Today's Web-enabled deluge of electronic data calls for automated methods of data analysis. Machine learning provides these, developing methods that can automatically detect patterns in data and then use the uncovered patterns to predict future data. This textbook offers a comprehensive and self-contained introduction to the field of machine learning, based on a unified, probabilistic approach. The coverage combines breadth and depth, offering necessary background material on such topics as probability, optimization, and linear algebra as well as discussion of recent developments in the field, including conditional random fields, L1 regularization, and deep learning. The book is written in an informal, accessible style, complete with pseudo-code for the most important algorithms. All topics are copiously illustrated with color images and worked examples drawn from such application domains as biology, text processing, computer vision, and robotics. Rather than providing a cookbook of different heuristic methods, the book stresses a principled model-based approach, often using the language of graphical models to specify models in a concise and intuitive way. Almost all the models described have been implemented in a MATLAB software package--PMTK (probabilistic modeling toolkit)--that is freely available online. The book is suitable for upper-level undergraduates with an introductory-level college math background and beginning graduate students.

Machine Learning : A Probabilistic Perspective

Planning algorithms are impacting technical disciplines and industries around the world, including robotics, computer-aided design, manufacturing, computer graphics, aerospace applications, drug design, and protein folding. This coherent and comprehensive book unifies material from several sources, including robotics, control theory, artificial intelligence, and algorithms. The treatment is centered on robot motion planning but integrates material on planning in discrete spaces. A major part of the book is devoted to planning under uncertainty, including decision theory, Markov decision processes, and information spaces, which are the “configuration spaces” of all sensor-based planning problems. The last part of the book delves into planning under differential constraints that arise when automating the motions of virtually any mechanical system. Developed from courses taught by the author, the book is intended for students, engineers, and researchers in robotics, artificial intelligence, and control theory as well as computer graphics, algorithms, and computational biology.

Planning Algorithms: Introductory Material

A new approach toward target representation and localization, the central component in visual tracking of nonrigid objects, is proposed. The feature histogram-based target representations are regularized by spatial masking with an isotropic kernel. The masking induces spatially-smooth similarity functions suitable for gradient-based optimization, hence, the target localization problem can be formulated using the basin of attraction of the local maxima. We employ a metric derived from the Bhattacharyya coefficient as similarity measure, and use the mean shift procedure to perform the optimization. In the presented tracking examples, the new method successfully coped with camera motion, partial occlusions, clutter, and target scale variations. Integration with motion filters and data association techniques is also discussed. We describe only a few of the potential applications: exploitation of background information, Kalman tracking using motion models, and face tracking.

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Kernel-based object tracking

In this book, Andrew Harvey sets out to provide a unified and comprehensive theory of structural time series models. Unlike the traditional ARIMA models, structural time series models consist explicitly of unobserved components, such as trends and seasonals, which have a direct interpretation. As a result the model selection methodology associated with structural models is much closer to econometric methodology. The link with econometrics is made even closer by the natural way in which the models can be extended to include explanatory variables and to cope with multivariate time series. From the technical point of view, state space models and the Kalman filter play a key role in the statistical treatment of structural time series models. The book includes a detailed treatment of the Kalman filter. This technique was originally developed in control engineering, but is becoming increasingly important in fields such as economics and operations research. This book is concerned primarily with modelling economic and social time series, and with addressing the special problems which the treatment of such series poses. The properties of the models and the methodological techniques used to select them are illustrated with various applications. These range from the modellling of trends and cycles in US macroeconomic time series to to an evaluation of the effects of seat belt legislation in the UK.

Forecasting, Structural Time Series Models and the Kalman Filter

Twitter, a popular microblogging service, has received much attention recently. An important characteristic of Twitter is its real-time nature. For example, when an earthquake occurs, people make many Twitter posts (tweets) related to the earthquake, which enables detection of earthquake occurrence promptly, simply by observing the tweets. As described in this paper, we investigate the real-time interaction of events such as earthquakes in Twitter and propose an algorithm to monitor tweets and to detect a target event. To detect a target event, we devise a classifier of tweets based on features such as the keywords in a tweet, the number of words, and their context. Subsequently, we produce a probabilistic spatiotemporal model for the target event that can find the center and the trajectory of the event location. We consider each Twitter user as a sensor and apply Kalman filtering and particle filtering, which are widely used for location estimation in ubiquitous/pervasive computing. The particle filter works better than other comparable methods for estimating the centers of earthquakes and the trajectories of typhoons. As an application, we construct an earthquake reporting system in Japan. Because of the numerous earthquakes and the large number of Twitter users throughout the country, we can detect an earthquake with high probability (96% of earthquakes of Japan Meteorological Agency (JMA) seismic intensity scale 3 or more are detected) merely by monitoring tweets. Our system detects earthquakes promptly and sends e-mails to registered users. Notification is delivered much faster than the announcements that are broadcast by the JMA.

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Earthquake shakes Twitter users: real-time event detection by social sensors

Most target tracking approaches either assume that the number of targets is constant throughout the time horizon of interest, or that information about target existence (birth and death) is provided by some external source. Here we show how target existence can be integrated within the tracking framework in a rigorous way. The notion of existence is not new, and has been considered before in e.g. [D. Musicki et al., (1994), (2002)]. We provide here a general probabilistic treatment that impacts as little as possible on existing tracking algorithms so that legacy tracking software (and more generally target tracking architectures) can be reused. We first show how the notion of existence can be incorporated into a single target tracking framework (retaining algorithmic invariance). To place the probabilistic recursions into context we relate this single target tracking architecture to the probabilistic data association filter. We then extend the single target results to incorporate existence for multi-target tracking and relate this to an importance sampling implementation of the joint probabilistic data association (JPDA) framework. The treatment presented is entirely general and so facilitates implementation with Kalman filters, extended/unscented Kalman filters, particle filters, etc, i.e. the approach developed is invariant to the filtering and data association mechanisms used, and therein lies the novelty. We apply the proposed framework to the difficult problem of tracking football players in video sequences, where we adopt a mixture Kalman filter implementation.

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A unifying framework for multi-target tracking and existence

The standard approach to tracking a single target in clutter, using the Kalman filter or extended Kalman filter, is to gate the measurements using the predicted measurement covariance and then to update the predicted state using probabilistic data association. When tracking with a particle filter, an analog to the predicted measurement covariance is not directly available and could only be constructed as an approximation to the current particle cloud. A common alternative is to use a form of soft gating, based upon a Student's-t likelihood, that is motivated by the concept of score functions in classical statistical hypothesis testing. In this paper, we combine the score function and probabilistic data association approaches to develop a new method for tracking in clutter using a particle filter. This is done by deriving an expected likelihood from known measurement and clutter statistics. The performance of this new approach is assessed on a series of bearings-only tracking scenarios with uncertain sensor location and non-Gaussian clutter.

Expected likelihood for tracking in clutter with particle filters

Signal processing with reduced combinatorial complexity for tracking evolving phenomena such as radar tracks associated with weighted measurement parameters includes selecting a current phenomenon and obtaining a set of measurement parameters associated with it. Beginning at a start node providing a first parent node having an identity, an identity for a child node of the patent is produced from the sets of parameters, the parent identity and a parameter selected from the set and corresponding to the child. This is iterated for other parameters in the set. Child nodes of like identity for the phenomenon are treated as a single node with multiple parameter relationships associated with at lest one parent node, whereas child nodes with differing identities are represented as separate nodes. The process is iterated for other phenomena and associated sets of measurement parameters, but child nodes of a previously processed phenomenon are not treated as parent nodes of a phenomenon processed immediately following. Updated sets of parameters weights associated with respective phenomena are derived by iterating over node relationships and identifies. This provides a probabilistic assessment of track evolution.

Signal processing with reduced combinational complexity

Littoral tracking refers to the tracking of targets on land and in sea near the boundary of the two regions. A ground-moving target continues to move on land and can not enter the sea. Similarly, a sea-moving target moves in the sea and the land serves as an infeasible region. Enforcing infeasible regions or hard constraints in the framework of the Kalman filter or interacting multiple model (IMM) estimator is not natural. However, these hard constraints can be easily enforced using the particle filter algorithm. We formulate the littoral tracking problem as a joint tracking and classification problem, where we assign a target class for each isolated land or water region. We use a reflecting boundary condition to enforce the region constraint. We demonstrate this concept for a single target using the airborne ground moving target indicator measurements. Numerical results show that the proposed algorithm produces robust classification probabilities using kinematic measurements.

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Littoral tracking using particle filter

A method is presented that circumvents the combinatorial explosion often assumed to exist when summing probabilities of joint association events in a multiple target tracking context. The approach involves no approximations in the summation and while the number of joint events grows exponentially with teh number of targets, the computational complexity of the approach is substantially less than exponential. Multiple target tracking algorithms that use this summation include mutual exclusion in a particle filtering context and the Joint Probabilistic Data Association Filter, a Kalman Filter based algorithm. The perceived computational expense associated with this combinatorial explosion has meant that such algorithms have been restricted to applications involving only a handful of targets. The approach presented here makes it possible to use such algorithms with a large number of targets.

Simon Maskell

Papers

A unifying framework for multi-target tracking and existence

Expected likelihood for tracking in clutter with particle filters

Signal processing with reduced combinational complexity

Littoral tracking using particle filter

Fast mutual exclusion