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.

Constraints on underspecified target trajectories

Abstract: Much of the recent interest in artificial neural networks is founded on the development of supervised learning algorithms for nonlinear problems [1, 30, 39, 42, 47]. These algorithms, the most well-known being backpropagation, are able to model a large class of nonlinear transformations by assigning credit to internal “hidden” units. The remaining units—those connected directly to the environment—are generally assumed to be provided with target states. This assumption appears to be a liability; it is by no means clear that such desired outputs can always be provided. Consider, for example, a network serving as a feedforward controller for a robot. Such a network must produce torques as a function of the environmental goal and the current state of the robot. In general, however, the environment provides only the goal and not the torques that achieve the goal. Furthermore, if we assume the existence of an oracle that provides the torques as training data, then there appears to be little reason (other than perhaps speed) not to use the oracle as the controller in place of the network.

Coherence functions with applications in large-margin classification methods

Abstract: Support vector machines (SVMs) naturally embody sparseness due to their use of hinge loss functions. However, SVMs can not directly estimate conditional class probabilities. In this paper we propose and study a family of coherence functions, which are convex and differentiable, as surrogates of the hinge function. The coherence function is derived by using the maximum-entropy principle and is characterized by a temperature parameter. It bridges the hinge function and the logit function in logistic regression. The limit of the coherence function at zero temperature corresponds to the hinge function, and the limit of the minimizer of its expected error is the minimizer of the expected error of the hinge loss. We refer to the use of the coherence function in large-margin classification as "C-learning," and we present efficient coordinate descent algorithms for the training of regularized C-learning models.

Langevin Monte Carlo without smoothness

Abstract: Langevin Monte Carlo (LMC) is an iterative algorithm used to generate samples from a distribution that is known only up to a normalizing constant. The nonasymptotic dependence of its mixing time on the dimension and target accuracy is understood mainly in the setting of smooth (gradient-Lipschitz) log-densities, a serious limitation for applications in machine learning. In this paper, we remove this limitation, providing polynomial-time convergence guarantees for a variant of LMC in the setting of nonsmooth log-concave distributions. At a high level, our results follow by leveraging the implicit smoothing of the log-density that comes from a small Gaussian perturbation that we add to the iterates of the algorithm and controlling the bias and variance that are induced by this perturbation.

Computational methods for meiotic recombination inference

Abstract: Meiotic recombination is one of major evolutionary mechanisms responsible for promoting genetic variation in a population, and is important for many problems in evolutionary biology and population genetics. In this thesis, we investigate two computational problems that arise in studying meiotic recombination. The first problem is concerned with two different type of meiotic recombination: crossovers and gene conversions. Although crossovers and gene conversions have different effects on the evolutionary history of chromosomes and therefore leave behind different footprints in the genome, it is a challenging task to tease apart their relative contributions to the observed genetic variation. In fact, the methods employed in recent studies of recombination rate variation in the human genome actually capture combined effects of crossovers and gene conversions. By explicitly incorporating overlapping gene conversion events, we propose a new statistical model that can jointly estimate the crossover rate, the gene conversion rate and the mean tract length, which is widely regarded as a very difficult problem. Our simulated results show that modeling overlapping gene conversions is crucial for improving the accuracy of the joint estimation of the aforementioned three fundamental parameters. Our analysis of real data from the telomere of the X chromosome of Drosophila melanogaster suggests that the ratio of the gene conversion rate to the crossover rate for the region may not be nearly as high as previously claimed. In the second problem, we investigate the molecular basis of meiotic recombination. In mammalian organisms, recombination events tend to cluster into short 1–2 kb genomic regions known as recombination hotspots. Recent studies have mainly focused on identifying cis and trans-acting elements that can modulate the activity of recombination hotspots in mammals, but most of the work neglects the role of nucleosomes, the basic unit of DNA packaging in eukaryotes. Our analysis on the correlation of H2A.Z nucleosome positions and recombination rates in Drosophila melanogaster suggests that nucleosome occupancy could also influence, at least partly, the activity of recombination.

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.