{"id":208,"date":"2020-04-24T12:30:17","date_gmt":"2020-04-24T12:30:17","guid":{"rendered":"https:\/\/blog-gn.dronacharya.info\/?p=208"},"modified":"2026-02-12T06:07:37","modified_gmt":"2026-02-12T06:07:37","slug":"the-mathematics-of-machine-learning","status":"publish","type":"post","link":"https:\/\/gnindia.dronacharya.info\/blog\/the-mathematics-of-machine-learning\/","title":{"rendered":"The Mathematics of Machine Learning"},"content":{"rendered":"<p>In current scenario, there has been an outstanding interest of people exploring into the world of data science and using Machine Learning (ML) practices to probe statistical regularities and build immaculate data-driven products. However, it&#8217;s also been observed that some actually lack the necessary mathematical awareness and background to get useful results.<\/p>\n<p>Recently, there has been an upsurge in the availability of many easy-to-use machine and deep learning packages such as scikit-learn, Weka, Tensorflow etc. <a href=\"https:\/\/ggnindia.dronacharya.info\/CSE-AI-ML\/home.aspx\" target=\"_blank\" rel=\"noopener noreferrer\">Machine Learning <\/a>theory is a field that combines statistical, probabilistic, <a href=\"https:\/\/gnindia.dronacharya.info\/CSE\/home.aspx\" target=\"_blank\" rel=\"noopener noreferrer\">computer science<\/a> and algorithmic aspects, arising from learning iteratively from data and finding hidden insights which can be used to build intelligent applications. Inspite of the immense possibilities of Machine and Deep Learning, a vast mathematical understanding of variety of these techniques is necessary for a better understanding of the inner workings of the algorithms and getting better results.<\/p>\n<p><strong><u>What Level of Maths Do You Need?<\/u><\/strong><\/p>\n<p>To be a <a href=\"https:\/\/ggnindia.dronacharya.info\/CSE-AI-ML\/home.aspx\" target=\"_blank\" rel=\"noopener noreferrer\">Machine Learning Engineer \/ Scientist<\/a>, the minimum level of mathematics is needed. Below are the some of the <a href=\"https:\/\/gnindia.dronacharya.info\/CSE\/1stYear\/EngineeringMathematics_II.aspx?Subject=EMII&amp;Semester=1stYear\" target=\"_blank\" rel=\"noopener noreferrer\">mathematics<\/a> concept and their importance.<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"size-medium wp-image-210 aligncenter\" src=\"https:\/\/blog-gn.dronacharya.info\/wp-content\/uploads\/2020\/04\/mathamatics-concept-300x205.jpg\" alt=\"\" width=\"300\" height=\"205\" srcset=\"https:\/\/gnindia.dronacharya.info\/blog\/wp-content\/uploads\/2020\/04\/mathamatics-concept-300x205.jpg 300w, https:\/\/gnindia.dronacharya.info\/blog\/wp-content\/uploads\/2020\/04\/mathamatics-concept-1024x701.jpg 1024w, https:\/\/gnindia.dronacharya.info\/blog\/wp-content\/uploads\/2020\/04\/mathamatics-concept-768x526.jpg 768w, https:\/\/gnindia.dronacharya.info\/blog\/wp-content\/uploads\/2020\/04\/mathamatics-concept.jpg 1132w\" sizes=\"(max-width: 300px) 85vw, 300px\" \/><\/p>\n<ul>\n<li><strong>Linear Algebra:<\/strong>\u00a0 Linear Algebra is very important aspect In Machine Learning. Topics such as Singular Value Decomposition, LU Decomposition, Principal Component Analysis (PCA), Eigen decomposition of a matrix, Matrix Operations, , Eigen Values &amp; Eigen Vectors , Projections QR Factorization \/ Decomposition, Symmetric Matrices, Orthogonalization &amp; Orthonormalization, , Norms and Vector Spaces are needed for \u00a0the better understanding of the optimization methods used for machine learning.<\/li>\n<li><strong>Probability Theory and Statistics:<\/strong>\u00a0 Machine Learning and Statistics are interconnected fields. Machine Learning can be defined as &#8216;doing statistics on a Mac&#8217;. Some of the fundamental Probability\u00a0 and Statistical Theory needed for Machine Learning are Random Variables, Probability Rules &amp; Axioms, Standard Distributions (Bernoulli, Binomial, Multinomial, Uniform and Gaussian), Combinatorics, Bayes&#8217; Theorem, Variance and Expectation, Maximum a Posteriori Estimation (MAP) and Sampling Methods, Conditional and Joint Distributions, Moment Generating Functions, Maximum Likelihood Estimation (MLE), Prior and Posterior.<\/li>\n<li><strong>Algorithms and Complex Optimizations:<\/strong> \u00a0For better understanding of the computational scalability and efficiency of Machine Learning and for exploiting sparsity in datasets algorithms and complex optimization plays an important role.\u00a0 Knowledge of data structures (Binary Trees, Hashing, Heap, Stack, etc), Graphs, Dynamic Programming, Randomized &amp; Sublinear Algorithm, Descents and Primal-Dual methods, Gradient\/Stochastic are needed.<\/li>\n<li><strong>Multivariate Calculus:<\/strong>\u00a0Some of the important topics includes \u00a0Intergral\u00a0 and Differential Calculus, Vector-Values Functions , Partial Derivatives, , Directional Gradient, Jacobian, Hessian, Laplacian and Lagrangian Distribution.<\/li>\n<li><strong>Others:<\/strong>\u00a0 Some of the Mathematics topics that are not described above also have importance in Machine Learning. These include Information Theory (Entropy, Information Gain), Real and Complex Analysis (Sets and Sequences, Topology, Metric Spaces, Single-Valued and Continuous Functions, Limits, Function Spaces and Manifolds.<\/li>\n<\/ul>\n<p><strong>So, have a strong base in mathematics in your first year of engineering from <\/strong><a href=\"https:\/\/gnindia.dronacharya.info\/CSE\/Faculty.aspx\" target=\"_blank\" rel=\"noopener noreferrer\"><strong>Best Engineering Faculty in Delhi NCR<\/strong><\/a><strong> and take your first step to be a Machine Learning Engineer. Study Engineering from <\/strong><a href=\"https:\/\/gnindia.dronacharya.info\/\" target=\"_blank\" rel=\"noopener noreferrer\"><strong>Top B.Tech College in Noida<\/strong><\/a><strong> .<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>In current scenario, there has been an outstanding interest of people exploring into the world of data science and using Machine Learning (ML) practices to probe statistical regularities and build immaculate data-driven products. However, it&#8217;s also been observed that some actually lack the necessary mathematical awareness and background to get useful results. Recently, there has&#8230; <\/p>\n<div class=\"link-more\"><a href=\"https:\/\/gnindia.dronacharya.info\/blog\/the-mathematics-of-machine-learning\/\" class=\"read-more\">Read More<\/a><\/div>\n","protected":false},"author":1,"featured_media":209,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[14],"tags":[120,119,115,114,113,118,117,116],"_links":{"self":[{"href":"https:\/\/gnindia.dronacharya.info\/blog\/wp-json\/wp\/v2\/posts\/208"}],"collection":[{"href":"https:\/\/gnindia.dronacharya.info\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gnindia.dronacharya.info\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gnindia.dronacharya.info\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gnindia.dronacharya.info\/blog\/wp-json\/wp\/v2\/comments?post=208"}],"version-history":[{"count":5,"href":"https:\/\/gnindia.dronacharya.info\/blog\/wp-json\/wp\/v2\/posts\/208\/revisions"}],"predecessor-version":[{"id":501,"href":"https:\/\/gnindia.dronacharya.info\/blog\/wp-json\/wp\/v2\/posts\/208\/revisions\/501"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/gnindia.dronacharya.info\/blog\/wp-json\/wp\/v2\/media\/209"}],"wp:attachment":[{"href":"https:\/\/gnindia.dronacharya.info\/blog\/wp-json\/wp\/v2\/media?parent=208"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gnindia.dronacharya.info\/blog\/wp-json\/wp\/v2\/categories?post=208"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gnindia.dronacharya.info\/blog\/wp-json\/wp\/v2\/tags?post=208"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}