We describe a new iterative method for parameter estimation of Gaussian mixtures.The new method is based on a framework developed by Kivinen and Warmuth for supervised online learning. In contrast to gradient descentand EM, which estimate the mixture's covariance matrices, the proposed method estimates the inverses of the covariance matrices. Furthennore, the new parameter estimation procedure can be applied in both online and batch settings. We show experimentally that it is typically fasterthan EM, and usually requires about half as many iterations as EM. 1 Introduction Mixture models, in particular mixtures of Gaussians, have been a popular tool for density estimation, clustering, and unsupervised learning with a wide range of applications (see for instance [5, 2] and the references therein). Mixture models are one of the most useful tools for handling incomplete data, in particular hidden variables.

We describe a real-time computer vision and machine learning system for modeling and recognizing human behaviors in two different scenarios: (1) complex, twohanded actionrecognition in the martial art of Tai Chi and (2) detection and recognition of individual human behaviors and multiple-person interactions in a visual surveillance task. In the latter case, the system is particularly concerned with detecting when interactions between people occur, and classifying them. Graphical models, such as Hidden Markov Models (HMMs) [6] and Coupled Hidden MarkovModels (CHMMs) [3, 2], seem appropriate for modeling and, classifying human behaviors because they offer dynamic time warping, a well-understood training algorithm, and a clear Bayesian semantics for both individual (HMMs) and interacting or coupled (CHMMs) generative processes. A major problem with this data-driven statistical approach, especially when modeling rare or anomalous behaviors, is the limited number of training examples. A major emphasis of our work, therefore, is on efficient Bayesian integration of both prior knowledge with evidence from data.

We describe a unifying method for proving relative loss bounds for online linearthreshold classification algorithms, such as the Perceptron and the Winnow algorithms. For classification problems the discrete loss is used, i.e., the total number of prediction mistakes. We introduce a continuous lossfunction, called the "linear hinge loss", that can be employed to derive the updates of the algorithms. We first prove bounds w.r.t. the linear hinge loss and then convert them to the discrete loss. We introduce anotion of "average margin" of a set of examples . We show how relative loss bounds based on the linear hinge loss can be converted to relative loss bounds i.t.o. the discrete loss using the average margin.

A new algorithm for Support Vector regression is described.

We consider recurrent analog neural nets where each gate is subject to Gaussian noise, or any other common noise distribution whose probability densityfunction is nonzero on a large set.

We present a method for learning complex appearance mappings.

The hierarchical representation of data has various applications in domains suchas data mining, machine vision, or information retrieval. In this paper we introduce an extension of the Expectation-Maximization (EM) algorithm that learns mixture hierarchies in a computationally efficient manner.Efficiency is achieved by progressing in a bottom-up fashion, i.e. by clustering the mixture components of a given level in the hierarchy to obtain those of the level above. This clustering requires only knowledge of the mixture parameters, there being no need to resort to intermediate samples. In addition to practical applications, the algorithm allows a new interpretation of EM that makes clear the relationship with nonparametric kernel-based estimation methods, provides explicit control overthe tradeoff between the bias and variance of EM estimates, and offers new insights about the behavior ofdeterministic annealing methods commonly used with EM to escape local minima of the likelihood.

Computer animation through the numerical simulation of physics-based graphics models offers unsurpassed realism, but it can be computationally demanding.This paper demonstrates the possibility of replacing the numerical simulation of nontrivial dynamic models with a dramatically more efficient "NeuroAnimator" that exploits neural networks. NeuroAnimators areautomatically trained off-line to emulate physical dynamics through the observation of physics-based models in action. Depending onthe model, its neural network emulator can yield physically realistic animation one or two orders of magnitude faster than conventional numericalsimulation. We demonstrate NeuroAnimators for a variety of physics-based models. 1 Introduction Animation based on physical principles has been an influential trend in computer graphics for over a decade (see, e.g., [1, 2, 3]). This is not only due to the unsurpassed realism that physics-based techniques offer.

These Ca2 signals are often organized in complex temporal and spatial patterns even under conditions of sustained stimulation.

I consider the problem of learning concepts from small numbers of positive examples,a feat which humans perform routinely but which computers arerarely capable of. Bridging machine learning and cognitive science perspectives, I present both theoretical analysis and an empirical study with human subjects for the simple task oflearning concepts corresponding toaxis-aligned rectangles in a multidimensional feature space. Existing learning models, when applied to this task, cannot explain how subjects generalize from only a few examples of the concept. I propose a principled Bayesian model based on the assumption that the examples are a random sample from the concept to be learned. The model gives precise fits to human behavior on this simple task and provides qualitati ve insights into more complex, realistic cases of concept learning.