Alex Cobb

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Demystify machine learning through computational engineering principles and applications in this two-course program from MIT ... Assess and respond to cost-accuracy tradeoffs in simulation and optimization, and make decisions about how to deploy computational resources. 0000002795 00000 n Whereas traditional machine learning makes use of features designed by human users or experts as a type of prior, representation learning tries to learn features from the data as well. I Equivalently, we can minimize log P(yjx; ).

Broadly speaking, Machine Learning refers to the automated identification of patterns in data. 0000013924 00000 n 0000114259 00000 n h�bb�f`b``��� LO Representation learning, such as deep learning, often requires us to deal with nonconvex optimization problems. The goal is to advance the theory and methods in machine learning where learning requires non-convex optimization. -`�Z����6S�ѹ�EY� )o��a���\�,-d-rw%[kk����M��T��4��^��V�q^1��X��tS�cK���J\��8`�19���=8^�*��t�, �t¢h.�d�{�OO�L��&q�SQ�/9�Rt�@��� ��b|���x���9m�M�Z���8{�چ�����2�8GQ.�O[/�b 9x�G���}0��c�,}}����d�ik��.��c�Xp�J����̊��*~UF8�I;��0S��u@w'ɶ���S���rV u�}vl�������Ţ�����X�`��4.v;��>����v���S���9-�~I�}]B��[�rl�}p��K����֧>W���\C.X��. Mathematical pro-gramming puts a premium on accuracy, speed, and robustness.

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Goal: minimize some loss function I For example, if we have some data (x;y), we may want to maximize P(yjx; ).

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C. E. Rasmussen & C. K. I. Williams, Gaussian Processes for Machine Learning, the MIT Press, 2006, ISBN … �M�Adɞ��" �Ad{�Ad"�Ad����&���퍼h~or��߷�v����9HG��E~��U���[�\\n�K6�EpL�hae?�R�s���Л�����>����� [HW+@����*��?�p3:�h���gĭ���3�Y�[�O5����ެ�(�� 0000114715 00000 n ߴ��x J/����� 0000003689 00000 n startxref Computer Science & Artificial Intelligence Laboratory. 0000065708 00000 n 0000137819 00000 n

0000100943 00000 n T� ��D��iO6`rR����[�dB m��!1#8��:*� �v{��.�$(���!��έ>C_�#%���� 0000159722 00000 n There is much more to this topic than will be covered in this class so you may be 0000049306 00000 n In this lecture, we will cover the basics of convex optimization as it applies to machine learning. Representation learning, such as deep learning, often requires us to deal with nonconvex optimization problems. Happy Birthday Yuri The single paper that made the largest impact on my PhD thesis. @�qٕ`��g2�_� N.����8�ow���� ��A�2��`s��� �)�@xJ �����0 ��޾`G���: ����\ �?�0'��@ %PDF-1.6 %���� 0000014058 00000 n If you would like to contact us about our work, please scroll down to the people section and click on Optimization for Machine Learning Editors: Suvrit Sra suvrit@gmail.com Max Planck Insitute for Biological Cybernetics 72076 Tu¨bingen, Germany Sebastian Nowozin nowozin@gmail.com Microsoft Research Cambridge, CB3 0FB, United Kingdom Stephen J. Wright swright@cs.uwisc.edu University of Wisconsin Madison, WI 53706 This is a draft containing only srachapter.tex and an abbreviated front … )+�R��h4��u�����ϯ^���ÿo_��B�_N�ίN>;}��7���)ON߼H��I'ޘA�prz��V\�����^ݬ7bPF[eW���->K���k���*�M��z�L�)����V>��W�V�C������Y�-����b��D΄�+h �6�{x��m��S�_k�m0���)c�[���T���Ư|D�շ+�Z%Fd�z%ҳ0�`�{�� ����${�:�-{�?�d�{�{F��O��Bk9(k@�N/@y��4*X����w���$.��a�o>�8��V�.��|@YM$>%i�L!>�ΪW�fi7���I�[��u�_�-.��{{(�O��'Ҁ�8���"N���3�7N&��-�e��G�����;��j���T��>��Lf�6F�J ��W��8}����>���M��Ы?�y�����b�m�!B������{磈��������7׉����z�"���*�������~j���$.�|�'w!5L>�9�]Ê��M�mP jB�B�M�Ґ��3� xG�㝉�@a 0000124149 00000 n

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192 67 0000066848 00000 n 0000004445 00000 n '���W�>��P��X]�O���3�@a � �wp���(��[)�K��!8�� pB��8��_��p�/����[�_�+(p�8 �`g���H1������ �����5�a�0�{�?濏X@��Cc5�? one of the group leads' people pages, where you can reach out to them directly. x��]�rd�q���>/gR;G��qnb�*��J��tR�(�]MiH��Y��װ+O�Lw��0. 0000048859 00000 n %PDF-1.2 Stochastic Optimization for Machine Learning Shai Shalev-Shwartz School of CS and Engineering, The Hebrew University of Jerusalem Nesterov’s 60 Birthday, February 2016 Shalev-Shwartz (HU) SO for ML Nesterov’2016 1 / 38.

Whereas traditional machine learning makes use of features designed by human users or experts as a type of prior, representation learning tries to learn features from the data as well. 0000113731 00000 n from the machine learning and optimization perspectives can be quite different. 18.657: Mathematics of Machine Learning Lecturer: Philippe Rigollet Lecture 11 Scribe: Kevin Li Oct. 14, 2015. 0000014325 00000 n trailer

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�������lˈ��V�I�ޖ�>F��_~��C�. 0 As such it has been a fertile ground for new statistical and algorithmic developments. 0000002830 00000 n 0000138609 00000 n 0000089441 00000 n +�5�7 Practice real-world … 0000067165 00000 n 0000001669 00000 n CONVEX OPTIMIZATION FOR MACHINE LEARNING. 0000090076 00000 n 5 0 obj 0000102720 00000 n

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0000014942 00000 n MIT Computer Science & Artificial Intelligence Lab, http://lis.csail.mit.edu/new/research.php. 0000100856 00000 n 0000136926 00000 n %%EOF Despite the recent great practical success of deep learning, the lack of the theoretical understanding of nonconvex optimization in deep learning has been a major challenge to the achievement of reliability and verifiability of systems with deep learning modules, and to the rigorous study of many proposed methods in deep learning. As the amount of available data is increasing, we are facing a rise in the importance of machine learning itself, and also in the demand of machine learning methods that are more adaptable to the data at hand, such as representation learning. 0000004881 00000 n 0000101601 00000 n %�쏢 Primal-dual subgradient methods for convex problems. By analyzing the properties of nonconvex optimization in machine learning, it is aimed to propose new machine learning models and optimization methods. 258 0 obj <>stream 0000003303 00000 n

�!`(��u{����Z ]O0�c�?x �/�w�?��@;�`� h �p�����Z�/ u�er�Ð� _�d�4�]:��� ! ?$�|X�L��ߗ�ۓ!|�B��F�*�����s���O4)�MpE���T�ñ.�Ϙ�{����]g�y�hqhX���hwM�����i%�`�\~���wD�������Iu�$��"]S��[ K��I��$�]� 0000003556 00000 n Overview of Optimization for Machine Learning Often in machine learning we are interested in learning the parameters of a model.

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xڍ�P��6�tw��,� )��,��.�KII�� H� �� �( ���tww�����7�3�>��s��ܳ�άgȧ��� >A~�@I��P ���@!\vv#������ ���R��P��H�2�4ԆA>� Aa������%�2�yK�A�G�6? xref <]/Prev 345972/XRefStm 2299>> Machine learning, however, is not simply a consumer of optimization technology but a rapidly evolving field that is itself generating new optimization ideas. 0000137220 00000 n 0000014190 00000 n 0000076789 00000 n 0000027206 00000 n 0000076658 00000 n <> 2. stream

*)��AZZFɠA�5聆0����@�F����������Y,+�R%�m�U�f�n�aX�#�C�aU�C&�gCVv��T X���� �T���&���A�A����M�.��R��M��I�Gx�R?H#��q�f��1�1f0?������@�Ɔ�9L'�5�x$������@�����.����?�%v ����SH320�Y�Ue2�_���2� ���� Since generalization is the bottom line in machine learning and training is normally done off-line, accuracy and small speed im-provements are of little concern in machine learning. Understand optimization techniques and their fundamental role in machine learning.

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0000102304 00000 n I We can also minimize other sorts of loss functions log can help for numerical reasons. 0000066171 00000 n 0000002761 00000 n

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