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Statistics Meets Optimization: Compu...

Yang, Fan.

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Statistics Meets Optimization: Computational Guarantees for Statistical Learning Algorithms.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Statistics Meets Optimization: Computational Guarantees for Statistical Learning Algorithms./
作者:	Yang, Fan.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, : 2018,
面頁冊數:	141 p.
附註:	Source: Dissertation Abstracts International, Volume: 80-08(E), Section: B.
Contained By:	Dissertation Abstracts International80-08B(E).
標題:	Electrical engineering. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10931587
ISBN:	9781392035030

Statistics Meets Optimization: Computational Guarantees for Statistical Learning Algorithms.
Yang, Fan.

Statistics Meets Optimization: Computational Guarantees for Statistical Learning Algorithms. - Ann Arbor : ProQuest Dissertations & Theses, 2018 - 141 p.

Source: Dissertation Abstracts International, Volume: 80-08(E), Section: B.

Thesis (Ph.D.)--University of California, Berkeley, 2018.

Modern technological advances have prompted massive scale data collection in many modern fields such as artificial intelligence, and traditional sciences alike. This has led to an increasing need for scalable machine learning algorithms and statistical methods to draw conclusions about the world. In all data-driven procedures, the data scientist faces the following fundamental questions: How should I design the learning algorithm and how long should I run it? Which samples should I collect for training and how many are sufficient to generalize conclusions to unseen data? These questions relate to statistical and computational properties of both the data and the algorithm. This thesis explores their role in the areas of non-convex optimization, non-parametric estimation, active learning and multiple testing.

ISBN: 9781392035030Subjects--Topical Terms:

649834
Electrical engineering.

Statistics Meets Optimization: Computational Guarantees for Statistical Learning Algorithms.
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520 $a Modern technological advances have prompted massive scale data collection in many modern fields such as artificial intelligence, and traditional sciences alike. This has led to an increasing need for scalable machine learning algorithms and statistical methods to draw conclusions about the world. In all data-driven procedures, the data scientist faces the following fundamental questions: How should I design the learning algorithm and how long should I run it? Which samples should I collect for training and how many are sufficient to generalize conclusions to unseen data? These questions relate to statistical and computational properties of both the data and the algorithm. This thesis explores their role in the areas of non-convex optimization, non-parametric estimation, active learning and multiple testing.
520 $a In the first part, we provide insights of different flavor concerning the interplay between statistical and computational properties of first-order type methods on common estimation procedures. The expectation-maximization (EM) algorithm estimates parameters of a latent variable model by running a first-order type method on a non-convex landscape. We identify and characterize a general class of Hidden Markov Models for which linear convergence of EM to a statistically optimal point is provable for a large initialization radius. For non-parametric estimation problems, functional gradient descent type (also called boosting) algorithms are used to estimate the best fit in infinite dimensional function spaces. We develop a new proof technique showing that early stopping the algorithm instead may also yield an optimal estimator without explicit regularization. In fact, the same key quantities (localized complexities) are underlying both traditional penalty-based and algorithmic regularization.
520 $a In the second part of the thesis, we explore how data collected adaptively with a constantly updated estimation can lead to significant reduction in sample complexity for multiple hypothesis testing problems. In particular, we show how adaptive strategies can be used to simultaneously control the false discovery rate over multiple tests and return the best alternative (among many) for each test with optimal sample complexity in an online manner.
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