Nando de Freitas

Sequential Monte Carlo methods in practice

Monte Carlo methods are revolutionizing the on-line analysis of data in fields as diverse as financial modeling, target tracking and computer vision. These methods, appearing under the names of bootstrap filters, condensation, optimal Monte Carlo filters, particle filters and survival of the fittest, have made it possible to solve numerically many complex, non-standard problems that were previously intractable. This book presents the first comprehensive treatment of these techniques, including convergence results and applications to tracking, guidance, automated target recognition, aircraft navigation, robot navigation, econometrics, financial modeling, neural networks, optimal control, optimal filtering, communications, reinforcement learning, signal enhancement, model averaging and selection, computer vision, semiconductor design, population biology, dynamic Bayesian networks, and time series analysis. This will be of great value to students, researchers and practitioners, who have some basic knowledge of probability. Arnaud Doucet received the Ph. D. degree from the University of Paris-XI Orsay in 1997. From 1998 to 2000, he conducted research at the Signal Processing Group of Cambridge University, UK. He is currently an assistant professor at the Department of Electrical Engineering of Melbourne University, Australia. His research interests include Bayesian statistics, dynamic models and Monte Carlo methods. Nando de Freitas obtained a Ph.D. degree in information engineering from Cambridge University in 1999. He is presently a research associate with the artificial intelligence group of the University of California at Berkeley. His main research interests are in Bayesian statistics and the application of on-line and batch Monte Carlo methods to machine learning. Neil Gordon obtained a Ph.D. in Statistics from Imperial College, University of London in 1993. He is with the Pattern and Information Processing group at the Defence Evaluation and Research Agency in the United Kingdom. His research interests are in time series, statistical data analysis, and pattern recognition with a particular emphasis on target tracking and missile guidance.

Matching words and pictures

We present a new approach for modeling multi-modal data sets, focusing on the specific case of segmented images with associated text. Learning the joint distribution of image regions and words has many applications. We consider in detail predicting words associated with whole images (auto-annotation) and corresponding to particular image regions (region naming). Auto-annotation might help organize and access large collections of images. Region naming is a model of object recognition as a process of translating image regions to words, much as one might translate from one language to another. Learning the relationships between image regions and semantic correlates (words) is an interesting example of multi-modal data mining, particularly because it is typically hard to apply data mining techniques to collections of images. We develop a number of models for the joint distribution of image regions and words, including several which explicitly learn the correspondence between regions and words. We study multi-modal and correspondence extensions to Hofmanns hierarchical clustering/aspect model, a translation model adapted from statistical machine translation (Brown et al.), and a multi-modal extension to mixture of latent Dirichlet allocation (MoM-LDA). All models are assessed using a large collection of annotated images of real scenes. We study in depth the difficult problem of measuring performance. For the annotation task, we look at prediction performance on held out data. We present three alternative measures, oriented toward different types of task. Measuring the performance of correspondence methods is harder, because one must determine whether a word has been placed on the right region of an image. We can use annotation performance as a proxy measure, but accurate measurement requires hand labeled data, and thus must occur on a smaller scale. We show results using both an annotation proxy, and manually labeled data.

An Introduction to MCMC for Machine Learning

This purpose of this introductory paper is threefold. First, it introduces the Monte Carlo method with emphasis on probabilistic machine learning. Second, it reviews the main building blocks of modern Markov chain Monte Carlo simulation, thereby providing and introduction to the remaining papers of this special issue. Lastly, it discusses new interesting research horizons.

A Boosted Particle Filter: Multitarget Detection and Tracking

The problem of tracking a varying number of non-rigid objects has two major difficulties. First, the observation models and target distributions can be highly non-linear and non-Gaussian. Second, the presence of a large, varying number of objects creates complex interactions with overlap and ambiguities. To surmount these difficulties, we introduce a vision system that is capable of learning, detecting and tracking the objects of interest. The system is demonstrated in the context of tracking hockey players using video sequences. Our approach combines the strengths of two successful algorithms: mixture particle filters and Adaboost. The mixture particle filter [17] is ideally suited to multi-target tracking as it assigns a mixture component to each player. The crucial design issues in mixture particle filters are the choice of the proposal distribution and the treatment of objects leaving and entering the scene. Here, we construct the proposal distribution using a mixture model that incorporates information from the dynamic models of each player and the detection hypotheses generated by Adaboost. The learned Adaboost proposal distribution allows us to quickly detect players entering the scene, while the filtering process enables us to keep track of the individual players. The result of interleaving Adaboost with mixture particle filters is a simple, yet powerful and fully automatic multiple object tracking system.

An Introduction to Sequential Monte Carlo Methods

Many real-world data analysis tasks involve estimating unknown quantities from some given observations. In most of these applications, prior knowledge about the phenomenon being modelled is available. This knowledge allows us to formulate Bayesian models, that is prior distributions for the unknown quantities and likelihood functions relating these quantities to the observations. Within this setting, all inference on the unknown quantities is based on the posterior distribution obtained from Bayes’ theorem. Often, the observations arrive sequentially in time and one is interested in performing inference on-line. It is therefore necessary to update the posterior distribution as data become available. Examples include tracking an aircraft using radar measurements, estimating a digital communications signal using noisy measurements, or estimating the volatility of financial instruments using stock market data. Computational simplicity in the form of not having to store all the data might also be an additional motivating factor for sequential methods.

A statistical model for general contextual object recognition

We consider object recognition as the process of attaching meaningful labels to specific regions of an image, and propose a model that learns spatial relationships between objects. Given a set of images and their associated text (e.g. keywords, captions, descriptions), the objective is to segment an image, in either a crude or sophisticated fashion, then to find the proper associations between words and regions. Previous models are limited by the scope of the representation. In particular, they fail to exploit spatial context in the images and words. We develop a more expressive model that takes this into account. We formulate a spatially consistent probabilistic mapping between continuous image feature vectors and the supplied word tokens. By learning both word-to-region associations and object relations, the proposed model augments scene segmentations due to smoothing implicit in spatial consistency. Context introduces cycles to the undirected graph, so we cannot rely on a straightforward implementation of the EM algorithm for estimating the model parameters and densities of the unknown alignment variables. Instead, we develop an approximate EM algorithm that uses loopy belief propagation in the inference step and iterative scaling on the pseudo-likelihood approximation in the parameter update step. The experiments indicate that our approximate inference and learning algorithm converges to good local solutions. Experiments on a diverse array of images show that spatial context considerably improves the accuracy of object recognition. Most significantly, spatial context combined with a nonlinear discrete object representation allows our models to cope well with over-segmented scenes.

Taking the Human Out of the Loop: A Review of Bayesian Optimization

Big Data applications are typically associated with systems involving large numbers of users, massive complex software systems, and large-scale heterogeneous computing and storage architectures. The construction of such systems involves many distributed design choices. The end products (e.g., recommendation systems, medical analysis tools, real-time game engines, speech recognizers) thus involve many tunable configuration parameters. These parameters are often specified and hard-coded into the software by various developers or teams. If optimized jointly, these parameters can result in significant improvements. Bayesian optimization is a powerful tool for the joint optimization of design choices that is gaining great popularity in recent years. It promises greater automation so as to increase both product quality and human productivity. This review paper introduces Bayesian optimization, highlights some of its methodological aspects, and showcases a wide range of applications.

Predicting Parameters in Deep Learning

We demonstrate that there is significant redundancy in the parameterization of several deep learning models. Given only a few weight values for each feature it is possible to accurately predict the remaining values. Moreover, we show that not only can the parameter values be predicted, but many of them need not be learned at all. We train several different architectures by learning only a small number of weights and predicting the rest. In the best case we are able to predict more than 95% of the weights of a network without any drop in accuracy.

Robust visual tracking for multiple targets

We address the problem of robust multi-target tracking within the application of hockey player tracking. The particle filter technique is adopted and modified to fit into the multi-target tracking framework. A rectification technique is employed to find the correspondence between the video frame coordinates and the standard hockey rink coordinates so that the system can compensate for camera motion and improve the dynamics of the players. A global nearest neighbor data association algorithm is introduced to assign boosting detections to the existing tracks for the proposal distribution in particle filters. The mean-shift algorithm is embedded into the particle filter framework to stabilize the trajectories of the targets for robust tracking during mutual occlusion. Experimental results show that our system is able to automatically and robustly track a variable number of targets and correctly maintain their identities regardless of background clutter, camera motion and frequent mutual occlusion between targets.

Fast particle smoothing: if I had a million particles

We propose efficient particle smoothing methods for generalized state-spaces models. Particle smoothing is an expensive O(N2) algorithm, where N is the number of particles. We overcome this problem by integrating dual tree recursions and fast multipole techniques with forward-backward smoothers, a new generalized two-filter smoother and a maximum a posteriori (MAP) smoother. Our experiments show that these improvements can substantially increase the practicality of particle smoothing.