Michael I. Jordan

Bio: Michael I. Jordan is an academic researcher from University of California, Berkeley. The author has contributed to research in topics: Computer science & Inference. The author has an hindex of 176, co-authored 1016 publications receiving 216204 citations. Previous affiliations of Michael I. Jordan include Stanford University & Princeton University.

Perseus: A Simple High-Order Regularization Method for Variational Inequalities

Abstract: This paper settles an open and challenging question pertaining to the design of simple high-order regularization methods for solving smooth and monotone variational inequalities (VIs). A VI involves finding x ⋆ ∈ X such that h F ( x ) , x − x ⋆ i ≥ 0 for all x ∈ X and we consider the setting where F : R d 7→ R d is smooth with up to ( p − 1) th -order derivatives. For the case of p = 2, Nesterov [2006] extended the cubic regularized Newton’s method to VIs with a global rate of O ( ǫ − 1 ). Monteiro and Svaiter [2012] proposed another second-order method which achieved an improved rate of O ( ǫ − 2 / 3 log(1 /ǫ )), but this method required a nontrivial binary search procedure as an inner loop. High-order methods based on similar binary search procedures have been further developed and shown to achieve a rate of O ( ǫ − 2 / ( p +1) log(1 /ǫ )) [Bullins and Lai, 2020, Lin and Jordan, 2021b, Jiang and Mokhtari, 2022]. However, such search procedure can be computationally prohibitive in practice [Nesterov, 2018] and the problem of finding a simple high-order regularization methods remains as an open and challenging question in optimization theory. We propose a p th -order method which does not require any binary search scheme and is guaranteed to converge to a weak solution with a global rate of O ( ǫ − 2 / ( p +1) ). A version with restarting attains a global linear and local superlinear convergence rate for smooth and strongly monotone VIs. Further, our method achieves a global rate of O ( ǫ − 2 /p ) for solving smooth and non-monotone VIs satisfying the Minty condition; moreover, the restarted version again attains a global linear and local superlinear convergence rate if the strong Minty condition holds.

Sampling User Executions for Bug Isolation

Abstract: Many computer scientists think of a program as either correct (i.e. it meets some specification) or incorrect (i.e. it does not meet some specification). But industrial software development is as much about economics as computer science. Software quality is a monetary balancing act among engineers’ salaries, time to market, user expectations, and other business concerns. We ship software when it seems correct enough to neither embarrass us nor alienate users. We ship software with known bugs that are not worth fixing, and users uncover new bugs that we never imagined. Practitioners clearly need something other than a Boolean notion of correctness, but such a notion has been difficult to quantify. In-house testing can only guess at field usage patterns, and poor guesses can leave users in bad shape. An obscure, low-priority bug that was difficult to reproduce in the testing lab may turn out to affect large numbers of users on a regular basis. Technical support channels provide one way for post-deployment feedback to reach engineers, but traditionally these mechanisms have been informal and overly dependent on human intervention. Widespread Internet connectivity makes possible a radical change to this situation. For the first time it is feasible to directly observe the reality of a software system’s deployment. Through sheer numbers, the user community brings far more resources to bear on exercising a piece of software than could possibly be provided by the software’s authors. Coupled with an instrumentation and reporting infrastructure, these users can potentially replace guesswork with real triage, directing scarce engineering resources to those areas that benefit the most people.

Stochastic Gradient and Langevin Processes

Abstract: We prove quantitative convergence rates at which discrete Langevin-like processes converge to the invariant distribution of a related stochastic differential equation We study the setup where the additive noise can be non-Gaussian and state-dependent and the potential function can be non-convex We show that the key properties of these processes depend on the potential function and the second moment of the additive noise We apply our theoretical findings to studying the convergence of Stochastic Gradient Descent (SGD) for non-convex problems and corroborate them with experiments using SGD to train deep neural networks on the CIFAR-10 dataset

Going deeper with convolutions

Abstract: We propose a deep convolutional neural network architecture codenamed Inception that achieves the new state of the art for classification and detection in the ImageNet Large-Scale Visual Recognition Challenge 2014 (ILSVRC14). The main hallmark of this architecture is the improved utilization of the computing resources inside the network. By a carefully crafted design, we increased the depth and width of the network while keeping the computational budget constant. To optimize quality, the architectural decisions were based on the Hebbian principle and the intuition of multi-scale processing. One particular incarnation used in our submission for ILSVRC14 is called GoogLeNet, a 22 layers deep network, the quality of which is assessed in the context of classification and detection.

Deep Learning

Abstract: Deep learning is a form of machine learning that enables computers to learn from experience and understand the world in terms of a hierarchy of concepts. Because the computer gathers knowledge from experience, there is no need for a human computer operator to formally specify all the knowledge that the computer needs. The hierarchy of concepts allows the computer to learn complicated concepts by building them out of simpler ones; a graph of these hierarchies would be many layers deep. This book introduces a broad range of topics in deep learning. The text offers mathematical and conceptual background, covering relevant concepts in linear algebra, probability theory and information theory, numerical computation, and machine learning. It describes deep learning techniques used by practitioners in industry, including deep feedforward networks, regularization, optimization algorithms, convolutional networks, sequence modeling, and practical methodology; and it surveys such applications as natural language processing, speech recognition, computer vision, online recommendation systems, bioinformatics, and videogames. Finally, the book offers research perspectives, covering such theoretical topics as linear factor models, autoencoders, representation learning, structured probabilistic models, Monte Carlo methods, the partition function, approximate inference, and deep generative models. Deep Learning can be used by undergraduate or graduate students planning careers in either industry or research, and by software engineers who want to begin using deep learning in their products or platforms. A website offers supplementary material for both readers and instructors.

Reinforcement Learning: An Introduction

Abstract: Reinforcement learning, one of the most active research areas in artificial intelligence, is a computational approach to learning whereby an agent tries to maximize the total amount of reward it receives when interacting with a complex, uncertain environment. In Reinforcement Learning, Richard Sutton and Andrew Barto provide a clear and simple account of the key ideas and algorithms of reinforcement learning. Their discussion ranges from the history of the field's intellectual foundations to the most recent developments and applications. The only necessary mathematical background is familiarity with elementary concepts of probability. The book is divided into three parts. Part I defines the reinforcement learning problem in terms of Markov decision processes. Part II provides basic solution methods: dynamic programming, Monte Carlo methods, and temporal-difference learning. Part III presents a unified view of the solution methods and incorporates artificial neural networks, eligibility traces, and planning; the two final chapters present case studies and consider the future of reinforcement learning.

Latent dirichlet allocation

Abstract: We describe latent Dirichlet allocation (LDA), a generative probabilistic model for collections of discrete data such as text corpora. LDA is a three-level hierarchical Bayesian model, in which each item of a collection is modeled as a finite mixture over an underlying set of topics. Each topic is, in turn, modeled as an infinite mixture over an underlying set of topic probabilities. In the context of text modeling, the topic probabilities provide an explicit representation of a document. We present efficient approximate inference techniques based on variational methods and an EM algorithm for empirical Bayes parameter estimation. We report results in document modeling, text classification, and collaborative filtering, comparing to a mixture of unigrams model and the probabilistic LSI model.

Latent Dirichlet Allocation

Abstract: We propose a generative model for text and other collections of discrete data that generalizes or improves on several previous models including naive Bayes/unigram, mixture of unigrams [6], and Hof-mann's aspect model, also known as probabilistic latent semantic indexing (pLSI) [3]. In the context of text modeling, our model posits that each document is generated as a mixture of topics, where the continuous-valued mixture proportions are distributed as a latent Dirichlet random variable. Inference and learning are carried out efficiently via variational algorithms. We present empirical results on applications of this model to problems in text modeling, collaborative filtering, and text classification.