{"id":241,"date":"2023-12-31T19:02:33","date_gmt":"2023-12-31T19:02:33","guid":{"rendered":"https:\/\/alandix.com\/aibook\/?page_id=241"},"modified":"2023-12-31T19:02:33","modified_gmt":"2023-12-31T19:02:33","slug":"chap07","status":"publish","type":"page","link":"https:\/\/alandix.com\/aibook\/second-edition\/toc2e\/chap07\/","title":{"rendered":"Chapter 7 \u2013 Statistical and Numerical Techniques"},"content":{"rendered":"<div class=\"embedurl\" data-url=\"https:\/\/alandix.com\/books\/aibook\/content\/chaps\/chap07.html\" ><!--  Chapter 7 Statistical and Numerical Techniques  -->\n\n<script>\nvar chapnos = 7;\nvar json_url = \"https:\\\/\\\/alandix.com\\\/books\\\/aibook\\\/content\\\/chaps\\\/chap07.json\";\n<\/script>\n\n\n\n\n\t<object style=\"width:100%; aspect-ratio: 10 \/ 7;\" type=\"application\/pdf\" data=\"https:\/\/alandix.com\/books\/aibook\/content\/slides-pdf\/AI-chap-07.pdf\"><\/object>\n\t<p> Download <a href=\"https:\/\/alandix.com\/books\/aibook\/content\/slides-pptx\/AI-chap-07.pptx\" download>chapter slides<\/a><\/p>\n\n\n<h3> Contents <\/h3>\n<div class=\"toc\">\n<dl>\n<dt>7.1&nbsp;&nbsp;Overview<\/dt>\n<dt>7.2&nbsp;&nbsp;Linear Regression<\/dt>\n<dt>7.3&nbsp;&nbsp;Vectors and Matrices<\/dt>\n<dt>7.4&nbsp;&nbsp;Eigenvalues and Principal Components<\/dt>\n<dt>7.5&nbsp;&nbsp;Clustering and K-means<\/dt>\n<dt>7.6&nbsp;&nbsp;Randomness<\/dt><dd><dl>\n<dt>7.6.1&nbsp;&nbsp;Simple Statistics<\/dt>\n<dt>7.6.2&nbsp;&nbsp;Distributions and Long-tail Data<\/dt>\n<dt>7.6.3&nbsp;&nbsp;Least Squares<\/dt>\n<dt>7.6.4&nbsp;&nbsp;Monte Carlo Techniques<\/dt>\n<\/dl><\/dd>\n<dt>7.7&nbsp;&nbsp;Non-linear Functions for Machine Learning<\/dt><dd><dl>\n<dt>7.7.1&nbsp;&nbsp;Support Vector Machines<\/dt>\n<dt>7.7.2&nbsp;&nbsp;Reservoir Computing<\/dt>\n<dt>7.7.3&nbsp;&nbsp;Kolmogorov-Arnold Networks<\/dt>\n<\/dl><\/dd>\n<dt>7.8&nbsp;&nbsp;Summary<\/dt>\n<\/dl><\/div>\n\n\n<h3> Glossary items referenced in this chapter <\/h3>\n<div class=\"toc\">\n<a href=\"https:\/\/alandix.com\/glossary\/aibook\/activation%20function\">activation function<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/aibook\/arithmetic%20mean\">arithmetic mean<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/aibook\/asymmetric%20distribution\">asymmetric distribution<\/a>, <strong><a href=\"https:\/\/alandix.com\/glossary\/aibook\/b-splines\">B-splines<\/a><\/strong>, <a href=\"https:\/\/alandix.com\/glossary\/aibook\/backpropagation\">backpropagation<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/aibook\/byzantine%20conditions\">Byzantine conditions<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/aibook\/cartesian%20coordinates\">Cartesian coordinates<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/aibook\/centroid\">centroid<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/aibook\/clustering\">clustering<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/aibook\/continuous%20distribution\">continuous distribution<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/aibook\/correlation%20matrix\">correlation matrix<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/aibook\/critical%20point\">critical point<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/aibook\/data%20reduction\">data reduction<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/aibook\/deep%20neural%20network\">deep neural network<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/aibook\/dependent%20variable\">dependent variable<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/aibook\/deterministic%20search\">deterministic search<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/aibook\/discontinuous\">discontinuous<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/aibook\/discrete%20distributions\">discrete distributions<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/aibook\/drunkards%20walk\">drunkards walk<\/a>, <strong><a href=\"https:\/\/alandix.com\/glossary\/aibook\/eigenvector\">eigenvector<\/a><\/strong>, <a href=\"https:\/\/alandix.com\/glossary\/aibook\/feedback%20phenomena\">feedback phenomena<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/aibook\/fpgas\">FPGAs<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/aibook\/fully%20connected\">fully connected<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/aibook\/go\">Go<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/aibook\/gradient%20descent\">gradient descent<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/aibook\/heuristic%20evaluation%20function\">heuristic evaluation function<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/aibook\/hill%20climbing%20algorithm\">hill climbing algorithm<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/aibook\/hybrid%20architecture\">hybrid architecture<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/aibook\/independent%20variable\">independent variable<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/aibook\/information%20visualisation\">information visualisation<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/aibook\/intercept\">intercept<\/a>, <strong><a href=\"https:\/\/alandix.com\/glossary\/aibook\/interquartile%20range\">interquartile range<\/a><\/strong>, <strong><a href=\"https:\/\/alandix.com\/glossary\/aibook\/k-means%20algorithm\">k-means algorithm<\/a><\/strong>, <a href=\"https:\/\/alandix.com\/glossary\/aibook\/kernel\">kernel<\/a>, <strong><a href=\"https:\/\/alandix.com\/glossary\/aibook\/kolmogorov-arnold%20networks\">Kolmogorov-Arnold Networks<\/a><\/strong>, <strong><a href=\"https:\/\/alandix.com\/glossary\/aibook\/kolmogorov-arnold%20representation%20theorem\">Kolmogorov-Arnold representation theorem<\/a><\/strong>, <a href=\"https:\/\/alandix.com\/glossary\/aibook\/least%20squares\">least squares<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/aibook\/linear%20discriminant%20analysis\">linear discriminant analysis<\/a>, <strong><a href=\"https:\/\/alandix.com\/glossary\/aibook\/linear%20regression\">linear regression<\/a><\/strong>, <a href=\"https:\/\/alandix.com\/glossary\/aibook\/linearly%20separable\">linearly separable<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/aibook\/local%20maximum\">local maximum<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/aibook\/long-tail%20distribution\">long-tail distribution<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/aibook\/machine%20learning\">machine learning<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/aibook\/memristor\">memristor<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/aibook\/mode\">mode<\/a>, <strong><a href=\"https:\/\/alandix.com\/glossary\/aibook\/monte%20carlo%20techniques\">Monte Carlo techniques<\/a><\/strong>, <a href=\"https:\/\/alandix.com\/glossary\/aibook\/monte%20carlo%20tree%20search\">Monte Carlo tree search<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/aibook\/multi-layer%20perceptron\">multi-layer perceptron<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/aibook\/multi-linear%20regression\">multi-linear regression<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/aibook\/neural%20network\">neural network<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/aibook\/non-linear%20functions\">non-linear functions<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/aibook\/non-linear%20transformations\">non-linear transformations<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/aibook\/normal%20distribution\">Normal distribution<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/aibook\/optimal\">optimal<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/aibook\/outliers\">outliers<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/aibook\/percentiles\">percentiles<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/aibook\/perceptron\">perceptron<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/aibook\/piecewise%20linear\">piecewise linear<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/aibook\/pre-whitening\">pre-whitening<\/a>, <strong><a href=\"https:\/\/alandix.com\/glossary\/aibook\/principal%20components%20analysis\">principal components analysis<\/a><\/strong>, <a href=\"https:\/\/alandix.com\/glossary\/aibook\/principal%20eigenvector\">principal eigenvector<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/aibook\/probability\">probability<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/aibook\/probability%20density\">probability density<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/aibook\/python\">Python<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/aibook\/quartile\">quartile<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/aibook\/randomising%20the%20order\">randomising the order<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/aibook\/readout\">readout<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/aibook\/regression%20line\">regression line<\/a>, <strong><a href=\"https:\/\/alandix.com\/glossary\/aibook\/reservoir%20computing\">reservoir computing<\/a><\/strong>, <a href=\"https:\/\/alandix.com\/glossary\/aibook\/residuals\">residuals<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/aibook\/search%20space\">search space<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/aibook\/search%20strategies\">search strategies<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/aibook\/sigmoid%20activation%20function\">sigmoid activation function<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/aibook\/sigmoid%20function\">sigmoid function<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/aibook\/similarity%20matrix\">similarity matrix<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/aibook\/similarity%20measure\">similarity measure<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/aibook\/simulated%20annealing\">simulated annealing<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/aibook\/smoothing\">smoothing<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/aibook\/social%20media\">social media<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/aibook\/square%20matrices\">square matrices<\/a>, <strong><a href=\"https:\/\/alandix.com\/glossary\/aibook\/standard%20deviation\">standard deviation<\/a><\/strong>, <a href=\"https:\/\/alandix.com\/glossary\/aibook\/statistical%20techniques\">statistical techniques<\/a>, <strong><a href=\"https:\/\/alandix.com\/glossary\/aibook\/support%20vector%20machine\">support vector machine<\/a><\/strong>, <a href=\"https:\/\/alandix.com\/glossary\/aibook\/symmetric%20matrix\">symmetric matrix<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/aibook\/time%20dependence\">time dependence<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/aibook\/transpose\">transpose<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/aibook\/uncertainty\">uncertainty<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/aibook\/uncertainty%20measure\">uncertainty measure<\/a>, <strong><a href=\"https:\/\/alandix.com\/glossary\/aibook\/variance\">variance<\/a><\/strong>, <a href=\"https:\/\/alandix.com\/glossary\/aibook\/wavelet\">wavelet<\/a><\/div>\n\n\n\n\n<\/div>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":2,"featured_media":0,"parent":221,"menu_order":7,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_themeisle_gutenberg_block_has_review":false,"footnotes":""},"class_list":["post-241","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/alandix.com\/aibook\/wp-json\/wp\/v2\/pages\/241","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/alandix.com\/aibook\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/alandix.com\/aibook\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/alandix.com\/aibook\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/alandix.com\/aibook\/wp-json\/wp\/v2\/comments?post=241"}],"version-history":[{"count":3,"href":"https:\/\/alandix.com\/aibook\/wp-json\/wp\/v2\/pages\/241\/revisions"}],"predecessor-version":[{"id":297,"href":"https:\/\/alandix.com\/aibook\/wp-json\/wp\/v2\/pages\/241\/revisions\/297"}],"up":[{"embeddable":true,"href":"https:\/\/alandix.com\/aibook\/wp-json\/wp\/v2\/pages\/221"}],"wp:attachment":[{"href":"https:\/\/alandix.com\/aibook\/wp-json\/wp\/v2\/media?parent=241"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}