{"id":579,"date":"2018-01-26T14:58:38","date_gmt":"2018-01-26T14:58:38","guid":{"rendered":"http:\/\/www.nullplug.org\/ML-Blog\/?p=579"},"modified":"2018-01-26T15:08:06","modified_gmt":"2018-01-26T15:08:06","slug":"problem-set-13","status":"publish","type":"post","link":"http:\/\/www.nullplug.org\/ML-Blog\/2018\/01\/26\/problem-set-13\/","title":{"rendered":"Problem Set 13"},"content":{"rendered":"<h2>Problem Set 13<\/h2>\n<p>This is to be completed by February 1st, 2018.<\/p>\n<h3>Exercises<\/h3>\n<ol>\n<li><a href=\"https:\/\/www.datacamp.com\/home\">Datacamp<\/a><\/li>\n<\/ol>\n<p>* Complete the lesson:<br \/>\na. Python Data Science Toolbox (Part II)<\/p>\n<ol>\n<li>\n<p>For a logistic regressor (multiclass ending in softmax) write down the update rules for gradient descent.<\/p>\n<\/li>\n<li>\n<p>For a two layer perceptron ending in softmax with intermediate relu non-linearity write down the update rules for gradient descent.<\/p>\n<\/li>\n<\/ol>\n<h3>Python Lab<\/h3>\n<ol>\n<li>Build a two layer perceptron (choose your non-linearity) in numpy for a multi-class classification problem and test it on MNIST.<\/li>\n<li>Build a MLP in Keras and test it on MNIST.<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>Problem Set 13 This is to be completed by February 1st, 2018. Exercises Datacamp * Complete the lesson: a. Python Data Science Toolbox (Part II) For a logistic regressor (multiclass ending in softmax) write down the update rules for gradient descent. For a two layer perceptron ending in softmax with intermediate relu non-linearity write down &hellip; <a href=\"http:\/\/www.nullplug.org\/ML-Blog\/2018\/01\/26\/problem-set-13\/\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;Problem Set 13&#8221;<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_monsterinsights_skip_tracking":false,"advanced_seo_description":"","jetpack_seo_html_title":"","jetpack_seo_noindex":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2},"jetpack_post_was_ever_published":false},"categories":[1],"tags":[],"class_list":["post-579","post","type-post","status-publish","format-standard","hentry","category-general"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p9dIpN-9l","jetpack_likes_enabled":true,"jetpack-related-posts":[{"id":572,"url":"http:\/\/www.nullplug.org\/ML-Blog\/2018\/01\/19\/572\/","url_meta":{"origin":579,"position":0},"title":"Problem Set  12","author":"Justin Noel","date":"January 19, 2018","format":false,"excerpt":"Problem Set 12 This is to be completed by January 25th, 2018. Exercises Datacamp Complete the lesson: a. Python Data Science Toolbox (Part I) Let $S\\subset \\Bbb R^n$ with $|S|<\\infty$. Let $\\mu=\\frac{1}{|S|}\\sum_{x_i\\in S} x_i$. Show that $$ \\frac{1}{|S|}\\sum_{(x_i,x_j)\\in S\\times S} ||x_i-x_j||^2 = 2\\sum_{x_i\\in S} ||x_i-\\mu||^2.$$ Prove that the $K$-means clustering\u2026","rel":"","context":"In &quot;General&quot;","block_context":{"text":"General","link":"http:\/\/www.nullplug.org\/ML-Blog\/category\/general\/"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":538,"url":"http:\/\/www.nullplug.org\/ML-Blog\/2017\/11\/24\/problem-set-6\/","url_meta":{"origin":579,"position":1},"title":"Problem Set 6","author":"Justin Noel","date":"November 24, 2017","format":false,"excerpt":"Problem Set 6 This is to be completed by November 30th, 2017. Exercises Datacamp Complete the lesson: a. Text Mining: Bag of Words Exercises from Elements of Statistical Learning Complete exercises: a. 4.2 b. 4.6 Run the perceptron learning algorithm by hand for the two class classification problem with $(X,Y)$-pairs\u2026","rel":"","context":"In &quot;General&quot;","block_context":{"text":"General","link":"http:\/\/www.nullplug.org\/ML-Blog\/category\/general\/"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":543,"url":"http:\/\/www.nullplug.org\/ML-Blog\/2017\/12\/04\/543\/","url_meta":{"origin":579,"position":2},"title":"Problem Set 7","author":"Justin Noel","date":"December 4, 2017","format":false,"excerpt":"Problem Set 7 This is to be completed by December 7th, 2017. Exercises Datacamp Complete the lesson: a. Credit risk modeling in R. Exercises from Elements of Statistical Learning Complete exercise: a. 4.5 (Use the reduced form of the logistic classifier that fits an (n,k-1)-matrix for a problem with n\u2026","rel":"","context":"In &quot;General&quot;","block_context":{"text":"General","link":"http:\/\/www.nullplug.org\/ML-Blog\/category\/general\/"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":531,"url":"http:\/\/www.nullplug.org\/ML-Blog\/2017\/11\/17\/problem-set-5\/","url_meta":{"origin":579,"position":3},"title":"Problem Set 5","author":"Justin Noel","date":"November 17, 2017","format":false,"excerpt":"Problem Set 5 This is to be completed by November 23rd, 2017. Exercises Datacamp Complete the lesson: a. Machine Learning Toolbox R Lab: Write a function in R that will take in a vector of discrete variables and will produce the corresponding one hot encodings. Write a function in R\u2026","rel":"","context":"In &quot;General&quot;","block_context":{"text":"General","link":"http:\/\/www.nullplug.org\/ML-Blog\/category\/general\/"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":563,"url":"http:\/\/www.nullplug.org\/ML-Blog\/2018\/01\/13\/problem-set-11\/","url_meta":{"origin":579,"position":4},"title":"Problem Set 11","author":"Justin Noel","date":"January 13, 2018","format":false,"excerpt":"Problem Set 11 This is to be completed by January 18th, 2018. Exercises Datacamp Complete the lesson: a. Intermediate Python for Data Science What is the maximum depth of a decision tree trained on $N$ samples? If we train a decision tree to an arbitrary depth, what will be the\u2026","rel":"","context":"In &quot;General&quot;","block_context":{"text":"General","link":"http:\/\/www.nullplug.org\/ML-Blog\/category\/general\/"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":377,"url":"http:\/\/www.nullplug.org\/ML-Blog\/2017\/10\/11\/problem-set-1\/","url_meta":{"origin":579,"position":5},"title":"Problem Set 1","author":"Justin Noel","date":"October 11, 2017","format":false,"excerpt":"Problem Set 1 This is to be completed by November 27th, 2017. (THIS IS A TYPO: This should read October 26th, 2017). It is okay if you finish by this ridiculous first due date. Forewarning For several of these exercises, you will be asked to install software and\/or setup accounts\u2026","rel":"","context":"In &quot;General&quot;","block_context":{"text":"General","link":"http:\/\/www.nullplug.org\/ML-Blog\/category\/general\/"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]}],"_links":{"self":[{"href":"http:\/\/www.nullplug.org\/ML-Blog\/wp-json\/wp\/v2\/posts\/579","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/www.nullplug.org\/ML-Blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.nullplug.org\/ML-Blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.nullplug.org\/ML-Blog\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"http:\/\/www.nullplug.org\/ML-Blog\/wp-json\/wp\/v2\/comments?post=579"}],"version-history":[{"count":2,"href":"http:\/\/www.nullplug.org\/ML-Blog\/wp-json\/wp\/v2\/posts\/579\/revisions"}],"predecessor-version":[{"id":581,"href":"http:\/\/www.nullplug.org\/ML-Blog\/wp-json\/wp\/v2\/posts\/579\/revisions\/581"}],"wp:attachment":[{"href":"http:\/\/www.nullplug.org\/ML-Blog\/wp-json\/wp\/v2\/media?parent=579"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.nullplug.org\/ML-Blog\/wp-json\/wp\/v2\/categories?post=579"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.nullplug.org\/ML-Blog\/wp-json\/wp\/v2\/tags?post=579"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}