We propose a recursive algorithm for clustering trajectories lying in multiple moving hyperplanes. Starting from a given or random initial condition, we use normalized gradient descent to update the coefficients of a time varying polynomial whose degree is the number of hyperplanes and whose derivatives at a trajectory give an estimate of the vector normal to the hyperplane containing that trajectory. As time proceeds, the estimates of the hyperplane normals are shown to track their true values in a stable fashion. The segmentation of the trajectories is then obtained by clustering their associated normal vectors. The final result is a simple recursive algorithm for segmenting a variable number of moving hyperplanes. We test our algorithm on the segmentation of dynamic scenes containing rigid motions and dynamic textures, e.g., a bird floating on water. Our method not only segments the bird motion from the surrounding water motion, but also determines patterns of motion in the scene (e.g., periodic motion) directly from the temporal evolution of the estimated polynomial coefficients. Our experiments also show that our method can deal with appearing and disappearing motions in the scene.

Sequence labeling, the task of assigning labels y: yl, ..., yL to an input sequence x: 1:1, ...,:cL, is

Policy gradient methods are reinforcement learning algorithms that adapt a parameterized policyby following a performance gradient estimate. Conventional policy gradient methods use Monte-Carlo techniques to estimate this gradient. Since Monte Carlo methods tend to have high variance, a large number of samples is required, resulting in slow convergence. In this paper, we propose a Bayesian framework that models the policy gradient as a Gaussian process. This reduces the number of samples needed to obtain accurate gradient estimates. Moreover, estimates of the natural gradient as well as a measure of the uncertainty in the gradient estimates are provided at little extra cost.

Chemical reaction networks by which individual cells gather and process information abouttheir chemical environments have been dubbed "signal transduction" networks. Despite this suggestive terminology, there have been few attempts to analyze chemical signaling systems with the quantitative tools of information theory. Gradientsensing in the social amoeba Dictyostelium discoideum is a well characterized signal transduction system in which a cell estimates the direction of a source of diffusing chemoattractant molecules based on the spatiotemporal sequence of ligand-receptor binding events at the cell membrane. Using Monte Carlo techniques (MCell) we construct a simulation in which a collection of individual ligandparticles undergoing Brownian diffusion in a three-dimensional volume interact with receptors on the surface of a static amoeboid cell. Adapting a method for estimation of spike train entropies described by Victor (originally due to Kozachenko and Leonenko), we estimate lower bounds on the mutual information betweenthe transmitted signal (direction of ligand source) and the received signal (spatiotemporal pattern of receptor binding/unbinding events). Hence we provide a quantitative framework for addressing the question: how much could the cell know, and when could it know it? We show that the time course of the mutual informationbetween the cell's surface receptors and the (unknown) gradient direction is consistent with experimentally measured cellular response times. We find that the acquisition of directional information depends strongly on the time constant at which the intracellular response is filtered.

Many computer aided diagnosis (CAD) problems can be best modelled as a multiple-instance learning (MIL) problem with unbalanced data: i.e., the training data typically consists of a few positive bags, and a very large number of negative instances.Existing MIL algorithms are much too computationally expensive for these datasets. We describe CH, a framework for learning a Convex Hull representation of multiple instances that is significantly faster than existing MIL algorithms. Our CH framework applies to any standard hyperplane-based learning algorithm, and for some algorithms, is guaranteed to find the global optimal solution. Experimentalstudies on two different CAD applications further demonstrate that the proposed algorithm significantly improves diagnostic accuracy when compared toboth MIL and traditional classifiers. Although not designed for standard MIL problems (which have both positive and negative bags and relatively balanced datasets),comparisons against other MIL methods on benchmark problems also indicate that the proposed method is competitive with the state-of-the-art.

We focus on the problem of estimating the graph structure associated with a discrete Markov random field.

In this paper, we propose a novel exemplar-based approach to extract dynamic foreground regions from a changing background within a collection of images or a video sequence. By using image segmentation as a pre-processing step, we convert this traditional pixel-wise labeling problem into a lower-dimensional supervised, binary labeling procedure on image segments. Our approach consists of three steps. First, a set of random image patches are spatially and adaptively sampled within each segment. Second, these sets of extracted samples are formed into two "bags of patches" to model the foreground/background appearance, respectively.

We focus on the problem of estimating the graph structure associated with a discrete Markov random field.

We introduce a novel adaptive nonparametric anomaly detection approach, called GEM, that is based on the minimal covering properties of K-point entropic graphs when constructed on N training samples from a nominal probability distribution. Such graphs have the property that as N their span recovers the entropy minimizing set that supports at least ρ K/N(100)% of the mass of the Lebesgue part of the distribution. When a test sample falls outside of the entropy minimizing set an anomaly can be declared at a statistical level of significance α 1 ρ. A method for implementing this nonparametric anomaly detector is proposed that approximates this minimum entropy set by the influence region of a K-point entropic graph built on the training data. By implementing an incremental leave-one-out k-nearest neighbor graph on resampled subsets of the training data GEM can efficiently detect outliers at a given level of significance and compute their empirical p-values. We illustrate GEM for several simulated and real data sets in high dimensional feature spaces.

In real-world planning problems, we must reason not only about our own goals, but about the goals of other agents with which we may interact. Often these agents' goals are neither completely aligned with our own nor directly opposed to them. Instead there are opportunities for cooperation: by joining forces, the agents can all achieve higher utility than they could separately. But, in order to cooperate, the agents must negotiate a mutually acceptable plan from among the many possible ones, and each agent must trust that the others will follow their parts of the deal. Research in multi-agent planning has often avoided the problem of making sure that all agents have an incentive to follow a proposed joint plan. On the other hand, while game theoretic algorithms handle incentives correctly, they often don't scale to large planning problems. In this paper we attempt to bridge the gap between these two lines of research: we present an efficient game-theoretic approximate planning algorithm, along with a negotiation protocol which encourages agents to compute and agree on joint plans that are fair and optimal in a sense defined below. We demonstrate our algorithm and protocol on two simple robotic planning problems.