{"id":51426,"date":"2020-07-07T11:22:22","date_gmt":"2020-07-07T15:22:22","guid":{"rendered":"https:\/\/ibkrcampus.com\/?p=51426"},"modified":"2022-11-21T09:45:49","modified_gmt":"2022-11-21T14:45:49","slug":"machine-learning-classification-methods-and-factor-investing","status":"publish","type":"post","link":"https:\/\/www.interactivebrokers.com\/campus\/ibkr-quant-news\/machine-learning-classification-methods-and-factor-investing\/","title":{"rendered":"Machine Learning Classification Methods and Factor Investing"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\"><em>The post\u202f<\/em><a href=\"https:\/\/alphaarchitect.com\/2018\/12\/21\/machine-learning-classification-methods-and-factor-investing\/\" target=\"_blank\" rel=\"noreferrer noopener\"><em>Machine Learning Classification Methods and Factor Investing<\/em><\/a>&nbsp;&nbsp;<em>appeared first on <a href=\"https:\/\/alphaarchitect.com\/blog\">Alpha Architect Blog<\/a>\u202f<\/em>. <em>Below is an excerpt.<\/em><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In the\u202f<a href=\"https:\/\/alphaarchitect.com\/2018\/06\/05\/machine-learning-financial-market-prediction-time-series-prediction-sklearn-keras\/\" target=\"_blank\" rel=\"noreferrer noopener\">last post<\/a>\u202fin our machine learning series, we showed how nonlinear regression&nbsp;algos\u202fmight improve regression forecasting relative to plain vanilla linear regression (i.e., when underlying reality is nonlinear with complex interactions).&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In this piece, we\u2019ll \u202f<a href=\"https:\/\/alphaarchitect.com\/2018\/12\/21\/machine-learning-classification-methods-and-factor-investing\/#part1\" target=\"_blank\" rel=\"noreferrer noopener\">first review<\/a>\u202f machine learning for classification, a problem which may be less familiar to investors, but fundamental to machine learning professionals. \u202f<a href=\"https:\/\/alphaarchitect.com\/2018\/12\/21\/machine-learning-classification-methods-and-factor-investing\/#part2\" target=\"_blank\" rel=\"noreferrer noopener\">Next<\/a>, we\u2019ll apply classification to the classic value\/momentum factors (spoiler: the results are pretty good).&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>An Introduction to Classification Algorithms<\/strong>&nbsp;<br><em>What Is Classification?<\/em>&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In this post:&nbsp;<\/p>\n\n\n\n<ol class=\"wp-block-list\"><li>We\u2019ll break down a classification example \u201c<a href=\"https:\/\/www.businessinsider.com\/military-phrases-2013-12\" target=\"_blank\" rel=\"noreferrer noopener\">Barney-style\u201d<\/a>\u202fwith&nbsp;<strong>Python<\/strong>&nbsp;code.&nbsp;<\/li><\/ol>\n\n\n\n<ol class=\"wp-block-list\" start=\"2\"><li>We\u2019ll present a high-level overview of classification algorithms.&nbsp;<\/li><\/ol>\n\n\n\n<ol class=\"wp-block-list\" start=\"3\"><li>Finally, in part 2, we\u2019ll apply classification to a portfolio to generate an investment strategy by classifying expected returns by quintile.&nbsp;<\/li><\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">From classification, it\u2019s a short step to deep learning problems like\u202f<a href=\"https:\/\/machinelearningmastery.com\/handwritten-digit-recognition-using-convolutional-neural-networks-python-keras\/\" target=\"_blank\" rel=\"noreferrer noopener\">handwriting recognition<\/a>, or\u202f<a href=\"https:\/\/cs231n.stanford.edu\/\" target=\"_blank\" rel=\"noreferrer noopener\">image labeling<\/a>. Classification is a fundamental building block that enables machine learning to perform incredible feats.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Classification essentials<\/strong>&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">We start (<a href=\"https:\/\/github.com\/druce\/Machine-learning-for-financial-market-prediction\/blob\/master\/Classification%20Mad%20Science.ipynb\" target=\"_blank\" rel=\"noreferrer noopener\">code is here<\/a>) by generating random data with two predictors (the x-axis and y-axis) and a variable with two labels (red or blue). The numbers are generated from a truncated normal with [0,100] bounds (<a href=\"https:\/\/docs.scipy.org\/doc\/scipy\/reference\/generated\/scipy.stats.truncnorm.html\" target=\"_blank\" rel=\"noreferrer noopener\">see here<\/a>\u202ffor details).&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" data-src=\"\/campus\/wp-content\/uploads\/sites\/2\/2020\/07\/image-16.png\" alt=\"Test Data\" class=\"wp-image-51427 lazyload\" src=\"data:image\/svg+xml;base64,PHN2ZyB3aWR0aD0iMSIgaGVpZ2h0PSIxIiB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciPjwvc3ZnPg==\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">2000 red dots are centered around x = 25, y = 25 with a standard deviation of 50, and assigned label = 0.&nbsp;<br>2000 blue dots are centered around x = 80, y = 80 with a standard deviation of 20, and assigned label = 1.&nbsp;<br>We would like to find a function that takes the coordinates x and y, and returns an accurate prediction of 0 (blue) or 1 (red).&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Logistic regression is a simple, popular classification algorithm.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Here are the basics of how it works:&nbsp;<\/p>\n\n\n\n<ol class=\"wp-block-list\"><li>Apply a linear\u202f<em>decision function<\/em>\u202fof x and y that outputs a numeric variable:\u202f<img decoding=\"async\" width=\"165\" height=\"18\" data-src=\"\/campus\/wp-content\/uploads\/sites\/2\/2020\/07\/alpha-architect-1.png\" alt=\"\" class=\"wp-image-51451 lazyload\" src=\"data:image\/svg+xml;base64,PHN2ZyB3aWR0aD0iMSIgaGVpZ2h0PSIxIiB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciPjwvc3ZnPg==\" style=\"--smush-placeholder-width: 165px; aspect-ratio: 165\/18;\"><\/li><\/ol>\n\n\n\n<ol class=\"wp-block-list\" start=\"2\"><li>Apply a\u202f<em>sigmoid<\/em>\u202f\u2018squashing\u2019 function to Z that maps large positive numbers to a probability estimate close to 1, and large negative numbers to a probability close to 0.&nbsp;<\/li><\/ol>\n\n\n\n<ol class=\"wp-block-list\" start=\"3\"><li>Apply a\u202f<em>loss function<\/em>\u202fthat measures prediction error. The loss should be close to 0 when the prediction is close to 1 for the blue observations (label=1);&nbsp;and also&nbsp;close to 0 when the prediction is close to 0 for the red observations (label=0).&nbsp;<\/li><\/ol>\n\n\n\n<ol class=\"wp-block-list\" start=\"4\"><li>Finally, find the parameters a, b, c of our linear function that minimize the loss function.&nbsp;<\/li><\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">If we can train our classifier so its average loss is near zero, we will obtain good matches between our predictions and observed values.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">We find\u202f<em>a<\/em>,\u202f<em>b<\/em>, and\u202f<em>c<\/em>\u202fthat minimize the loss via\u202f<em>gradient descent<\/em>: choose random starting values for\u202f<em>a<\/em>,\u202f<em>b<\/em>,\u202f<em>c<\/em>, determine in which direction they need to be updated to reduce the total loss over all training observations, and iteratively update\u202f<em>a<\/em>,\u202f<em>b<\/em>, and\u202f<em>c<\/em>\u202funtil we find values that achieve a minimum loss.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">We obtain a classification (blue\/red shading) that looks like this:&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" width=\"550\" height=\"493\" data-src=\"\/campus\/wp-content\/uploads\/sites\/2\/2020\/07\/LogisticRegression.png\" alt=\"Logistic R\" class=\"wp-image-51457 lazyload\" data-srcset=\"https:\/\/ibkrcampus.com\/campus\/wp-content\/uploads\/sites\/2\/2020\/07\/LogisticRegression.png 550w, https:\/\/ibkrcampus.com\/campus\/wp-content\/uploads\/sites\/2\/2020\/07\/LogisticRegression-300x269.png 300w\" data-sizes=\"(max-width: 550px) 100vw, 550px\" src=\"data:image\/svg+xml;base64,PHN2ZyB3aWR0aD0iMSIgaGVpZ2h0PSIxIiB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciPjwvc3ZnPg==\" style=\"--smush-placeholder-width: 550px; aspect-ratio: 550\/493;\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Now, let\u2019s look a little more closely at the math behind these four steps. (If you\u2019re not into the math, you can\u202f<a href=\"https:\/\/alphaarchitect.com\/2018\/12\/21\/machine-learning-classification-methods-and-factor-investing\/#skip\" target=\"_blank\" rel=\"noreferrer noopener\">skip down<\/a>, but it\u2019s not very difficult, and after all Alpha Architect is a quant finance blog!)&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>Decision function:<\/em>\u202f<img decoding=\"async\" data-src=\"\/campus\/wp-content\/uploads\/sites\/2\/2020\/07\/alpha-architect-2.png\" alt=\"\" class=\"wp-image-51459 lazyload\" width=\"165\" height=\"18\" src=\"data:image\/svg+xml;base64,PHN2ZyB3aWR0aD0iMSIgaGVpZ2h0PSIxIiB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciPjwvc3ZnPg==\" style=\"--smush-placeholder-width: 165px; aspect-ratio: 165\/18;\">\u202fis proportional to the\u202f<a href=\"https:\/\/en.wikipedia.org\/wiki\/Distance_from_a_point_to_a_line#Line_defined_by_an_equation\" target=\"_blank\" rel=\"noreferrer noopener\">Euclidian distance<\/a>\u202ffrom (x, y) to the line defined by\u202f<img decoding=\"async\" width=\"120\" height=\"17\" data-src=\"\/campus\/wp-content\/uploads\/sites\/2\/2020\/07\/alpha-architect-3.png\" alt=\"\" class=\"wp-image-51461 lazyload\" src=\"data:image\/svg+xml;base64,PHN2ZyB3aWR0aD0iMSIgaGVpZ2h0PSIxIiB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciPjwvc3ZnPg==\" style=\"--smush-placeholder-width: 120px; aspect-ratio: 120\/17;\">. It represents how far a point is from the decision boundary, the\u202f<em>classification margin<\/em>.&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>In this piece, we\u2019ll \u202ffirst review\u202f machine learning for classification, a problem which may be less familiar to investors, but fundamental to machine learning professionals. \u202fNext, we\u2019ll apply classification to the classic value\/momentum factors. <\/p>\n","protected":false},"author":454,"featured_media":22628,"comment_status":"closed","ping_status":"open","sticky":true,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":"","jetpack_post_was_ever_published":false},"categories":[339,343,349,338,341],"tags":[851,7959,4922,4405,852,595,494],"contributors-categories":[13651],"class_list":["post-51426","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-development","tag-algo-trading","tag-classification-algorithms","tag-econometrics","tag-logistic-regression","tag-machine-learning","tag-python","tag-quant","contributors-categories-alpha-architect"],"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) - 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