Large Scale Optimization Methods For Machine Learning

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Large Scale Optimization Methods For Machine Learning

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Author : Shuai Zheng
language : en
Publisher:
Release Date : 2019

Large Scale Optimization Methods For Machine Learning written by Shuai Zheng and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with categories.

Optimization Methods For Large Scale Problems And Applications To Machine Learning

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Author : Luca Bravi
language : en
Publisher:
Release Date : 2016

Optimization Methods For Large Scale Problems And Applications To Machine Learning written by Luca Bravi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with categories.

Stochastic Optimization For Large Scale Machine Learning

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Author : Vinod Kumar Chauhan
language : en
Publisher: CRC Press
Release Date : 2021-11-18

Stochastic Optimization For Large Scale Machine Learning written by Vinod Kumar Chauhan and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-18 with Computers categories.

Advancements in the technology and availability of data sources have led to the `Big Data' era. Working with large data offers the potential to uncover more fine-grained patterns and take timely and accurate decisions, but it also creates a lot of challenges such as slow training and scalability of machine learning models. One of the major challenges in machine learning is to develop efficient and scalable learning algorithms, i.e., optimization techniques to solve large scale learning problems. Stochastic Optimization for Large-scale Machine Learning identifies different areas of improvement and recent research directions to tackle the challenge. Developed optimisation techniques are also explored to improve machine learning algorithms based on data access and on first and second order optimisation methods. Key Features: Bridges machine learning and Optimisation. Bridges theory and practice in machine learning. Identifies key research areas and recent research directions to solve large-scale machine learning problems. Develops optimisation techniques to improve machine learning algorithms for big data problems. The book will be a valuable reference to practitioners and researchers as well as students in the field of machine learning.

Large Scale Optimization Methods For Data Science Applications

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Author : Haihao Lu (Ph.D.)
language : en
Publisher:
Release Date : 2019

Large Scale Optimization Methods For Data Science Applications written by Haihao Lu (Ph.D.) and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with categories.

In this thesis, we present several contributions of large scale optimization methods with the applications in data science and machine learning. In the first part, we present new computational methods and associated computational guarantees for solving convex optimization problems using first-order methods. We consider general convex optimization problem, where we presume knowledge of a strict lower bound (like what happened in empirical risk minimization in machine learning). We introduce a new functional measure called the growth constant for the convex objective function, that measures how quickly the level sets grow relative to the function value, and that plays a fundamental role in the complexity analysis. Based on such measure, we present new computational guarantees for both smooth and non-smooth convex optimization, that can improve existing computational guarantees in several ways, most notably when the initial iterate is far from the optimal solution set. The usual approach to developing and analyzing first-order methods for convex optimization always assumes that either the gradient of the objective function is uniformly continuous (in the smooth setting) or the objective function itself is uniformly continuous. However, in many settings, especially in machine learning applications, the convex function is neither of them. For example, the Poisson Linear Inverse Model, the D-optimal design problem, the Support Vector Machine problem, etc. In the second part, we develop a notion of relative smoothness, relative continuity and relative strong convexity that is determined relative to a user-specified "reference function" (that should be computationally tractable for algorithms), and we show that many differentiable convex functions are relatively smooth or relatively continuous with respect to a correspondingly fairly-simple reference function. We extend the mirror descent algorithm to our new setting, with associated computational guarantees. Gradient Boosting Machine (GBM) introduced by Friedman is an extremely powerful supervised learning algorithm that is widely used in practice -- it routinely features as a leading algorithm in machine learning competitions such as Kaggle and the KDDCup. In the third part, we propose the Randomized Gradient Boosting Machine (RGBM) and the Accelerated Gradient Boosting Machine (AGBM). RGBM leads to significant computational gains compared to GBM, by using a randomization scheme to reduce the search in the space of weak-learners. AGBM incorporate Nesterov's acceleration techniques into the design of GBM, and this is the first GBM type of algorithm with theoretically-justified accelerated convergence rate. We demonstrate the effectiveness of RGBM and AGBM over GBM in obtaining a model with good training and/or testing data fidelity..

Large Scale Convex Optimization

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Author : Ernest K. Ryu
language : en
Publisher: Cambridge University Press
Release Date : 2022-12-01

Large Scale Convex Optimization written by Ernest K. Ryu and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-12-01 with Mathematics categories.

Starting from where a first course in convex optimization leaves off, this text presents a unified analysis of first-order optimization methods – including parallel-distributed algorithms – through the abstraction of monotone operators. With the increased computational power and availability of big data over the past decade, applied disciplines have demanded that larger and larger optimization problems be solved. This text covers the first-order convex optimization methods that are uniquely effective at solving these large-scale optimization problems. Readers will have the opportunity to construct and analyze many well-known classical and modern algorithms using monotone operators, and walk away with a solid understanding of the diverse optimization algorithms. Graduate students and researchers in mathematical optimization, operations research, electrical engineering, statistics, and computer science will appreciate this concise introduction to the theory of convex optimization algorithms.

Large Scale Optimization Methods

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Author : Nuri Denizcan Vanli
language : en
Publisher:
Release Date : 2021

Large Scale Optimization Methods written by Nuri Denizcan Vanli and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with categories.

Large-scale optimization problems appear quite frequently in data science and machine learning applications. In this thesis, we show the efficiency of coordinate descent (CD) and mirror descent (MD) methods in solving large-scale optimization problems.

Optimization For Learning And Control

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Author : Anders Hansson
language : en
Publisher: John Wiley & Sons
Release Date : 2023-06-20

Optimization For Learning And Control written by Anders Hansson and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-06-20 with Technology & Engineering categories.

Optimization for Learning and Control Comprehensive resource providing a masters’ level introduction to optimization theory and algorithms for learning and control Optimization for Learning and Control describes how optimization is used in these domains, giving a thorough introduction to both unsupervised learning, supervised learning, and reinforcement learning, with an emphasis on optimization methods for large-scale learning and control problems. Several applications areas are also discussed, including signal processing, system identification, optimal control, and machine learning. Today, most of the material on the optimization aspects of deep learning that is accessible for students at a Masters’ level is focused on surface-level computer programming; deeper knowledge about the optimization methods and the trade-offs that are behind these methods is not provided. The objective of this book is to make this scattered knowledge, currently mainly available in publications in academic journals, accessible for Masters’ students in a coherent way. The focus is on basic algorithmic principles and trade-offs. Optimization for Learning and Control covers sample topics such as: Optimization theory and optimization methods, covering classes of optimization problems like least squares problems, quadratic problems, conic optimization problems and rank optimization. First-order methods, second-order methods, variable metric methods, and methods for nonlinear least squares problems. Stochastic optimization methods, augmented Lagrangian methods, interior-point methods, and conic optimization methods. Dynamic programming for solving optimal control problems and its generalization to reinforcement learning. How optimization theory is used to develop theory and tools of statistics and learning, e.g., the maximum likelihood method, expectation maximization, k-means clustering, and support vector machines. How calculus of variations is used in optimal control and for deriving the family of exponential distributions. Optimization for Learning and Control is an ideal resource on the subject for scientists and engineers learning about which optimization methods are useful for learning and control problems; the text will also appeal to industry professionals using machine learning for different practical applications.

Large Scale Optimization Methods For Metric And Kernel Learning

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Author : Prateek Jain
language : en
Publisher:
Release Date : 2009

Large Scale Optimization Methods For Metric And Kernel Learning written by Prateek Jain and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with categories.

A large number of machine learning algorithms are critically dependent on the underlying distance/metric/similarity function. Learning an appropriate distance function is therefore crucial to the success of many methods. The class of distance functions that can be learned accurately is characterized by the amount and type of supervision available to the particular application. In this thesis, we explore a variety of such distance learning problems using different amounts/types of supervision and provide efficient and scalable algorithms to learn appropriate distance functions for each of these problems. First, we propose a generic regularized framework for Mahalanobis metric learning and prove that for a wide variety of regularization functions, metric learning can be used for efficiently learning a kernel function incorporating the available side-information. Furthermore, we provide a method for fast nearest neighbor search using the learned distance/kernel function. We show that a variety of existing metric learning methods are special cases of our general framework. Hence, our framework also provides a kernelization scheme and fast similarity search scheme for such methods. Second, we consider a variation of our standard metric learning framework where the side-information is incremental, streaming and cannot be stored. For this problem, we provide an efficient online metric learning algorithm that compares favorably to existing methods both theoretically and empirically. Next, we consider a contrasting scenario where the amount of supervision being provided is extremely small compared to the number of training points. For this problem, we consider two different modeling assumptions: 1) data lies on a low-dimensional linear subspace, 2) data lies on a low-dimensional non-linear manifold. The first assumption, in particular, leads to the problem of matrix rank minimization over polyhedral sets, which is a problem of immense interest in numerous fields including optimization, machine learning, computer vision, and control theory. We propose a novel online learning based optimization method for the rank minimization problem and provide provable approximation guarantees for it. The second assumption leads to our geometry-aware metric/kernel learning formulation, where we jointly model the metric/kernel over the data along with the underlying manifold. We provide an efficient alternating minimization algorithm for this problem and demonstrate its wide applicability and effectiveness by applying it to various machine learning tasks such as semi-supervised classification, colored dimensionality reduction, manifold alignment etc. Finally, we consider the task of learning distance functions under no supervision, which we cast as a problem of learning disparate clusterings of the data. To this end, we propose a discriminative approach and a generative model based approach and we provide efficient algorithms with convergence guarantees for both the approaches.

Exploiting Structure In Large Scale Optimization For Machine Learning

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Author : Cho-Jui Hsieh
language : en
Publisher:
Release Date : 2015

Exploiting Structure In Large Scale Optimization For Machine Learning written by Cho-Jui Hsieh and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with categories.

With an immense growth of data, there is a great need for solving large-scale machine learning problems. Classical optimization algorithms usually cannot scale up due to huge amount of data and/or model parameters. In this thesis, we will show that the scalability issues can often be resolved by exploiting three types of structure in machine learning problems: problem structure, model structure, and data distribution. This central idea can be applied to many machine learning problems. In this thesis, we will describe in detail how to exploit structure for kernel classification and regression, matrix factorization for recommender systems, and structure learning for graphical models. We further provide comprehensive theoretical analysis for the proposed algorithms to show both local and global convergent rate for a family of in-exact first-order and second-order optimization methods.

Optimization Methods For Structured Machine Learning Problems

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Author : Nikolaos Tsipinakis
language : en
Publisher:
Release Date : 2019

Optimization Methods For Structured Machine Learning Problems written by Nikolaos Tsipinakis and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with categories.

Solving large-scale optimization problems lies at the core of modern machine learning applications. Unfortunately, obtaining a sufficiently accurate solution quickly is a difficult task. However, the problems we consider in many machine learning applications exhibit a particular structure. In this thesis we study optimization methods and improve their convergence behavior by taking advantage of such structures. In particular, this thesis constitutes of two parts: In the first part of the thesis, we consider the Temporal Difference learning (TD) problem in off-line Reinforcement Learning (RL). In off-line RL, it is typically the case that the number of samples is small compared to the number of features. Therefore, recent advances have focused on efficient algorithms to incorporate feature selection via `1-regularization which effectively avoids over-fitting. Unfortunately, the TD optimization problem reduces to a fixed-point problem where convexity of the objective function cannot be assumed. Further, it remains unclear whether existing algorithms have the ability to offer good approximations for the task of policy evaluation and improvement (either they are non-convergent or do not solve the fixed-point problem). In this part of the thesis, we attempt to solve the `1- regularized fixed-point problem with the help of Alternating Direction Method of Multipliers (ADMM) and we argue that the proposed method is well suited to the structure of the aforementioned fixed-point problem. In the second part of the thesis, we study multilevel methods for large-scale optimization and extend their theoretical analysis to self-concordant functions. In particular, we address the following issues that arise in the analysis of second-order optimization methods based either on sampling, randomization or sketching: (a) the analysis of the iterates is not scale-invariant and (b) lack of global fast convergence rates without restrictive assumptions. We argue that, with the analysis undertaken in this part of the thesis, the analysis of randomized second-order methods can be considered on-par with the analysis of the classical Newton method. Further, we demonstrate how our proposed method can exploit typical spectral structures of the Hessian that arise in machine learning applications to further improve the convergence rates.