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

Dynamic Bayesian Networks: Representation, Inference and Learning by Kevin Patrick Murphy Doctor of Philosophy in Computer Science University of California, Berkeley Professor Stuart Russell, Chair Modelling sequential data is important in many areas of science and engineering. Hidden Markov models (HMMs) and Kalman filter models (KFMs) are popular for this because they are simple and flexible. For example, HMMs have been used for speech recognition and bio-sequence analysis, and KFMs have been used for problems ranging from tracking planes and missiles to predicting the economy. However, HMMs and KFMs are limited in their “expressive power”. Dynamic Bayesian Networks (DBNs) generalize HMMs by allowing the state space to be represented in factored form, instead of as a single discrete random variable. DBNs generalize KFMs by allowing arbitrary probability distributions, not just (unimodal) linear-Gaussian. In this thesis, I will discuss how to represent many different kinds of models as DBNs, how to perform exact and approximate inference in DBNs, and how to learn DBN models from sequential data. In particular, the main novel technical contributions of this thesis are as follows: a way of representing Hierarchical HMMs as DBNs, which enables inference to be done in O(T ) time instead of O(T ), where T is the length of the sequence; an exact smoothing algorithm that takes O(log T ) space instead of O(T ); a simple way of using the junction tree algorithm for online inference in DBNs; new complexity bounds on exact online inference in DBNs; a new deterministic approximate inference algorithm called factored frontier; an analysis of the relationship between the BK algorithm and loopy belief propagation; a way of applying Rao-Blackwellised particle filtering to DBNs in general, and the SLAM (simultaneous localization and mapping) problem in particular; a way of extending the structural EM algorithm to DBNs; and a variety of different applications of DBNs. However, perhaps the main value of the thesis is its catholic presentation of the field of sequential data modelling.

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Dynamic bayesian networks: representation, inference and learning

This paper discusses the recursive Bayesian formulation of the simultaneous localization and mapping (SLAM) problem in which probability distributions or estimates of absolute or relative locations of landmarks and vehicle pose are obtained. The paper focuses on three key areas: computational complexity; data association; and environment representation

Simultaneous localization and mapping (SLAM): part II

Recently, Rao-Blackwellized particle filters (RBPF) have been introduced as an effective means to solve the simultaneous localization and mapping problem. This approach uses a particle filter in which each particle carries an individual map of the environment. Accordingly, a key question is how to reduce the number of particles. In this paper, we present adaptive techniques for reducing this number in a RBPF for learning grid maps. We propose an approach to compute an accurate proposal distribution, taking into account not only the movement of the robot, but also the most recent observation. This drastically decreases the uncertainty about the robot's pose in the prediction step of the filter. Furthermore, we present an approach to selectively carry out resampling operations, which seriously reduces the problem of particle depletion. Experimental results carried out with real mobile robots in large-scale indoor, as well as outdoor, environments illustrate the advantages of our methods over previous approaches

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Improved Techniques for Grid Mapping With Rao-Blackwellized Particle Filters

A fundamental problem in text data mining is to extract meaningful structure from document streams that arrive continuously over time. E-mail and news articles are two natural examples of such streams, each characterized by topics that appear, grow in intensity for a period of time, and then fade away. The published literature in a particular research field can be seen to exhibit similar phenomena over a much longer time scale. Underlying much of the text mining work in this area is the following intuitive premise—that the appearance of a topic in a document stream is signaled by a “burst of activity,” with certain features rising sharply in frequency as the topic emerges.

The goal of the present work is to develop a formal approach for modeling such “bursts,” in such a way that they can be robustly and efficiently identified, and can provide an organizational framework for analyzing the underlying content. The approach is based on modeling the stream using an infinite-state automaton, in which bursts appear naturally as state transitionss it can be viewed as drawing an analogy with models from queueing theory for bursty network traffic. The resulting algorithms are highly efficient, and yield a nested representation of the set of bursts that imposes a hierarchical structure on the overall stream. Experiments with e-mail and research paper archives suggest that the resulting structures have a natural meaning in terms of the content that gave rise to them.

Bursty and Hierarchical Structure in Streams

We present distributed regression, an efficient and general framework for in-network modeling of sensor data. In this framework, the nodes of the sensor network collaborate to optimally fit a global function to each of their local measurements. The algorithm is based upon kernel linear regression, where the model takes the form of a weighted sum of local basis functions; this provides an expressive yet tractable class of models for sensor network data. Rather than transmitting data to one another or outside the network, nodes communicate constraints on the model parameters, drastically reducing the communication required. After the algorithm is run, each node can answer queries for its local region, or the nodes can efficiently transmit the parameters of the model to a user outside the network. We present an evaluation of the algorithm based upon data from a 48-node sensor network deployment at the Intel Research - Berkeley Lab, demonstrating that our distributed algorithm converges to the optimal solution at a fast rate and is very robust to packet losses.

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Distributed regression: an efficient framework for modeling sensor network data

Simultaneous Localization and Mapping (SLAM) is a fundamental problem in mobile robotics: while a robot navigates in an unknown environment, it must incrementally build a map of its surroundings and, at the same time, localize itself within that map. One popular solution is to treat SLAM as an estimation problem and apply the Kalman filter; this approach is elegant, but it does not scale well: the size of the belief state and the time complexity of the filter update both grow quadratically in the number of landmarks in the map. This paper presents a filtering technique that maintains a tractable approximation of the belief state as a thin junction tree. The junction tree grows under filter updates and is periodically "thinned" via efficient maximum likelihood projections so inference remains tractable. When applied to the SLAM problem, these thin junction tree filters have a linear-space belief state and a linear-time filtering operation. Further approximation yields a filtering operation that is often constant-time. Experiments on a suite of SLAM problems validate the approach.

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Thin junction tree filters for simultaneous localization and mapping

The hierarchical hidden Markov model (HHMM) is a generalization of the hidden Markov model (HMM) that models sequences with structure at many length/time scales [FST98]. Unfortunately, the original inference algorithm is rather complicated, and takes O(T3) time, where is the length of the sequence, making it impractical for many domains. In this paper, we show how HHMMs are a special kind of dynamic Bayesian network (DBN), and thereby derive a much simpler inference algorithm, which only takes O(T) time. Furthermore, by drawing the connection between HHMMs and DBNs, we enable the application of many standard approximation techniques to further speed up inference.

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Linear-time inference in Hierarchical HMMs

Many inference problems that arise in sensor networks require the computation of a global conclusion that is consistent with local information known to each node. A large class of these problems---including probabilistic inference, regression, and control problems---can be solved by message passing on a data structure called a junction tree. In this paper, we present a distributed architecture for solving these problems that is robust to unreliable communication and node failures. In this architecture, the nodes of the sensor network assemble themselves into a junction tree and exchange messages between neighbors to solve the inference problem efficiently and exactly. A key part of the architecture is an efficient distributed algorithm for optimizing the choice of junction tree to minimize the communication and computation required by inference. We present experimental results from a prototype implementation on a 97-node Mica2 mote network, as well as simulation results for three applications: distributed sensor calibration, optimal control, and sensor field modeling. These experiments demonstrate that our distributed architecture can solve many important inference problems exactly, efficiently, and robustly.

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A robust architecture for distributed inference in sensor networks

Camera networks are perhaps the most common type of sensor network and are deployed in a variety of real-world applications including surveillance, intelligent environments and scientific remote monitoring. A key problem in deploying a network of cameras is calibration, i.e., determining the location and orientation of each sensor so that observations in an image can be mapped to locations in the real world. This paper proposes a fully distributed approach for camera network calibration. The cameras collaborate to track an object that moves through the environment and reason probabilistically about which camera poses are consistent with the observed images. This reasoning employs sophisticated techniques for handling the difficult nonlinearities imposed by projective transformations, as well as the dense correlations that arise between distant cameras. Our method requires minimal overlap of the cameras' fields of view and makes very few assumptions about the motion of the object. In contrast to existing approaches, which are centralized, our distributed algorithm scales easily to very large camera networks. We evaluate the system on a real camera network with 25 nodes as well as simulated camera networks of up to 50 cameras and demonstrate that our approach performs well even when communication is lossy.

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Mark A. Paskin

Papers

Distributed regression: an efficient framework for modeling sensor network data

Thin junction tree filters for simultaneous localization and mapping

Linear-time inference in Hierarchical HMMs

A robust architecture for distributed inference in sensor networks

Distributed localization of networked cameras