We describe semi-Markov conditional random fields (semi-CRFs), a conditionally trained version of semi-Markov chains. Intuitively, a semi-CRF on an input sequence x outputs a "segmentation" of x, in which labels are assigned to segments (i.e., subsequences) of x rather than to individual elements x

We introduce a novel active-learning scenario in which a user wants to work with a learning algorithm to identify useful anomalies. These are distinguished from the traditional statistical definition of anomalies as outliers or merely ill-modeled points. Our distinction is that the usefulness of anomalies is categorized subjectively by the user. We make two additional assumptions. First, there exist extremely few useful anomalies to be hunted down within a massive dataset.

We propose a gossip-based distributed algorithm for Gaussian mixture learning, Newscast EM. The algorithm operates on network topologies where each node observes a local quantity and can communicate with other nodes in an arbitrary point-to-point fashion. The main difference between Newscast EM and the standard EM algorithm is that the M-step in our case is implemented in a decentralized manner: (random) pairs of nodes repeatedly exchange their local parameter estimates and combine them by (weighted) averaging. We provide theoretical evidence and demonstrate experimentally that, under this protocol, nodes converge exponentially fast to the correct estimates in each M-step of the EM algorithm.

We present an algorithm to perform blind, one-microphone speech separation.

A new distance measure between probability density functions (pdfs) is introduced, which we refer to as the Laplacian pdf distance. The Laplacian pdf distance exhibits a remarkable connection to Mercer kernel based learning theory via the Parzen window technique for density estimation. In a kernel feature space defined by the eigenspectrum of the Laplacian data matrix, this pdf distance is shown to measure the cosine of the angle between cluster mean vectors. The Laplacian data matrix, and hence its eigenspec-trum, can be obtained automatically based on the data at hand, by optimal Parzen window selection. We show that the Laplacian pdf distance has an interesting interpretation as a risk function connected to the probability of error.

Clustering and prediction of sets of curves is an important problem in many areas of science and engineering. It is often the case that curves tend to be misaligned from each other in a continuous manner, either in space (across the measurements) or in time. We develop a probabilistic framework that allows for joint clustering and continuous alignment of sets of curves in curve space (as opposed to a fixed-dimensional featurevector space). The proposed methodology integrates new probabilistic alignment models with model-based curve clustering algorithms. The probabilistic approach allows for the derivation of consistent EM learning algorithms for the joint clustering-alignment problem. Experimental results are shown for alignment of human growth data, and joint clustering and alignment of gene expression time-course data.

We address the problem of learning a symmetric positive definite matrix. The central issue is to design parameter updates that preserve positive definiteness. Our updates are motivated with the von Neumann divergence. Rather than treating the most general case, we focus on two key applications that exemplify our methods: Online learning with a simple square loss and finding a symmetric positive definite matrix subject to symmetric linear constraints. The updates generalize the Exponentiated Gradient (EG) update and AdaBoost, respectively: the parameter is now a symmetric positive definite matrix of trace one instead of a probability vector (which in this context is a diagonal positive definite matrix with trace one). The generalized updates use matrix logarithms and exponentials to preserve positive definiteness. Most importantly, we show how the analysis of each algorithm generalizes to the non-diagonal case. We apply both new algorithms, called the Matrix Exponentiated Gradient (MEG) update and DefiniteBoost, to learn a kernel matrix from distance measurements.

This paper investigates a new learning model in which the input data is corrupted with noise. We present a general statistical framework to tackle this problem. Based on the statistical reasoning, we propose a novel formulation of support vector classification, which allows uncertainty in input data. We derive an intuitive geometric interpretation of the proposed formulation, and develop algorithms to efficiently solve it. Empirical results are included to show that the newly formed method is superior to the standard SVM for problems with noisy input.

Visual action recognition is an important problem in computer vision. In this paper, we propose a new method to probabilistically model and recognize actions of articulated objects, such as hand or body gestures, in image sequences. Our method consists of three levels of representation. At the low level, we first extract a feature vector invariant to scale and in-plane rotation by using the Fourier transform of a circular spatial histogram. Then, spectral partitioning [20] is utilized to obtain an initial clustering; this clustering is then refined using a temporal smoothness constraint. Gaussian mixture model (GMM) based clustering and density estimation in the subspace of linear discriminant analysis (LDA) are then applied to thousands of image feature vectors to obtain an intermediate level representation. Finally, at the high level we build a temporal multiresolution histogram model for each action by aggregating the clustering weights of sampled images belonging to that action. We discuss how this high level representation can be extended to achieve temporal scaling invariance and to include Bigram or Multi-gram transition information. Both image clustering and action recognition/segmentation results are given to show the validity of our three tiered representation.

We study a number of open issues in spectral clustering: (i) Selecting the appropriate scale of analysis, (ii) Handling multi-scale data, (iii) Clustering with irregular background clutter, and, (iv) Finding automatically the number of groups. We first propose that a'local' scale should be used to compute the affinity between each pair of points. This local scaling leads to better clustering especially when the data includes multiple scales and when the clusters are placed within a cluttered background. We further suggest exploiting the structure of the eigenvectors to infer automatically the number of groups. This leads to a new algorithm in which the final randomly initialized k-means stage is eliminated.