind <span class=\"hljs-keyword\">in<\/span> <span class=\"hljs-built_in\">zip<\/span>(kernels, plt_ind):\n    grid = GridSearchCV(KernelDensity(kernel=k),\n                        {<span class=\"hljs-string\">'bandwidth'<\/span>: h_vals},\n                        scoring=my_scores)\n    grid.fit(x_train)\n    kde = grid.best_estimator_\n    log_dens = kde.score_samples(x_test)\n    plt.subplot(ind)\n    plt.fill(x_test, np.exp(log_dens), c=<span class=\"hljs-string\">'cyan'<\/span>)\n    plt.title(k + <span class=\"hljs-string\">\" h=\"<\/span> + <span class=\"hljs-string\">\"{:.2f}\"<\/span>.<span class=\"hljs-built_in\">format<\/span>(kde.bandwidth))\n\nfig.subplots_adjust(hspace=<span class=\"hljs-number\">.5<\/span>, wspace=<span class=\"hljs-number\">.3<\/span>)\nplt.show()\n<\/code><\/pre>\n<p><img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2024\/01\/kernel-density-estimation-in-python-using-scikit-learn-6.png\" alt=\"\u0627\u0645\u062a\u06cc\u0627\u0632\u062f\u0647\u06cc \u0633\u0641\u0627\u0631\u0634\u06cc \u0647\u0633\u062a\u0647 \u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641\" title=\"\"><\/p>\n<h2 id=\"thefinaloptimizedmodel\"><span class=\"ez-toc-section\" id=\"%d9%85%d8%af%d9%84_%d9%86%d9%87%d8%a7%db%8c%db%8c_%d8%a8%d9%87%db%8c%d9%86%d9%87_%d8%b4%d8%af%d9%87\"><\/span>\u0645\u062f\u0644 \u0646\u0647\u0627\u06cc\u06cc \u0628\u0647\u06cc\u0646\u0647 \u0634\u062f\u0647<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u0645\u062b\u0627\u0644 \u0628\u0627\u0644\u0627 \u0646\u0634\u0627\u0646 \u0645\u06cc \u062f\u0647\u062f \u06a9\u0647 \u0686\u06af\u0648\u0646\u0647 \u06a9\u0631\u0646\u0644 \u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641 \u0686\u06af\u0627\u0644\u06cc \u0631\u0627 \u0628\u0647 \u0631\u0648\u0634 \u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641 \u062a\u062e\u0645\u06cc\u0646 \u0645\u06cc \u0632\u0646\u0646\u062f.  \u06cc\u06a9 \u0645\u0631\u062d\u0644\u0647 \u0646\u0647\u0627\u06cc\u06cc \u0631\u0627\u0647 \u0627\u0646\u062f\u0627\u0632\u06cc \u0627\u0633\u062a <code>GridSearchCV()<\/code> \u0628\u0647 \u0637\u0648\u0631\u06cc \u06a9\u0647 \u0646\u0647 \u062a\u0646\u0647\u0627 \u067e\u0647\u0646\u0627\u06cc \u0628\u0627\u0646\u062f \u0628\u0647\u06cc\u0646\u0647 \u0631\u0627 \u06a9\u0634\u0641 \u0645\u06cc \u06a9\u0646\u062f\u060c \u0628\u0644\u06a9\u0647 \u0647\u0633\u062a\u0647 \u0628\u0647\u06cc\u0646\u0647 \u0631\u0627 \u0628\u0631\u0627\u06cc \u062f\u0627\u062f\u0647 \u0647\u0627\u06cc \u0645\u062b\u0627\u0644 \u0645\u0627 \u0646\u06cc\u0632 \u06a9\u0634\u0641 \u0645\u06cc \u06a9\u0646\u062f.  \u062f\u0631 \u0627\u06cc\u0646\u062c\u0627 \u06a9\u062f \u0646\u0647\u0627\u06cc\u06cc \u0627\u0633\u062a \u06a9\u0647 \u062a\u062e\u0645\u06cc\u0646 \u0686\u06af\u0627\u0644\u06cc \u0646\u0647\u0627\u06cc\u06cc \u0648 \u067e\u0627\u0631\u0627\u0645\u062a\u0631\u0647\u0627\u06cc \u062a\u0646\u0638\u06cc\u0645 \u0634\u062f\u0647 \u0622\u0646 \u0631\u0627 \u0646\u06cc\u0632 \u062f\u0631 \u0639\u0646\u0648\u0627\u0646 \u0646\u0645\u0648\u062f\u0627\u0631 \u062a\u0631\u0633\u06cc\u0645 \u0645\u06cc \u06a9\u0646\u062f:<\/p>\n<pre><code class=\"hljs\">grid = GridSearchCV(KernelDensity(),\n                    {<span class=\"hljs-string\">'bandwidth'<\/span>: h_vals, <span class=\"hljs-string\">'kernel'<\/span>: kernels},\n                    scoring=my_scores)\ngrid.fit(x_train)\nbest_kde = grid.best_estimator_\nlog_dens = best_kde.score_samples(x_test)\nplt.fill(x_test, np.exp(log_dens), c=<span class=\"hljs-string\">'green'<\/span>)\nplt.title(<span class=\"hljs-string\">\"Best Kernel: \"<\/span> + best_kde.kernel+<span class=\"hljs-string\">\" h=\"<\/span>+<span class=\"hljs-string\">\"{:.2f}\"<\/span>.<span class=\"hljs-built_in\">format<\/span>(best_kde.bandwidth))\nplt.show()\n<\/code><\/pre>\n<p><img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2024\/01\/kernel-density-estimation-in-python-using-scikit-learn-7.png\" alt=\"\u0645\u062f\u0644 \u0628\u0647\u06cc\u0646\u0647 \u062a\u0631\u0627\u06a9\u0645 \u0647\u0633\u062a\u0647\" title=\"\"><\/p>\n<h2 id=\"conclusion\"><span class=\"ez-toc-section\" id=\"%d9%86%d8%aa%db%8c%d8%ac%d9%87\"><\/span>\u0646\u062a\u06cc\u062c\u0647<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u062a\u062e\u0645\u06cc\u0646 \u0686\u06af\u0627\u0644\u06cc \u0647\u0633\u062a\u0647 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 <code>scikit-learn<\/code>\u06a9\u062a\u0627\u0628\u062e\u0627\u0646\u0647 <code>sklearn.neighbors<\/code> \u062f\u0631 \u0627\u06cc\u0646 \u0645\u0642\u0627\u0644\u0647 \u0645\u0648\u0631\u062f \u0628\u062d\u062b \u0642\u0631\u0627\u0631 \u06af\u0631\u0641\u062a\u0647 \u0627\u0633\u062a.  \u0645\u062b\u0627\u0644\u200c\u0647\u0627 \u0628\u0631\u0627\u06cc \u062f\u0627\u062f\u0647\u200c\u0647\u0627\u06cc \u062a\u06a9 \u0645\u062a\u063a\u06cc\u0631\u0647 \u0627\u0631\u0627\u0626\u0647 \u0634\u062f\u0647\u200c\u0627\u0646\u062f\u060c \u0627\u0645\u0627 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0622\u0646 \u0631\u0627 \u0628\u0631\u0627\u06cc \u062f\u0627\u062f\u0647\u200c\u0647\u0627\u06cc\u06cc \u0628\u0627 \u0627\u0628\u0639\u0627\u062f \u0686\u0646\u062f\u06af\u0627\u0646\u0647 \u0646\u06cc\u0632 \u0627\u0639\u0645\u0627\u0644 \u06a9\u0631\u062f.<\/p>\n<p>\u062f\u0631 \u062d\u0627\u0644\u06cc \u06a9\u0647 \u06cc\u06a9 \u0631\u0648\u0634 \u0634\u0647\u0648\u062f\u06cc \u0648 \u0633\u0627\u062f\u0647 \u0628\u0631\u0627\u06cc \u062a\u062e\u0645\u06cc\u0646 \u0686\u06af\u0627\u0644\u06cc \u0628\u0631\u0627\u06cc \u062a\u0648\u0632\u06cc\u0639 \u0647\u0627\u06cc \u0645\u0646\u0628\u0639 \u0646\u0627\u0634\u0646\u0627\u062e\u062a\u0647 \u0627\u0633\u062a\u060c \u06cc\u06a9 \u062f\u0627\u0646\u0634\u0645\u0646\u062f \u062f\u0627\u062f\u0647 \u0628\u0627\u06cc\u062f \u0628\u0627 \u0627\u062d\u062a\u06cc\u0627\u0637 \u0627\u0632 \u0622\u0646 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0646\u062f \u0632\u06cc\u0631\u0627 \u0646\u0641\u0631\u06cc\u0646 \u0627\u0628\u0639\u0627\u062f \u0645\u06cc \u062a\u0648\u0627\u0646\u062f \u0628\u0647 \u0637\u0648\u0631 \u0642\u0627\u0628\u0644 \u062a\u0648\u062c\u0647\u06cc \u0633\u0631\u0639\u062a \u0622\u0646 \u0631\u0627 \u06a9\u0627\u0647\u0634 \u062f\u0647\u062f.<\/p>\n<\/div>\n<p><script>\n                        !function(f,b,e,v,n,t,s)\n                        {if(f.fbq)return;n=f.fbq=function(){n.callMethod?\n                        n.callMethod.apply(n,arguments):n.queue.push(arguments)};\n                        if(!f._fbq)f._fbq=n;n.push=n;n.loaded=!0;n.version='2.0';\n                        n.queue=();t=b.createElement(e);t.async=!0;\n                        t.src=v;s=b.getElementsByTagName(e)(0);\n                        s.parentNode.insertBefore(t,s)}(window, 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style=\"padding-left: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 30px; height: 30px;\"><\/div>\n        <\/div>\n    <\/div>\n<\/div>\n                \n\n<div class=\"kksr-legend\" style=\"font-size: 24px;\">\n            <span class=\"kksr-muted\">\u0627\u0645\u062a\u06cc\u0627\u0632 \u0634\u0645\u0627 \u0628\u0647 \u0627\u06cc\u0646 \u0645\u0637\u0644\u0628<\/span>\n    <\/div>\n    <\/div>\n","protected":false},"excerpt":{"rendered":"<p><span class=\"span-reading-time rt-reading-time\" style=\"display: block;\"><span class=\"rt-label rt-prefix\">\u0632\u0645\u0627\u0646 \u0644\u0627\u0632\u0645 \u0628\u0631\u0627\u06cc \u0645\u0637\u0627\u0644\u0639\u0647: <\/span> <span class=\"rt-time\"> 3<\/span> <span class=\"rt-label rt-postfix\">\u062f\u0642\u06cc\u0642\u0647<\/span><\/span>\u0645\u0639\u0631\u0641\u06cc \u0627\u06cc\u0646 \u0645\u0642\u0627\u0644\u0647 \u0645\u0642\u062f\u0645\u0647\u200c\u0627\u06cc \u0628\u0631 \u062a\u062e\u0645\u06cc\u0646 \u0686\u06af\u0627\u0644\u06cc \u0647\u0633\u062a\u0647 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u06a9\u062a\u0627\u0628\u062e\u0627\u0646\u0647 \u06cc\u0627\u062f\u06af\u06cc\u0631\u06cc \u0645\u0627\u0634\u06cc\u0646 \u067e\u0627\u06cc\u062a\u0648\u0646 \u0627\u0633\u062a. scikit-learn. \u062a\u062e\u0645\u06cc\u0646 \u0686\u06af\u0627\u0644\u06cc \u0647\u0633\u062a\u0647 (KDE) \u06cc\u06a9 \u0631\u0648\u0634 \u0646\u0627\u067e\u0627\u0631\u0627\u0645\u062a\u0631\u06cc\u06a9 \u0628\u0631\u0627\u06cc \u062a\u062e\u0645\u06cc\u0646 \u062a\u0627\u0628\u0639 \u0686\u06af\u0627\u0644\u06cc \u0627\u062d\u062a\u0645\u0627\u0644 \u06cc\u06a9 \u0645\u062a\u063a\u06cc\u0631 \u062a\u0635\u0627\u062f\u0641\u06cc \u0645\u0639\u06cc\u0646 \u0627\u0633\u062a. \u0627\u0632 \u0622\u0646 \u0628\u0627 \u0646\u0627\u0645 \u0633\u0646\u062a\u06cc \u0622\u0646 \u0646\u06cc\u0632 \u06cc\u0627\u062f \u0645\u06cc \u0634\u0648\u062f \u067e\u0646\u062c\u0631\u0647 Parzen-Rosenblatt 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[&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":15738,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1743,620],"tags":[],"class_list":["post-15737","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-python","category-programming"],"acf":[],"_links":{"self":[{"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/posts\/15737","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/comments?post=15737"}],"version-history":[{"count":0,"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/posts\/15737\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/media\/15738"}],"wp:attachment":[{"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/media?parent=15737"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/categories?post=15737"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/tags?post=15737"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}