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 3), 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.

This paper reviews a significant component of the rich field of statistical multiresolution (MR) modeling and processing. These MR methods have found application and permeated the literature of a widely scattered set of disciplines, and one of our principal objectives is to present a single, coherent picture of this framework. A second goal is to describe how this topic fits into the even larger field of MR methods and concepts–in particular making ties to topics such as wavelets and multigrid methods. A third is to provide several alternate viewpoints for this body of work, as the methods and concepts we describe intersect with a number of other fields. The principle focus of our presentation is the class of MR Markov processes defined on pyramidally organized trees. The attractiveness of these models stems from both the very efficient algorithms they admit and their expressive power and broad applicability. We show how a variety of methods and models relate to this framework including models for self-similar and 1/f processes. We also illustrate how these methods have been used in practice. We discuss the construction of MR models on trees and show how questions that arise in this context make contact with wavelets, state space modeling of time series, system and parameter identification, and hidden

A large variety of algorithms in coding, signal processing, and artificial intelligence may be viewed as instances of the summary-product algorithm (or belief/probability

The preferential conservation of transcription factor binding sites implies that non-coding sequence data from related species will prove a powerful asset to motif discovery. We present a unified probabilistic framework for motif discovery that incorporates of evolutionary information. We treat aligned DNA sequence as a mixture of evolutionary models, for motif and background, and, following the example of the MEME program, provide an algorithm to estimate the parameters by Expectation-Maximization. We examine a variety of evolutionary models and show that our approach can take advantage of phylogenic information to avoid false positives and discover motifs upstream of groups of characterized target genes. We compare our method to traditional motif finding on only conserved regions. An implementation will be made available

... this paper is to use experimental or observational data to estimate decision regimes that result in a maximal mean response. To explicate our objective and state assumptions, we use the potential outcomes model. The proposed method makes smooth, parametric assumptions only on quantities directly relevant to the goal of estimating the optimal rules. We illustrate the proposed methodology via a small simulation.

In this paper, we present an on-line recognition method for hand-sketched symbols. The method is independent of stroke-order,-number, and-direction, as well as invariant to rotation, scaling, and translation of symbols. Zernike moment descriptors are used to represent symbols and three different classification techniques are compared: Support Vector Machines (SVM), Minimum Mean Distance (MMD), and Nearest Neighbor (NN). We have obtained 97 % accuracy rate on a dataset consisting of 7,410 sketched symbols using Zernike moment features and a SVM classifier. This method has been implemented in a software recognition package, HHreco [7]. 1.

A wide variety of machine learning problems can be described as minimizing a regularized risk functional, with different algorithms using different notions of risk and different regularizers. Examples include linear Support Vector Machines (SVMs), Gaussian Processes, Logistic Regression, Conditional Random Fields (CRFs), and Lasso amongst others. This paper describes the theory and implementation of a scalable and modular convex solver which solves all these estimation problems. It can be parallelized on a cluster of workstations, allows for data-locality, and can deal with regularizers such as L1 and L2 penalties. In addition to the unified framework we present tight convergence bounds, which show that our algorithm converges in O(1/ɛ) steps to ɛ precision for general convex problems and in O(log(1/ɛ)) steps for continuously differentiable problems. We demonstrate the performance of our general purpose solver on a variety of publicly available datasets.

The wide deployment of wireless sensor and RFID (Radio Frequency IDentification) devices is one of the key enablers for next-generation pervasive computing applications, including large-scale environmental monitoring and control, context-aware computing, and “smart digital homes”. Sensory readings are inherently unreliable and typically exhibit strong temporal and spatial correlations (within and across different sensing devices); effective reasoning over such unreliable streams introduces a host of new data management challenges. The Data Furnace project at Intel Research and UC-Berkeley aims to build a probabilistic data management infrastructure for pervasive computing environments that handles the uncertain nature of such data as a first-class citizen through a principled framework grounded in probabilistic models and inference techniques. 1

Tuning an algorithm’s parameters for robust and high performance is a tedious and time-consuming task that often requires knowledge about both the domain and the algorithm of interest. Furthermore, the optimal parameter configuration to use may differ considerably across problem instances. In this report, we define and tackle the algorithm configuration problem, which is to automatically choose the optimal parameter configuration for a given algorithm on a per-instance base. We employ an indirect approach that predicts algorithm runtime for the problem instance at hand and each (continuous) parameter configuration, and then simply chooses the configuration that minimizes the prediction. This approach is based on similar work by Leyton-Brown et al. [LBNS02, NLBD + 04] who tackle the algorithm selection problem [Ric76] (given a problem instance, choose the best algorithm to solve it). While all previous studies for runtime prediction focussed on tree search algorithm, we demonstrate that it is possible to fairly accurately predict the runtime of SAPS [HTH02], one of the best-performing stochastic local search algorithms for SAT. We also show that our approach automatically picks parameter configurations that speed up SAPS by an average factor of more than two when compared to its default parameter configuration. Finally, we introduce sequential Bayesian learning to the problem of runtime prediction, enabling an incremental learning approach and yielding very informative estimates of predictive uncertainty. 1

Abstract—This paper describes a novel solution to the rigid point pattern matching problem in Euclidean spaces of any dimension. Although we assume rigid motion, jitter is allowed. We present a noniterative, polynomial time algorithm that is guaranteed to find an optimal solution for the noiseless case. First, we model point pattern matching as a weighted graph matching problem, where weights correspond to Euclidean distances between nodes. We then formulate graph matching as a problem of finding a maximum probability configuration in a graphical model. By using graph rigidity arguments, we prove that a sparse graphical model yields equivalent results to the fully connected model in the noiseless case. This allows us to obtain an algorithm that runs in polynomial time and is provably optimal for exact matching between noiseless point sets. For inexact matching, we can still apply the same algorithm to find approximately optimal solutions. Experimental results obtained by our approach show improvements in accuracy over current methods, particularly when matching patterns of different sizes. Index Terms—Point pattern matching, graph matching, graphical models, Markov random fields, junction tree algorithm. 1