This paper proposes a new approach to model-based clustering under prior knowledge.

We present a method for learning a low-dimensional representation which is shared across a set of multiple related tasks. The method builds upon the wellknown 1-normregularization problem using a new regularizer which controls the number of learned features common for all the tasks. We show that this problem is equivalent to a convex optimization problem and develop an iterative algorithm for solving it. The algorithm has a simple interpretation: it alternately performs a supervised and an unsupervised step, where in the latter step we learn commonacross-tasks representationsand in the former step we learn task-specific functions using these representations. We report experiments on a simulated and a real data set which demonstrate that the proposed method dramatically improves the performance relativeto learning each task independently. Our algorithm can also be used, as a special case, to simply select - not learn - a few common features across the tasks.

We rigorously establish a close relationship between message passing algorithms and models of neurodynamics by showing that the equations of a continuous Hopfield networkcan be derived from the equations of belief propagation on a binary Markov random field. As Hopfield networks are equipped with a Lyapunov function, convergenceis guaranteed. As a consequence, in the limit of many weak connections perneuron, Hopfield networks exactly implement a continuous-time variant of belief propagation starting from message initialisations that prevent from running into convergence problems. Our results lead to a better understanding of the role of message passing algorithms in real biological neural networks.

In large-scale applications, the data are often highly sparse. CRS combines sketching and sampling in that it converts sketches of the data into conditional random samples online in the estimation stage, with the sample size determined retrospectively.

We describe Hidden Semi-Markov Support Vector Machines (SHM SVMs), an extension of HM SVMs to semi-Markov chains. This allows us to predict segmentations ofsequences based on segment-based features measuring properties such as the length of the segment. We propose a novel technique to partition the problem into sub-problems. The independently obtained partial solutions can then be recombined in an efficient way, which allows us to solve label sequence learning problemswith several thousands of labeled sequences. We have tested our algorithm for predicting gene structures, an important problem in computational biology. Results on a well-known model organism illustrate the great potential of SHM SVMs in computational biology.

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 acceptableplan 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'tscale 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 andprotocol on two simple robotic planning problems.

Discriminative learning methods for classification perform well when training and test data are drawn from the same distribution. In many situations, though, we have labeled training data for a source domain, and we wish to learn a classifier which performs well on a target domain with a different distribution. Under what conditions can we adapt a classifier trained on the source domain for use in the target domain? Intuitively, a good feature representation is a crucial factor in the success of domain adaptation. We formalize this intuition theoretically with a generalization bound for domain adaption. Our theory illustrates the tradeoffs inherent indesigning a representation for domain adaptation and gives a new justification for a recently proposed model. It also points toward a promising new model for domain adaptation: one which explicitly minimizes the difference between the source and target domains, while at the same time maximizing the margin of the training set.

We present a new statistical framework called hidden Markov Dirichlet process (HMDP) to jointly model the genetic recombinations among possibly infinite number of founders and the coalescence-with-mutation events in the resulting genealogies. TheHMDP posits that a haplotype of genetic markers is generated by a sequence of recombination events that select an ancestor for each locus from an unbounded set of founders according to a 1st-order Markov transition process. Conjoining this process with a mutation model, our method accommodates both between-lineage recombination and within-lineage sequence variations, and leads to a compact and natural interpretation of the population structure and inheritance process underlying haplotype data. We have developed an efficient sampling algorithm forHMDP based on a two-level nested Pólya urn scheme. On both simulated and real SNP haplotype data, our method performs competitively or significantly better than extant methods in uncovering the recombination hotspots along chromosomal loci;and in addition it also infers the ancestral genetic patterns and offers a highly accurate map of ancestral compositions of modern populations.

Such a problem can occur in many real-world tasks, e.g. an image usually

Planning in partially observable domains is a notoriously difficult problem. However, inmany real-world scenarios, planning can be simplified by decomposing the task into a hierarchy of smaller planning problems. Several approaches have been proposed to optimize a policy that decomposes according to a hierarchy specified a priori. In this paper, we investigate the problem of automatically discovering the hierarchy. More precisely, we frame the optimization of a hierarchical policy as a non-convex optimization problem that can be solved with general nonlinear solvers, a mixed-integer nonlinear approximation or a form of bounded hierarchical policyiteration. By encoding the hierarchical structure as variables of the optimization problem, we can automatically discover a hierarchy. Our method is flexible enough to allow any parts of the hierarchy to be specified based on prior knowledge while letting the optimization discover the unknown parts. It can also discover hierarchical policies, including recursive policies, that are more compact (potentially infinitely fewer parameters) and often easier to understand given the decomposition induced by the hierarchy.