{"id":2711,"date":"2019-05-13T15:12:07","date_gmt":"2019-05-13T19:12:07","guid":{"rendered":"https:\/\/ibkrcampus.com\/?p=2711"},"modified":"2023-03-23T14:34:20","modified_gmt":"2023-03-23T18:34:20","slug":"gini-index-for-decision-trees-part-ii","status":"publish","type":"post","link":"https:\/\/www.interactivebrokers.com\/campus\/ibkr-quant-news\/gini-index-for-decision-trees-part-ii\/","title":{"rendered":"Gini Index For Decision Trees &#8211; Part II"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\"><strong>Let\u2019s understand how the Gini Index works by looking at this simple example.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"394\" height=\"235\" data-src=\"\/campus\/wp-content\/uploads\/sites\/2\/2023\/03\/gini-index-table.png\" alt=\"\" class=\"wp-image-187262 lazyload\" data-srcset=\"https:\/\/ibkrcampus.com\/campus\/wp-content\/uploads\/sites\/2\/2023\/03\/gini-index-table.png 394w, https:\/\/ibkrcampus.com\/campus\/wp-content\/uploads\/sites\/2\/2023\/03\/gini-index-table-300x179.png 300w\" data-sizes=\"(max-width: 394px) 100vw, 394px\" src=\"data:image\/svg+xml;base64,PHN2ZyB3aWR0aD0iMSIgaGVpZ2h0PSIxIiB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciPjwvc3ZnPg==\" style=\"--smush-placeholder-width: 394px; aspect-ratio: 394\/235;\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Let\u2019s start by calculating the Gini Index for \u2018Past Trend\u2019.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">P(Past Trend=Positive): 6\/10<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">P(Past Trend=Negative): 4\/10<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">If (Past Trend = Positive &amp; Return = Up), probability = 4\/6<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">If (Past Trend = Positive &amp; Return = Down), probability = 2\/6<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Gini index = 1 \u2013 ((4\/6)^2 + (2\/6)^2) = 0.45<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">If (Past Trend = Negative &amp; Return = Up), probability = 0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">If (Past Trend = Negative &amp; Return = Down), probability = 4\/4<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Gini index = 1 \u2013 ((0)^2 + (4\/4)^2) = 0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Weighted sum of the Gini Indices can be calculated as follows:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Gini Index for Past Trend = (6\/10)*0.45 + (4\/10)*0 = 0.27<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Calculation of Gini Index for Open Interest<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">P(Open Interest=High): 4\/10<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">P(Open Interest=Low): 6\/10<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">If (Open Interest = High &amp; Return = Up), probability = 2\/4<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">If (Open Interest = High &amp; Return = Down), probability = 2\/4<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Gini index = 1 \u2013 ((2\/4)^2 + (2\/4)^2) = 0.5<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">If (Open Interest = Low &amp; Return = Up), probability = 2\/6<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">If (Open Interest = Low &amp; Return = Down), probability = 4\/6<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Gini index = 1 \u2013 ((2\/6)^2 + (4\/6)^2) = 0.45<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Weighted sum of the Gini Indices can be calculated as follows:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Gini Index for Open Interest = (4\/10)*0.5 + (6\/10)*0.45 = 0.47<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Calculation of Gini Index for Trading Volume<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">P(Trading Volume=High): 7\/10<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">P(Trading Volume=Low): 3\/10<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">If (Trading Volume = High &amp; Return = Up), probability = 4\/7<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">If (Trading Volume = High &amp; Return = Down), probability = 3\/7<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Gini index = 1 \u2013 ((4\/7)^2 + (3\/7)^2) = 0.49<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">If (Trading Volume = Low &amp; Return = Up), probability = 0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">If (Trading Volume = Low &amp; Return = Down), probability = 3\/3<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Gini index = 1 \u2013 ((0)^2 + (1)^2) = 0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Weighted sum of the Gini Indices can be calculated as follows:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Gini Index for Trading Volume = (7\/10)*0.49 + (3\/10)*0 = 0.34<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"390\" height=\"94\" data-src=\"\/campus\/wp-content\/uploads\/sites\/2\/2023\/03\/gini-index-table-2.png\" alt=\"\" class=\"wp-image-187263 lazyload\" data-srcset=\"https:\/\/ibkrcampus.com\/campus\/wp-content\/uploads\/sites\/2\/2023\/03\/gini-index-table-2.png 390w, https:\/\/ibkrcampus.com\/campus\/wp-content\/uploads\/sites\/2\/2023\/03\/gini-index-table-2-300x72.png 300w\" data-sizes=\"(max-width: 390px) 100vw, 390px\" src=\"data:image\/svg+xml;base64,PHN2ZyB3aWR0aD0iMSIgaGVpZ2h0PSIxIiB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciPjwvc3ZnPg==\" style=\"--smush-placeholder-width: 390px; aspect-ratio: 390\/94;\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">From the above table, we observe that \u2018Past Trend\u2019 has the lowest Gini Index and hence it will be chosen as the root node for the decision tree.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">We will repeat the same procedure to determine the sub-nodes or branches of the decision tree.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">We will calculate the Gini Index for the \u2018Positive\u2019 branch of Past Trend as follows:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"386\" height=\"154\" data-src=\"\/campus\/wp-content\/uploads\/sites\/2\/2023\/03\/gini-index-table-3.png\" alt=\"\" class=\"wp-image-187264 lazyload\" data-srcset=\"https:\/\/ibkrcampus.com\/campus\/wp-content\/uploads\/sites\/2\/2023\/03\/gini-index-table-3.png 386w, https:\/\/ibkrcampus.com\/campus\/wp-content\/uploads\/sites\/2\/2023\/03\/gini-index-table-3-300x120.png 300w\" data-sizes=\"(max-width: 386px) 100vw, 386px\" src=\"data:image\/svg+xml;base64,PHN2ZyB3aWR0aD0iMSIgaGVpZ2h0PSIxIiB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciPjwvc3ZnPg==\" style=\"--smush-placeholder-width: 386px; aspect-ratio: 386\/154;\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><em>Stay tuned for the next installment in this series, in which Shagufta will continue discussing Calculations of Gini Index for Trading Volume!<\/em><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Let\u2019s understand how the Gini Index works by looking at this simple example.<\/p>\n","protected":false},"author":93,"featured_media":3564,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":"","jetpack_post_was_ever_published":false},"categories":[339,343,349,338,350,341],"tags":[595],"contributors-categories":[13654],"class_list":["post-2711","post","type-post","status-publish","format-standard","has-post-thumbnail","category-data-science","category-programing-languages","category-python-development","category-ibkr-quant-news","category-quant-asia-pacific","category-quant-development","tag-python","contributors-categories-quantinsti"],"pp_statuses_selecting_workflow":false,"pp_workflow_action":"current","pp_status_selection":"publish","acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v26.9 (Yoast SEO v28.3) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>Gini Index For Decision Trees &#8211; Part II | IBKR 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