{"id":1824,"date":"2025-07-04T16:56:25","date_gmt":"2025-07-04T15:56:25","guid":{"rendered":"https:\/\/cyberenlightener.com\/?page_id=1824"},"modified":"2025-08-13T06:51:18","modified_gmt":"2025-08-13T05:51:18","slug":"machine-learning","status":"publish","type":"page","link":"https:\/\/cyberenlightener.com\/?page_id=1824","title":{"rendered":"Introduction to Machine Learning"},"content":{"rendered":"\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">\ud83c\udf93 Tutorial: Introduction to Machine Learning \u2013 Learning Paradigms \u2013 PAC Learning<\/h1>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">\ud83e\udde0 1. What is Machine Learning?<\/h2>\n\n\n\n<p><strong>Machine Learning (ML)<\/strong> is a subfield of artificial intelligence (AI) that focuses on building systems that learn from data to make decisions or predictions without being explicitly programmed.<\/p>\n\n\n\n<p><strong>Arthur Samuel&#8217;s definition (1959):<\/strong><\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p><em>\u201cMachine Learning is the field of study that gives computers the ability to learn without being explicitly programmed.\u201d<\/em><\/p>\n<\/blockquote>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">\ud83c\udfaf 2. Goals of Machine Learning<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Discover patterns in data<\/li>\n\n\n\n<li>Make predictions on unseen data<\/li>\n\n\n\n<li>Improve performance with experience<\/li>\n\n\n\n<li>Generalize well to new situations<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">\ud83d\udcda 3. Learning Paradigms in ML<\/h2>\n\n\n\n<p>Machine learning problems can be broadly classified into three <strong>learning paradigms<\/strong> based on the supervision in training data:<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u2705 3.1 Supervised Learning<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Input:<\/strong> Labeled dataset (<code>X<\/code>, <code>Y<\/code>)<\/li>\n\n\n\n<li><strong>Goal:<\/strong> Learn a function <code>f : X \u2192 Y<\/code> to map input to output<\/li>\n\n\n\n<li><strong>Examples:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Classification (e.g., spam detection)<\/li>\n\n\n\n<li>Regression (e.g., house price prediction)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">\u2753 3.2 Unsupervised Learning<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Input:<\/strong> Unlabeled dataset (<code>X<\/code>)<\/li>\n\n\n\n<li><strong>Goal:<\/strong> Discover structure or patterns in data<\/li>\n\n\n\n<li><strong>Examples:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Clustering (e.g., customer segmentation)<\/li>\n\n\n\n<li>Dimensionality reduction (e.g., PCA)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">\u2696\ufe0f 3.3 Reinforcement Learning<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Input:<\/strong> Environment and rewards<\/li>\n\n\n\n<li><strong>Goal:<\/strong> Learn to make sequences of decisions to maximize reward<\/li>\n\n\n\n<li><strong>Examples:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Game playing (e.g., AlphaGo)<\/li>\n\n\n\n<li>Robotics (e.g., walking, grasping)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">\ud83e\uddea 3.4 Semi-Supervised Learning<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Mix of labeled and unlabeled data<\/li>\n\n\n\n<li>Useful when labeling is expensive<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">\ud83e\uddd1\u200d\ud83e\udd1d\u200d\ud83e\uddd1 3.5 Self-Supervised Learning<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Learns supervision signal from the data itself (e.g., predicting missing words in a sentence)<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">4. PAC LEARNING<\/h2>\n\n\n\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\" hidden class=\"wp-block-file__embed\" data=\"https:\/\/cyberenlightener.com\/wp-content\/uploads\/2025\/07\/PAC-Learning-and-Exercises_ML-LECTURE-1_ROY-1-1.pdf\" type=\"application\/pdf\" style=\"width:100%;height:600px\" aria-label=\"Embed of PAC Learning and Exercises_ML-LECTURE-1_ROY (1) (1).\"><\/object><a id=\"wp-block-file--media-ae5d79ad-a5f3-47f8-aaa8-d25bfb26d6d0\" href=\"https:\/\/cyberenlightener.com\/wp-content\/uploads\/2025\/07\/PAC-Learning-and-Exercises_ML-LECTURE-1_ROY-1-1.pdf\">PAC Learning and Exercises_ML-LECTURE-1_ROY (1) (1)<\/a><a href=\"https:\/\/cyberenlightener.com\/wp-content\/uploads\/2025\/07\/PAC-Learning-and-Exercises_ML-LECTURE-1_ROY-1-1.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-ae5d79ad-a5f3-47f8-aaa8-d25bfb26d6d0\">Download<\/a><\/div>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th><strong>Concept \/ Term<\/strong><\/th><th><strong>Definition \/ Explanation<\/strong><\/th><\/tr><\/thead><tbody><tr><td><strong>Instance Space (\ud835\udc7f)<\/strong><\/td><td>The set of all possible input examples. In PAC learning, typically: <strong>\ud835\udc4b = {0,1}\u207f<\/strong> \u2014 all binary vectors of length <strong>n<\/strong>.<\/td><\/tr><tr><td><strong>Concept \/ Target Function (\ud835\udc84)<\/strong><\/td><td>The unknown function we aim to learn. It maps instances to labels: <strong>\ud835\udc50 : X \u2192 {0,1}<\/strong>.<\/td><\/tr><tr><td><strong>Hypothesis Class (\ud835\udc6f)<\/strong><\/td><td>A set of possible functions (hypotheses) that the learning algorithm can choose from: <strong>H \u2286 2\u02e3<\/strong>, meaning each hypothesis h \u2208 H maps instances to {0,1}.<\/td><\/tr><tr><td><strong>Distribution (\ud835\udc6b)<\/strong><\/td><td>An unknown probability distribution over the instance space \ud835\udc4b. The training data is drawn <strong>i.i.d.<\/strong> from this distribution.<\/td><\/tr><tr><td><strong>Training Examples<\/strong><\/td><td>A sequence of labeled examples drawn i.i.d. from \ud835\udc6b: <strong>(x\u2081, c(x\u2081)), &#8230;, (x\u2098, c(x\u2098))<\/strong>.<\/td><\/tr><tr><td><strong>Learning Algorithm (\ud835\udc68)<\/strong><\/td><td>The algorithm that receives training data and returns a hypothesis <strong>h \u2208 H<\/strong> that approximates the target function <strong>c<\/strong>.<\/td><\/tr><tr><td><strong>PAC Guarantee<\/strong><\/td><td>The output hypothesis <strong>h<\/strong> satisfies: <strong>Pr\u2093\u223c\ud835\udc6b[h(x) \u2260 c(x)] \u2264 \u03b5<\/strong> with probability at least <strong>1 \u2212 \u03b4<\/strong>.<\/td><\/tr><tr><td><strong>\u03b5 (epsilon)<\/strong><\/td><td>The <strong>accuracy parameter<\/strong> \u2014 how close the hypothesis should be to the target function. Smaller \u03b5 means higher accuracy.<\/td><\/tr><tr><td><strong>\u03b4 (delta)<\/strong><\/td><td>The <strong>confidence parameter<\/strong> \u2014 how confident we want to be that the learning algorithm will return a good hypothesis.<\/td><\/tr><tr><td><strong>PAC (Probably Approximately Correct)<\/strong><\/td><td>&#8220;Probably&#8221; = with probability \u2265 1 \u2212 \u03b4, &#8220;Approximately Correct&#8221; = error \u2264 \u03b5.<\/td><\/tr><tr><td><strong>PAC Learnability<\/strong><\/td><td>A concept class <strong>C<\/strong> is PAC-learnable if there exists a <strong>polynomial-time algorithm<\/strong> that for any \u03b5, \u03b4 \u2208 (0,1), can return a hypothesis with PAC guarantees.<\/td><\/tr><tr><td><strong>Sample Complexity (\ud835\udc8e)<\/strong><\/td><td>The number of training examples needed to achieve PAC guarantees. Formula (with VC dimension): <strong>m = O(VCdim(H) \u22c5 log(1\/\u03b5) + log(1\/\u03b4))<\/strong><\/td><\/tr><tr><td><strong>VC Dimension (VCdim(H))<\/strong><\/td><td>The <strong>Vapnik-Chervonenkis dimension<\/strong> \u2014 a measure of the capacity\/complexity of the hypothesis class H.<\/td><\/tr><tr><td><strong>One-sided Error<\/strong><\/td><td>Hypothesis never makes <strong>false positives<\/strong> (i.e., always predicts 0 for negative instances).<\/td><\/tr><tr><td><strong>Two-sided Error<\/strong><\/td><td>Errors are allowed on both <strong>positive and negative<\/strong> examples.<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>Probably Approximately Correct (PAC)<\/strong> learning is a foundational framework in computational learning theory, introduced by Leslie Valiant, that formalizes the concept of learnability from a theoretical, algorithmic perspective. It defines learning as the process of inferring a hypothesis that closely approximates an unknown target concept based on randomly drawn labeled examples, without relying on explicit programming. A concept class is considered PAC-learnable if a learning algorithm can, with high probability, produce a hypothesis that performs well on unseen data, using only a feasible (polynomial) number of training examples and computational steps. The framework assumes the presence of an unknown data distribution and allows the learner to receive examples either passively (as positive instances) or actively through queries to an oracle. Crucially, PAC learning emphasizes generalization: the learned hypothesis must not just fit the training data but should also perform well on new instances from the same distribution. The theory identifies specific classes of Boolean functions\u2014such as bounded CNF and monotone DNF expressions\u2014that are efficiently learnable, while also highlighting inherent limitations due to computational intractability and cryptographic hardness in learning more complex or unrestricted functions. Extensions to the PAC model address practical concerns like noise in data, real-valued outputs, and domain-specific biases, while the notion of VC dimension helps quantify the capacity of a hypothesis space and determine the number of examples needed for learning. Overall, PAC learning offers a rigorous, probability-based approach to understanding what can be learned, how efficiently it can be learned, and under what conditions learning is possible.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>VC Dimension <\/strong><\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">\ud83d\udd0d <strong>Definition<\/strong><\/h3>\n\n\n\n<p>The <strong>Vapnik\u2013Chervonenkis (VC) Dimension<\/strong> is a fundamental measure of the capacity or expressiveness of a <strong>hypothesis class<\/strong> (denoted as \ud835\udcd7). It quantifies how well a model can fit various labelings of data.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\ud83d\udca1 <strong>Key Concepts<\/strong><\/h3>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th><strong>Concept<\/strong><\/th><th><strong>Description<\/strong><\/th><\/tr><\/thead><tbody><tr><td><strong>Shattering<\/strong><\/td><td>A set of points is <em>shattered<\/em> by hypothesis class \ud835\udcd7 if \ud835\udcd7 can realize all possible labelings (2\u207f combinations for n points).<\/td><\/tr><tr><td><strong>VC Dimension<\/strong><\/td><td>The <strong>maximum number of points<\/strong> that can be shattered by \ud835\udcd7. Denoted as <strong>VC(\ud835\udcd7)<\/strong>.<\/td><\/tr><tr><td><strong>Intuition<\/strong><\/td><td>Measures the ability of \ud835\udcd7 to fit any training data perfectly. Higher VC means higher complexity.<\/td><\/tr><tr><td><strong>Zero Error Bound<\/strong><\/td><td>If a hypothesis from \ud835\udcd7 achieves zero error on N examples, then <strong>N \u2264 VC(\ud835\udcd7)<\/strong>.<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\ud83d\udcca <strong>Example Interpretation<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>If VC(\ud835\udcd7) = 3, then:\n<ul class=\"wp-block-list\">\n<li>\ud835\udcd7 can shatter any configuration of <strong>3 points<\/strong>.<\/li>\n\n\n\n<li>It <strong>cannot<\/strong> shatter all configurations of <strong>4 points<\/strong>.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\ud83e\udde0 <strong>Why It Matters<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A core concept in <strong>statistical learning theory<\/strong>.<\/li>\n\n\n\n<li>Helps <strong>balance model complexity vs. overfitting<\/strong>.<\/li>\n\n\n\n<li>Used to understand <strong>generalization<\/strong> in machine learning.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\ud83d\udcd8 <strong>Historical Note<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Introduced by <strong>Vladimir Vapnik<\/strong> and <strong>Alexey Chervonenkis<\/strong>.<\/li>\n\n\n\n<li>Applicable to binary classifiers, geometric set families, and more.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<figure class=\"wp-block-image size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"696\" height=\"1024\" src=\"https:\/\/cyberenlightener.com\/wp-content\/uploads\/2025\/07\/WhatsApp-Image-2025-07-21-at-20.26.46-696x1024.jpeg\" alt=\"\" class=\"wp-image-1952\" style=\"width:682px;height:auto\" srcset=\"https:\/\/cyberenlightener.com\/wp-content\/uploads\/2025\/07\/WhatsApp-Image-2025-07-21-at-20.26.46-696x1024.jpeg 696w, https:\/\/cyberenlightener.com\/wp-content\/uploads\/2025\/07\/WhatsApp-Image-2025-07-21-at-20.26.46-204x300.jpeg 204w, https:\/\/cyberenlightener.com\/wp-content\/uploads\/2025\/07\/WhatsApp-Image-2025-07-21-at-20.26.46-768x1129.jpeg 768w, https:\/\/cyberenlightener.com\/wp-content\/uploads\/2025\/07\/WhatsApp-Image-2025-07-21-at-20.26.46-1044x1536.jpeg 1044w, https:\/\/cyberenlightener.com\/wp-content\/uploads\/2025\/07\/WhatsApp-Image-2025-07-21-at-20.26.46.jpeg 1088w\" sizes=\"auto, (max-width: 696px) 100vw, 696px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"702\" height=\"1024\" src=\"https:\/\/cyberenlightener.com\/wp-content\/uploads\/2025\/07\/WhatsApp-Image-2025-07-21-at-20.26.47-702x1024.jpeg\" alt=\"\" class=\"wp-image-1953\" srcset=\"https:\/\/cyberenlightener.com\/wp-content\/uploads\/2025\/07\/WhatsApp-Image-2025-07-21-at-20.26.47-702x1024.jpeg 702w, https:\/\/cyberenlightener.com\/wp-content\/uploads\/2025\/07\/WhatsApp-Image-2025-07-21-at-20.26.47-206x300.jpeg 206w, https:\/\/cyberenlightener.com\/wp-content\/uploads\/2025\/07\/WhatsApp-Image-2025-07-21-at-20.26.47-768x1120.jpeg 768w, https:\/\/cyberenlightener.com\/wp-content\/uploads\/2025\/07\/WhatsApp-Image-2025-07-21-at-20.26.47-1053x1536.jpeg 1053w, https:\/\/cyberenlightener.com\/wp-content\/uploads\/2025\/07\/WhatsApp-Image-2025-07-21-at-20.26.47.jpeg 1097w\" sizes=\"auto, (max-width: 702px) 100vw, 702px\" \/><\/figure>\n\n\n\n<p><strong>Vapnik, V. N., &amp; Chervonenkis, A. Y. (2015). On the uniform convergence of relative frequencies of events to their probabilities. In&nbsp;<em>Measures of complexity: festschrift for alexey chervonenkis<\/em>&nbsp;(pp. 11-30). Cham: Springer International Publishing.<\/strong><\/p>\n\n\n\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\" hidden class=\"wp-block-file__embed\" data=\"https:\/\/cyberenlightener.com\/wp-content\/uploads\/2025\/07\/convergence-Summary-1.pdf\" type=\"application\/pdf\" style=\"width:100%;height:600px\" aria-label=\"Embed of convergence Summary (1).\"><\/object><a id=\"wp-block-file--media-98bb106d-3897-4a5c-be52-de85ee5d8378\" href=\"https:\/\/cyberenlightener.com\/wp-content\/uploads\/2025\/07\/convergence-Summary-1.pdf\">convergence Summary (1)<\/a><a href=\"https:\/\/cyberenlightener.com\/wp-content\/uploads\/2025\/07\/convergence-Summary-1.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-98bb106d-3897-4a5c-be52-de85ee5d8378\">Download<\/a><\/div>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"818\" height=\"238\" src=\"https:\/\/cyberenlightener.com\/wp-content\/uploads\/2025\/07\/image.png\" alt=\"\" class=\"wp-image-1956\" srcset=\"https:\/\/cyberenlightener.com\/wp-content\/uploads\/2025\/07\/image.png 818w, https:\/\/cyberenlightener.com\/wp-content\/uploads\/2025\/07\/image-300x87.png 300w, https:\/\/cyberenlightener.com\/wp-content\/uploads\/2025\/07\/image-768x223.png 768w\" sizes=\"auto, (max-width: 818px) 100vw, 818px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"727\" height=\"308\" src=\"https:\/\/cyberenlightener.com\/wp-content\/uploads\/2025\/07\/image-1.png\" alt=\"\" class=\"wp-image-1958\" srcset=\"https:\/\/cyberenlightener.com\/wp-content\/uploads\/2025\/07\/image-1.png 727w, https:\/\/cyberenlightener.com\/wp-content\/uploads\/2025\/07\/image-1-300x127.png 300w\" sizes=\"auto, (max-width: 727px) 100vw, 727px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"845\" height=\"218\" src=\"https:\/\/cyberenlightener.com\/wp-content\/uploads\/2025\/07\/image-2.png\" alt=\"\" class=\"wp-image-1959\" srcset=\"https:\/\/cyberenlightener.com\/wp-content\/uploads\/2025\/07\/image-2.png 845w, https:\/\/cyberenlightener.com\/wp-content\/uploads\/2025\/07\/image-2-300x77.png 300w, https:\/\/cyberenlightener.com\/wp-content\/uploads\/2025\/07\/image-2-768x198.png 768w\" sizes=\"auto, (max-width: 845px) 100vw, 845px\" \/><\/figure>\n\n\n\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\" hidden class=\"wp-block-file__embed\" data=\"https:\/\/cyberenlightener.com\/wp-content\/uploads\/2025\/07\/4-VC-Dimension-questionsROY.pdf\" type=\"application\/pdf\" style=\"width:100%;height:600px\" aria-label=\"Embed of 4 VC Dimension questionsROY.\"><\/object><a id=\"wp-block-file--media-818a1127-b20f-4acb-a26b-ce5511a023ae\" href=\"https:\/\/cyberenlightener.com\/wp-content\/uploads\/2025\/07\/4-VC-Dimension-questionsROY.pdf\">4 VC Dimension questionsROY<\/a><a href=\"https:\/\/cyberenlightener.com\/wp-content\/uploads\/2025\/07\/4-VC-Dimension-questionsROY.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-818a1127-b20f-4acb-a26b-ce5511a023ae\">Download<\/a><\/div>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>FIND-S: FINDING A MAXIMALLY SPECIFIC HYPOTHESIS<\/strong><\/h2>\n\n\n\n<p>(Ref : Mitchell, T. M. (1997). <em>Machine Learning<\/em>. McGraw-Hill.)<\/p>\n\n\n\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\" hidden class=\"wp-block-file__embed\" data=\"https:\/\/cyberenlightener.com\/wp-content\/uploads\/2025\/08\/Find-S-algorithm-tutorial-SSROY-1.pdf\" type=\"application\/pdf\" style=\"width:100%;height:600px\" aria-label=\"Embed of Find-S algorithm tutorial-SSROY (1).\"><\/object><a id=\"wp-block-file--media-99640e95-78c7-4b6c-ab0a-10e94e793b55\" href=\"https:\/\/cyberenlightener.com\/wp-content\/uploads\/2025\/08\/Find-S-algorithm-tutorial-SSROY-1.pdf\">Find-S algorithm tutorial-SSROY (1)<\/a><a href=\"https:\/\/cyberenlightener.com\/wp-content\/uploads\/2025\/08\/Find-S-algorithm-tutorial-SSROY-1.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-99640e95-78c7-4b6c-ab0a-10e94e793b55\">Download<\/a><\/div>\n\n\n\n<figure class=\"wp-block-gallery has-nested-images columns-default is-cropped wp-block-gallery-1 is-layout-flex wp-block-gallery-is-layout-flex\">\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"863\" height=\"576\" data-id=\"2092\" src=\"https:\/\/cyberenlightener.com\/wp-content\/uploads\/2025\/08\/2.jpg\" alt=\"\" class=\"wp-image-2092\" srcset=\"https:\/\/cyberenlightener.com\/wp-content\/uploads\/2025\/08\/2.jpg 863w, https:\/\/cyberenlightener.com\/wp-content\/uploads\/2025\/08\/2-300x200.jpg 300w, https:\/\/cyberenlightener.com\/wp-content\/uploads\/2025\/08\/2-768x513.jpg 768w\" sizes=\"auto, (max-width: 863px) 100vw, 863px\" \/><\/figure>\n<\/figure>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>A Systematic Approach to Learning with the Candidate Elimination Algorithm<\/strong><\/h2>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"787\" height=\"272\" src=\"https:\/\/cyberenlightener.com\/wp-content\/uploads\/2025\/08\/4.jpg\" alt=\"\" class=\"wp-image-2097\" srcset=\"https:\/\/cyberenlightener.com\/wp-content\/uploads\/2025\/08\/4.jpg 787w, https:\/\/cyberenlightener.com\/wp-content\/uploads\/2025\/08\/4-300x104.jpg 300w, https:\/\/cyberenlightener.com\/wp-content\/uploads\/2025\/08\/4-768x265.jpg 768w\" sizes=\"auto, (max-width: 787px) 100vw, 787px\" \/><\/figure>\n\n\n\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\" hidden class=\"wp-block-file__embed\" data=\"https:\/\/cyberenlightener.com\/wp-content\/uploads\/2025\/08\/Candidate-elimination-tutorial-1SSROY-1.pdf\" type=\"application\/pdf\" style=\"width:100%;height:600px\" aria-label=\"Embed of Candidate elimination tutorial-1SSROY (1).\"><\/object><a id=\"wp-block-file--media-24d5fee5-3cc8-4c25-96fa-deae34af0300\" href=\"https:\/\/cyberenlightener.com\/wp-content\/uploads\/2025\/08\/Candidate-elimination-tutorial-1SSROY-1.pdf\">Candidate elimination tutorial-1SSROY (1)<\/a><a href=\"https:\/\/cyberenlightener.com\/wp-content\/uploads\/2025\/08\/Candidate-elimination-tutorial-1SSROY-1.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-24d5fee5-3cc8-4c25-96fa-deae34af0300\">Download<\/a><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Revisit again : <strong>Candidate Elimination Algorithm \u2014 Simple Steps<\/strong><\/h2>\n\n\n\n<p><strong>Step 1 \u2013 Initialization<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>S<\/strong> = most specific hypothesis (matches nothing yet)<\/li>\n\n\n\n<li><strong>G<\/strong> = most general hypothesis (matches everything)<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>Step 2 \u2013 Process each training example:<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>When the example is Positive (Yes)<\/strong><\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Adjust <strong>S<\/strong> so it becomes just general enough to include this example.<\/li>\n\n\n\n<li>Remove from <strong>G<\/strong> any hypothesis that does not include this example.<\/li>\n<\/ol>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>When the example is Negative (No)<\/strong><\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Remove from <strong>S<\/strong> any hypothesis that still includes this example.<\/li>\n\n\n\n<li>Specialize each hypothesis in <strong>G<\/strong> that includes this example, just enough to exclude it, while still including all positive examples so far.<\/li>\n\n\n\n<li>Remove any hypotheses from <strong>G<\/strong> that are more specific than others or duplicate.<\/li>\n<\/ol>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>Step 3 \u2013 Completion<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>After all examples are processed, the version space is the set of hypotheses between <strong>S<\/strong> and <strong>G<\/strong>.<\/li>\n\n\n\n<li><strong>S<\/strong> represents the narrowest possible rule consistent with the data.<\/li>\n\n\n\n<li><strong>G<\/strong> represents the broadest possible rule consistent with the data.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-gallery has-nested-images columns-default is-cropped wp-block-gallery-2 is-layout-flex wp-block-gallery-is-layout-flex\">\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"718\" height=\"530\" data-id=\"2098\" src=\"https:\/\/cyberenlightener.com\/wp-content\/uploads\/2025\/08\/5.jpg\" alt=\"\" class=\"wp-image-2098\" srcset=\"https:\/\/cyberenlightener.com\/wp-content\/uploads\/2025\/08\/5.jpg 718w, https:\/\/cyberenlightener.com\/wp-content\/uploads\/2025\/08\/5-300x221.jpg 300w\" sizes=\"auto, (max-width: 718px) 100vw, 718px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"701\" height=\"539\" data-id=\"2099\" src=\"https:\/\/cyberenlightener.com\/wp-content\/uploads\/2025\/08\/6.jpg\" alt=\"\" class=\"wp-image-2099\" srcset=\"https:\/\/cyberenlightener.com\/wp-content\/uploads\/2025\/08\/6.jpg 701w, https:\/\/cyberenlightener.com\/wp-content\/uploads\/2025\/08\/6-300x231.jpg 300w\" sizes=\"auto, (max-width: 701px) 100vw, 701px\" \/><\/figure>\n<\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<figure class=\"wp-block-gallery has-nested-images columns-default is-cropped wp-block-gallery-3 is-layout-flex wp-block-gallery-is-layout-flex\">\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"721\" height=\"507\" data-id=\"2101\" src=\"https:\/\/cyberenlightener.com\/wp-content\/uploads\/2025\/08\/7.jpg\" alt=\"\" class=\"wp-image-2101\" srcset=\"https:\/\/cyberenlightener.com\/wp-content\/uploads\/2025\/08\/7.jpg 721w, https:\/\/cyberenlightener.com\/wp-content\/uploads\/2025\/08\/7-300x211.jpg 300w\" sizes=\"auto, (max-width: 721px) 100vw, 721px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"710\" height=\"362\" data-id=\"2100\" src=\"https:\/\/cyberenlightener.com\/wp-content\/uploads\/2025\/08\/8.jpg\" alt=\"\" class=\"wp-image-2100\" srcset=\"https:\/\/cyberenlightener.com\/wp-content\/uploads\/2025\/08\/8.jpg 710w, https:\/\/cyberenlightener.com\/wp-content\/uploads\/2025\/08\/8-300x153.jpg 300w\" sizes=\"auto, (max-width: 710px) 100vw, 710px\" \/><\/figure>\n<\/figure>\n","protected":false},"excerpt":{"rendered":"<p>\ud83c\udf93 Tutorial: Introduction to Machine Learning \u2013 Learning Paradigms \u2013 PAC Learning \ud83e\udde0 1. What is Machine Learning? Machine Learning (ML) is a subfield of artificial intelligence (AI) that focuses on building systems that learn from data to make decisions or predictions without being explicitly programmed. Arthur Samuel&#8217;s definition (1959): \u201cMachine Learning is the field [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"class_list":["post-1824","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/cyberenlightener.com\/index.php?rest_route=\/wp\/v2\/pages\/1824","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/cyberenlightener.com\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/cyberenlightener.com\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/cyberenlightener.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/cyberenlightener.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1824"}],"version-history":[{"count":10,"href":"https:\/\/cyberenlightener.com\/index.php?rest_route=\/wp\/v2\/pages\/1824\/revisions"}],"predecessor-version":[{"id":2102,"href":"https:\/\/cyberenlightener.com\/index.php?rest_route=\/wp\/v2\/pages\/1824\/revisions\/2102"}],"wp:attachment":[{"href":"https:\/\/cyberenlightener.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1824"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}