{"id":16641,"date":"2020-01-14T21:41:15","date_gmt":"2020-01-15T02:41:15","guid":{"rendered":"http:\/\/bangla.salearningschool.com\/recent-posts\/misc-optimization-machine-learning\/"},"modified":"2020-02-08T09:42:10","modified_gmt":"2020-02-08T14:42:10","slug":"misc-optimization-machine-learning","status":"publish","type":"post","link":"http:\/\/bangla.sitestree.com\/?p=16641","title":{"rendered":"Misc. Optimization. Machine Learning"},"content":{"rendered":"

“What is machine learning optimization?<\/h1>\n

Optimization<\/strong> is the most essential ingredient in the recipe of machine learning<\/strong> algorithms. It starts with defining some kind of loss function\/cost function and ends with minimizing the it using one or the other optimization<\/strong> routine.Sep 5, 2018″
\nhttps:\/\/towardsdatascience.com\/demystifying-optimizations-for-machine-learning-c6c6405d3eea<\/a><\/p>\n

Ordered vector space<\/h1>\n

“<\/strong><\/em>Given a vector space V<\/em> over the real numbers<\/a> R<\/strong> and a preorder<\/a> \u2264 on the set<\/a> V<\/em>, the pair (V<\/em>, \u2264) is called a preordered vector space<\/strong> if for all x<\/em>, y<\/em>, z<\/em> in V<\/em> and 0 \u2264 \u03bb<\/em> in R<\/strong> the following two axioms are satisfied<\/p>\n

    \n
  1. x<\/em> \u2264 y<\/em> implies x<\/em> + z<\/em> \u2264 y<\/em> + z<\/em><\/li>\n
  2. y<\/em> \u2264 x<\/em> implies \u03bby<\/em> \u2264 \u03bbx<\/em>.<\/li>\n<\/ol>\n

    If \u2264 is a partial order<\/a>, (V<\/em>, \u2264) is called an ordered vector space<\/strong>. The two axioms imply that translations<\/a> and positive homotheties<\/a> are automorphisms of the order structure and the mapping x<\/em> \u21a6 \u2212x<\/em> is an isomorphism to the dual order structure<\/a>. Ordered vector spaces are ordered groups<\/a> under their addition operation.“<\/strong><\/em>
    \n    https:\/\/en.wikipedia.org\/wiki\/Ordered_vector_space<\/a><\/p>\n

    Algebra<\/a> > Vector Algebra<\/a> ><\/p>\n

    Vector Ordering<\/h1>\n

    “If the first nonzero<\/a> component of the vector difference \"A-B\" is \">0\", then \"A\u227bB\". If the first nonzero<\/a> component of \"A-B\" is \"<0\", then \"A\u227aB\".”<\/p>\n

    http:\/\/mathworld.wolfram.com\/VectorOrdering.html<\/a><\/p>\n

    Vectors:<\/p>\n

    https:\/\/www.mathsisfun.com\/algebra\/vectors.html<\/a><\/p>\n

    Vector: Dot Product: Costheta<\/p>\n

    https:\/\/www.mathsisfun.com\/algebra\/vectors-dot-product.html<\/a><\/p>\n

    Vector Cross Product
    \n    https:\/\/www.mathsisfun.com\/algebra\/vectors-cross-product.html<\/a><\/p>\n

    “Optimization lies at the heart of machine learning. Most machine learning problems reduce to optimization problems.”
    \n    https:\/\/www.quora.com\/What-is-the-relationship-between-machine-learning-and-mathematical-optimization<\/a><\/p>\n

    “Why is optimization important?
    \nThe purpose of optimization<\/strong> is to achieve the \u201cbest\u201d design relative to a set of prioritized criteria or constraints. These include maximizing factors such as productivity, strength, reliability, longevity, efficiency, and utilization. … This decision-making process is known as optimization<\/strong>.”
    \n    https:\/\/digitalcommons.usu.edu\/cgi\/viewcontent.cgi?article=1031&context=ncete_publications<\/a><\/p>\n

    *** . *** . ***<\/strong><\/em>
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    \n<\/em>
    \nBSc. Eng. in Comp. Sc. & Eng. (BUET)<\/strong><\/em>
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    \nMSc. in Data Science and Analytics (Ryerson University, Canada)<\/strong><\/em>
    \nLinkedin<\/strong>:     https:\/\/ca.linkedin.com\/in\/sayedjustetc<\/a>
    \n<\/em><\/p>\n

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    \n<\/em><\/p>\n","protected":false},"excerpt":{"rendered":"

    “What is machine learning optimization? Optimization is the most essential ingredient in the recipe of machine learning algorithms. It starts with defining some kind of loss function\/cost function and ends with minimizing the it using one or the other optimization routine.Sep 5, 2018″ https:\/\/towardsdatascience.com\/demystifying-optimizations-for-machine-learning-c6c6405d3eea Ordered vector space “Given a vector space V over the real … <\/p>\n

    Continue reading<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[1910,1908,182],"tags":[],"class_list":["post-16641","post","type-post","status-publish","format-standard","hentry","category-ai-ml-ds-rl-dl-nn-nlp-data-mining-optimization","category-math-and-statistics-for-data-science-and-engineering","category---blog","item-wrap"],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack-related-posts":[{"id":16701,"url":"http:\/\/bangla.sitestree.com\/?p=16701","url_meta":{"origin":16641,"position":0},"title":"Misc. Math. Data Science. Machine Learning. Optimization. Vector, PCA, Basis, Covariance","author":"Sayed","date":"January 30, 2020","format":false,"excerpt":"Misc. Math. Data Science. Machine Learning. Optimization. Vector, PCA, Basis, Covariance Orthonormality: Orthonormal Vectors \"In linear algebra, two vectors in an inner product space are orthonormal if they are orthogonal and unit vectors. A set of vectors form an orthonormal set if all vectors in the set are mutually orthogonal\u2026","rel":"","context":"In "AI ML DS RL DL NN NLP Data Mining Optimization"","block_context":{"text":"AI ML DS RL DL NN NLP Data Mining Optimization","link":"http:\/\/bangla.sitestree.com\/?cat=1910"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/bangla.sitestree.com\/wp-content\/uploads\/2020\/01\/image-8-e1580436936625.png?resize=350%2C200","width":350,"height":200},"classes":[]},{"id":63958,"url":"http:\/\/bangla.sitestree.com\/?p=63958","url_meta":{"origin":16641,"position":1},"title":"Misc: Optimization: Machine Learning: Data Science Resources","author":"Sayed","date":"June 3, 2021","format":false,"excerpt":"http:\/\/web.mit.edu\/15.053\/www\/AMP-Chapter-09.pdf https:\/\/www.cs.cmu.edu\/~anupamg\/adv-approx\/lecture14.pdf http:\/\/bangla.salearningschool.com\/recent-posts\/misc-optimization\/ https:\/\/www.futurelearn.com\/info\/courses\/maths-linear-quadratic-relations\/0\/steps\/12128 https:\/\/www.mathsisfun.com\/algebra\/systems-linear-equations-matrices.html https:\/\/www.wolframalpha.com\/input\/?i=subspace https:\/\/www.cse.iitk.ac.in\/users\/rmittal\/prev_course\/s14\/notes\/lec3.pdf https:\/\/observablehq.com\/@eliaskal\/point-combinations-linear-conic-affine-convex https:\/\/www.cse.iitk.ac.in\/users\/rmittal\/prev_course\/s14\/course_s14.html http:\/\/bangla.salearningschool.com\/recent-posts\/misc-math-might-relate-to-optimization\/ http:\/\/bangla.salearningschool.com\/recent-posts\/part-x-engineering-optimization-mathematical-optimization\/ https:\/\/www.dr-eriksen.no\/teaching\/GRA6035\/2010\/lecture4.pdf https:\/\/www.mathsisfun.com\/calculus\/concave-up-down-convex.html https:\/\/www-ljk.imag.fr\/membres\/Anatoli.Iouditski\/cours\/convex\/chapitre_3.pdf http:\/\/bangla.salearningschool.com\/recent-posts\/optimization-and-linear-algebra-math-from-the-internet\/ https:\/\/www.thestudentroom.co.uk\/showthread.php?t=1247928 https:\/\/en.wikipedia.org\/wiki\/Hessian_matrix https:\/\/en.wikipedia.org\/wiki\/Newton%27s_method_in_optimization https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/9781118733639.app6 http:\/\/bangla.salearningschool.com\/recent-posts\/optimization-and-linear-algebra-math-from-the-internet\/ https:\/\/en.wikipedia.org\/wiki\/Interior-point_method https:\/\/web.stanford.edu\/~boyd\/papers\/rt_cvx_sig_proc.html Must Read https:\/\/www.microsoft.com\/en-us\/research\/wp-content\/uploads\/2016\/02\/ivantash-optimization_methods_and_their_applications_in_dsp.pdf https:\/\/www.researchgate.net\/publication\/269211254_The_analysis_and_optimization_algorithms_of_the_electronic_circuits_design good one http:\/\/www.bcamath.org\/documentos_public\/courses\/Nogales_2012-13_02_18-22.pdf https:\/\/en.wikipedia.org\/wiki\/Convex_analysis https:\/\/www.khanacademy.org\/search?page_search_query=Optimization%20problems%20(calculus) http:\/\/bangla.salearningschool.com\/recent-posts\/overview-on-optimization-concepts-from-the-internet\/ http:\/\/bangla.salearningschool.com\/recent-posts\/misc-optimization-machine-learning\/ http:\/\/bangla.salearningschool.com\/recent-posts\/misc-math-data-science-machine-learning-optimization-vector-pca-basis-covariance\/ https:\/\/www.mathsisfun.com\/algebra\/matrix-inverse-row-operations-gauss-jordan.html http:\/\/bangla.salearningschool.com\/recent-posts\/misc-math-for-data-science-engineering-and-or-optimization\/","rel":"","context":"In "\u09ac\u09cd\u09b2\u0997 \u0964 Blog"","block_context":{"text":"\u09ac\u09cd\u09b2\u0997 \u0964 Blog","link":"http:\/\/bangla.sitestree.com\/?cat=182"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":16689,"url":"http:\/\/bangla.sitestree.com\/?p=16689","url_meta":{"origin":16641,"position":2},"title":"Misc. Math for Data Science, Engineering, and\/or Optimization","author":"Sayed","date":"January 28, 2020","format":false,"excerpt":"What is the Inverse of a Matrix? https:\/\/www.mathsisfun.com\/algebra\/matrix-inverse.html What is Norm? \"In linear algebra, functional analysis, and related areas of mathematics, a norm is a function that satisfies certain properties pertaining to scalability and additivity, and assigns a strictly positive real number to each vector in a vector space over\u2026","rel":"","context":"In "AI ML DS RL DL NN NLP Data Mining Optimization"","block_context":{"text":"AI ML DS RL DL NN NLP Data Mining Optimization","link":"http:\/\/bangla.sitestree.com\/?cat=1910"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":22124,"url":"http:\/\/bangla.sitestree.com\/?p=22124","url_meta":{"origin":16641,"position":3},"title":"search engine optimization and google webmaster tools #SEO","author":"Author-Check- Article-or-Video","date":"March 10, 2021","format":false,"excerpt":"From: http:\/\/sitestree.com\/?p=2621 Categories:SEOTags:search engine optimization, google webmaster, SEO Post Data:2015-10-19 00:51:51 Shop Online: https:\/\/www.ShopForSoul.com\/ (Big Data, Cloud, Security, Machine Learning): Courses: http:\/\/Training.SitesTree.com In Bengali: http:\/\/Bangla.SaLearningSchool.com http:\/\/SitesTree.com 8112223 Canada Inc.\/JustEtc: http:\/\/JustEtc.net (Software\/Web\/Mobile\/Big-Data\/Machine Learning) Shop Online: https:\/\/www.ShopForSoul.com\/ Medium: https:\/\/medium.com\/@SayedAhmedCanada","rel":"","context":"In "FromSitesTree.com"","block_context":{"text":"FromSitesTree.com","link":"http:\/\/bangla.sitestree.com\/?cat=1917"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":68337,"url":"http:\/\/bangla.sitestree.com\/?p=68337","url_meta":{"origin":16641,"position":4},"title":"bengali search engine optimization google webmaster tools #Bengali Literature","author":"Author-Check- Article-or-Video","date":"August 1, 2021","format":false,"excerpt":"From: http:\/\/sitestree.com\/?p=2616 Categories:Bengali LiteratureTags:Bengali, search engine optimization, google webmaster Post Data:2015-10-18 12:43:39 Shop Online: https:\/\/www.ShopForSoul.com\/ (Big Data, Cloud, Security, Machine Learning): Courses: http:\/\/Training.SitesTree.com In Bengali: http:\/\/Bangla.SaLearningSchool.com http:\/\/SitesTree.com 8112223 Canada Inc.\/JustEtc: http:\/\/JustEtc.net (Software\/Web\/Mobile\/Big-Data\/Machine Learning) Shop Online: https:\/\/www.ShopForSoul.com\/ Medium: https:\/\/medium.com\/@SayedAhmedCanada","rel":"","context":"In "FromSitesTree.com"","block_context":{"text":"FromSitesTree.com","link":"http:\/\/bangla.sitestree.com\/?cat=1917"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":16500,"url":"http:\/\/bangla.sitestree.com\/?p=16500","url_meta":{"origin":16641,"position":5},"title":"Overview on optimization concepts: From the Internet","author":"Sayed","date":"December 10, 2019","format":false,"excerpt":"Optimization Concepts: Convex sets: \"A convex set is a set of points such that, given any two points A, B in that set, the line AB joining them lies entirely within that set. Intuitively, this means that the set is connected (so that you can pass between any two points\u2026","rel":"","context":"In "AI ML DS RL DL NN NLP Data Mining Optimization"","block_context":{"text":"AI ML DS RL DL NN NLP Data Mining Optimization","link":"http:\/\/bangla.sitestree.com\/?cat=1910"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]}],"_links":{"self":[{"href":"http:\/\/bangla.sitestree.com\/index.php?rest_route=\/wp\/v2\/posts\/16641","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/bangla.sitestree.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/bangla.sitestree.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/bangla.sitestree.com\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"http:\/\/bangla.sitestree.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=16641"}],"version-history":[{"count":1,"href":"http:\/\/bangla.sitestree.com\/index.php?rest_route=\/wp\/v2\/posts\/16641\/revisions"}],"predecessor-version":[{"id":16652,"href":"http:\/\/bangla.sitestree.com\/index.php?rest_route=\/wp\/v2\/posts\/16641\/revisions\/16652"}],"wp:attachment":[{"href":"http:\/\/bangla.sitestree.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=16641"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/bangla.sitestree.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=16641"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/bangla.sitestree.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=16641"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}