{"id":127,"date":"2025-01-12T22:16:11","date_gmt":"2025-01-12T14:16:11","guid":{"rendered":"https:\/\/www.toothlessos.xyz\/?p=127"},"modified":"2025-01-12T22:16:11","modified_gmt":"2025-01-12T14:16:11","slug":"machine-learning-all-about-distributions","status":"publish","type":"post","link":"https:\/\/www.toothlessos.xyz\/index.php\/2025\/01\/12\/machine-learning-all-about-distributions\/","title":{"rendered":"Machine learning: All about distributions"},"content":{"rendered":"\n

Forewords<\/h2>\n\n\n\n

I am recently starting the “Introduction to Machine Learning” course at college. Therefore, I decide to start a new series on the topic of machine learning, in which I will note down important take aways from ML.<\/p>\n\n\n\n

All about distributions<\/h2>\n\n\n\n
\"\"<\/figure>\n\n\n\n

The essence of machine learning lies in statistics<\/strong> and optimization<\/strong> (an argument borrowed from my professor). The datasets that we look at have some inherent patterns or distributions, while we create probabilistic models to fit<\/strong> these inherent patterns. We then use optimization tools to actually do the fitting.<\/p>\n\n\n\n

I know this summary can be abstract, so next let’s look at some examples together.<\/p>\n\n\n\n

The examples<\/h2>\n\n\n\n

We first consider the classic example of linear regression<\/strong>:<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n
\"\"<\/figure>\n\n\n\n

Another example worth looking at is classification<\/strong>, which will be introduced in more details in the following logs. <\/p>\n\n\n\n

For now, the most important takeaway is: Regression<\/strong> and classification<\/strong> are two of the most important and fundamental applications of machine learning.<\/p>\n\n\n\n

Appendix: KL-Divergence and Cross-entropy<\/h2>\n\n\n\n
\"\"<\/figure>\n\n\n\n
\"\"<\/figure>\n\n\n\n

Remarks<\/em><\/strong>: It’s worth noting that KL-divergence and cross-entropy both characterize the difference between two distributions. This may sound familiar to you.<\/p>\n\n\n\n

Spoiler: Cross-entropy can be used as an objective of optimization too! (Or you may also call it a loss function)<\/p>\n\n\n\n

Reference & Extended Readings<\/h2>\n\n\n\n
    \n
  1. STATS 302@DKU<\/li>\n\n\n\n
  2. \u201c\u4ea4\u53c9\u71b5\u201d\u5982\u4f55\u505a\u635f\u5931\u51fd\u6570\uff1f\u6253\u5305\u7406\u89e3\u201c\u4fe1\u606f\u91cf\u201d\u3001\u201c\u6bd4\u7279\u201d\u3001\u201c\u71b5\u201d\u3001\u201cKL\u6563\u5ea6\u201d\u3001\u201c\u4ea4\u53c9\u71b5\u201d_\u54d4\u54e9\u54d4\u54e9_bilibili<\/a><\/li>\n\n\n\n
  3. \u201c\u635f\u5931\u51fd\u6570\u201d\u662f\u5982\u4f55\u8bbe\u8ba1\u51fa\u6765\u7684\uff1f\u76f4\u89c2\u7406\u89e3\u201c\u6700\u5c0f\u4e8c\u4e58\u6cd5\u201d\u548c\u201c\u6781\u5927\u4f3c\u7136\u4f30\u8ba1\u6cd5\u201d_\u54d4\u54e9\u54d4\u54e9_bilibili<\/a><\/li>\n\n\n\n
  4. \u300a\u52a8\u624b\u5b66\u6df1\u5ea6\u5b66\u4e60\u300b \u2014 \u52a8\u624b\u5b66\u6df1\u5ea6\u5b66\u4e60 2.0.0 documentation<\/a><\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"

    Forewords I am recently starting the “Introductio […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[19],"tags":[23,22,21,20],"class_list":["post-127","post","type-post","status-publish","format-standard","hentry","category-ml","tag-cross-entropy-loss","tag-kl-divergence","tag-linear-regression","tag-machine-learning"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.toothlessos.xyz\/index.php\/wp-json\/wp\/v2\/posts\/127","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.toothlessos.xyz\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.toothlessos.xyz\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.toothlessos.xyz\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.toothlessos.xyz\/index.php\/wp-json\/wp\/v2\/comments?post=127"}],"version-history":[{"count":18,"href":"https:\/\/www.toothlessos.xyz\/index.php\/wp-json\/wp\/v2\/posts\/127\/revisions"}],"predecessor-version":[{"id":151,"href":"https:\/\/www.toothlessos.xyz\/index.php\/wp-json\/wp\/v2\/posts\/127\/revisions\/151"}],"wp:attachment":[{"href":"https:\/\/www.toothlessos.xyz\/index.php\/wp-json\/wp\/v2\/media?parent=127"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.toothlessos.xyz\/index.php\/wp-json\/wp\/v2\/categories?post=127"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.toothlessos.xyz\/index.php\/wp-json\/wp\/v2\/tags?post=127"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}