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.

Learning in decentralized systems: a nonparametric approach

Abstract: Rapid advances in information technology result in increased deployment of decentralized decision-making systems embedded within large-scale infrastructure consisting of data collection and processing devices. In such a system, each statistical decision is performed on the basis of limited amount of data due to constraints given by the decentralized system. For instance, the constraints maybe imposed by limits in energy source, communication bandwidth, computation or time budget. A fundamental research problem arised in decentralized systems involves the development methods that takes into account not only the statistical accuracy of decision-making procedures, but also the constraints imposed by the system limits. It is this general problem that drives the focus of this thesis. In particular, we focus on the development and analysis of statistical learning methods for decentralized decision-making by employing a nonparametric approach. The nonparametric approach imposes very little a priori assumption on the data; such flexibility allows it to be applicable to a wide range of applications. Coupled with tools from convex analysis and empirical process theory we develop computationally efficient algorithms and analyze their statistical 1 behavior both theoretically and empirically. Our specific contributions include the following. We develop a novel kernel-based algorithm for centralized detection and estimation in the ad hoc sensor networks through the challenging task of sensor mote localization. Next, we develop and analyze a nonparametric decentralized detection algorithm using the methodology of convex surrogate loss functions and marginalized kernels. The analysis of this algorithm leads to an in-depth study of the correspondence between the class of surrogate loss functions widely used in statistical machine learning and the class of divergence functionals widely used in information theory. This correspondence allows us to provide an interesting decision-theoretic justification to a given choice of divergence functionals, which often arise from asymptotic analysis. In addition, this correspondence also motivates the development and analysis of a novel M-estimation procedure for estimating divergence functionals and the likelihood ratio. Finally, we also investigate a sequential setting of the decentralized detection algorithm, and settle an open question regarding the characterization of optimal decision rules in such a setting.

On the Adaptivity of Stochastic Gradient-Based Optimization

Abstract: Stochastic-gradient-based optimization has been a core enabling methodology in applications to large-scale problems in machine learning and related areas. Despite the progress, the gap between theory and practice remains significant, with theoreticians pursuing mathematical optimality at a cost of obtaining specialized procedures in different regimes (e.g., modulus of strong convexity, magnitude of target accuracy, signal-to-noise ratio), and with practitioners not readily able to know which regime is appropriate to their problem, and seeking broadly applicable algorithms that are reasonably close to optimality. To bridge these perspectives it is necessary to study algorithms that are adaptive to different regimes. We present the stochastically controlled stochastic gradient (SCSG) method for composite convex finite-sum optimization problems and show that SCSG is adaptive to both strong convexity and target accuracy. The adaptivity is achieved by batch variance reduction with adaptive batch sizes and a novel technique, which we referred to as geometrization, which sets the length of each epoch as a geometric random variable. The algorithm achieves strictly better theoretical complexity than other existing adaptive algorithms, while the tuning parameters of the algorithm only depend on the smoothness parameter of the objective.

Inference and Learning in Networks of Queues

Abstract: Probabilistic models of the performance of computer systems are useful both for predicting system performance in new conditions, and for diagnosing past performance problems. The most popular performance models are networks of queues. However, no current methods exist for parameter estimation or inference in networks of queues with missing data. In this paper, we present a novel viewpoint that combines queueing networks and graphical models, allowing Markov chain Monte Carlo to be applied. We demonstrate the eectiveness of our sampler on real-world data from a benchmark Web application.

Distributed Estimation of Generalized Matrix Rank: Efficient Algorithms and Lower Bounds

Abstract: We study the following generalized matrix rank estimation problem: given an $n \times n$ matrix and a constant $c \geq 0$, estimate the number of eigenvalues that are greater than $c$. In the distributed setting, the matrix of interest is the sum of $m$ matrices held by separate machines. We show that any deterministic algorithm solving this problem must communicate $\Omega(n^2)$ bits, which is order-equivalent to transmitting the whole matrix. In contrast, we propose a randomized algorithm that communicates only $\widetilde O(n)$ bits. The upper bound is matched by an $\Omega(n)$ lower bound on the randomized communication complexity. We demonstrate the practical effectiveness of the proposed algorithm with some numerical experiments.

A Marked Poisson Process Driven Latent Shape Model for 3D Segmentation of Reflectance Confocal Microscopy Image Stacks of Human Skin

Abstract: Segmenting objects of interest from 3D data sets is a common problem encountered in biological data. Small field of view and intrinsic biological variability combined with optically subtle changes of intensity, resolution, and low contrast in images make the task of segmentation difficult, especially for microscopy of unstained living or freshly excised thick tissues. Incorporating shape information in addition to the appearance of the object of interest can often help improve segmentation performance. However, the shapes of objects in tissue can be highly variable and design of a flexible shape model that encompasses these variations is challenging. To address such complex segmentation problems, we propose a unified probabilistic framework that can incorporate the uncertainty associated with complex shapes, variable appearance, and unknown locations. The driving application that inspired the development of this framework is a biologically important segmentation problem: the task of automatically detecting and segmenting the dermal-epidermal junction (DEJ) in 3D reflectance confocal microscopy (RCM) images of human skin. RCM imaging allows noninvasive observation of cellular, nuclear, and morphological detail. The DEJ is an important morphological feature as it is where disorder, disease, and cancer usually start. Detecting the DEJ is challenging, because it is a 2D surface in a 3D volume which has strong but highly variable number of irregularly spaced and variably shaped “peaks and valleys.” In addition, RCM imaging resolution, contrast, and intensity vary with depth. Thus, a prior model needs to incorporate the intrinsic structure while allowing variability in essentially all its parameters. We propose a model which can incorporate objects of interest with complex shapes and variable appearance in an unsupervised setting by utilizing domain knowledge to build appropriate priors of the model. Our novel strategy to model this structure combines a spatial Poisson process with shape priors and performs inference using Gibbs sampling. Experimental results show that the proposed unsupervised model is able to automatically detect the DEJ with physiologically relevant accuracy in the range 10– $20 ~\mu m$ .

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.