We construct a nonlinear mapping from a high-dimensional sample space to a low-dimensional vector space, effectively recovering a Cartesian coordinate system for the manifold from which the data is sampled. The mapping preserves local geometric relations in the manifold and is pseudo-invertible. We show how to estimate the intrinsic dimensionality of the manifold from samples, decompose the sample data into locally linear low-dimensional patches, merge these patches into a single lowdimensional coordinatesystem, and compute forward and reverse mappings between the sample and coordinate spaces. The objective functions are convex and their solutions are given in closed form.

The problem of learning a semantic representation of a text document from data is addressed, in the situation where a corpus of unlabeled paired documents is available, each pair being formed by a short English documentand its French translation. This representation can then be used for any retrieval, categorization or clustering task, both in a standard andin a cross-lingual setting. By using kernel functions, in this case simple bag-of-words inner products, each part of the corpus is mapped to a high-dimensional space. The correlations between the two spaces are then learnt by using kernel Canonical Correlation Analysis. A set of directions is found in the first and in the second space that are maximally correlated.Since we assume the two representations are completely independentapart from the semantic content, any correlation between them should reflect some semantic similarity. Certain patterns of English words that relate to a specific meaning should correlate with certain patternsof French words corresponding to the same meaning, across the corpus. Using the semantic representation obtained in this way we first demonstrate that the correlations detected between the two versions of the corpus are significantly higher than random, and hence that a representation basedon such features does capture statistical patterns that should reflect semantic information. Then we use such representation both in cross-language and in single-language retrieval tasks, observing performance that is consistently and significantly superior to LSI on the same data.

Learning to Take Concurrent ActionsKhashayar Rohanimanesh Department of Computer Science University of Massachusetts Amherst, MA 01003 khash@cs.umass.edu Abstract We investigate a general semi-Markov Decision Process (SMDP) framework for modeling concurrent decision making, where agents learn optimal plans over concurrent temporally extended actions. We introduce three types of parallel termination schemes - all, any and continue - and theoretically and experimentally compare them. 1 Introduction We investigate a general framework for modeling concurrent actions. The notion of concurrent action is formalized in a general way, to capture both situations where a single agent can execute multiple parallel processes, as well as the multi-agent case where many agents act in parallel. Concurrency clearly allows agents to achieve goals more quickly: in making breakfast, we interleave making toast and coffee with other activities such as getting milk; in driving, we search for road signs while controlling the wheel, accelerator and brakes.

We argue that human inductive generalization is best explained in a Bayesian framework, rather than by traditional models based on similarity computations.We go beyond previous work on Bayesian concept learning by introducing an unsupervised method for constructing flexible hypothesisspaces, and we propose a version of the Bayesian Occam's razorthat trades off priors and likelihoods to prevent under-or over-generalization in these flexible spaces. We analyze two published data sets on inductive reasoning as well as the results of a new behavioral study that we have carried out.

We introduce the notion of Morton-style factorial coding and illustrate how it may help understand information integration and perceptual coding inthe brain. We show that by focusing on average responses one may miss the existence of factorial coding mechanisms that become only apparent when analyzing spike count histograms.

We propose a model that can learn parts-based representations of high-dimensional data.

We focus on the problem of efficient learning of dependency trees. It is well-known that given the pairwise mutual information coefficients, a minimum-weight spanning tree algorithm solves this problem exactly and in polynomial time. However, for large data-sets it is the construction ofthe correlation matrix that dominates the running time. We have developed a new spanning-tree algorithm which is capable of exploiting partial knowledge about edge weights. The partial knowledge we maintain isa probabilistic confidence interval on the coefficients, which we derive by examining just a small sample of the data. The algorithm is able to flag the need to shrink an interval, which translates to inspection ofmore data for the particular attribute pair. Experimental results show running time that is near-constant in the number of records, without significantloss in accuracy of the generated trees. Interestingly, our spanning-tree algorithm is based solely on Tarjan's red-edge rule, which is generally considered a guaranteed recipe for bad performance.

The application of latent/hidden variable Dynamic Bayesian Networks isconstrained by the complexity of marginalising over latent variables. For this reason either small latent dimensions or Gaussian latentconditional tables linearly dependent on past states are typically considered in order that inference is tractable. We suggest an alternative approach in which the latent variables are modelled using deterministic conditional probability tables.

Abstract Missing

We propose analysis of information in speech using three sources - language (phone), speaker and channeL Information in speech is measured as mutual information between the source and the set of features extracted from speech signaL We assume that distribution offeatures can be modeled using Gaussian distribution. The mutual information is computed using the results of analysis of variability in speech. We observe similarity in the results of phone variability and phone information, and show that the results of the proposed analysis have more meaningful interpretations than the analysis of variability. 1 Introduction Speech signal carries information about the linguistic message, the speaker, the communication channeL In the previous work [1, 2], we proposed analysis of information inspeech as analysis of variability in a set of features extracted from the speech signal. The variability was measured as covariance of the features, and analysis was performed using using multivariate analysis of variance (MANOVA). Total variability was divided into three types of variabilities, namely, intra-phone (or phone) variability, speaker variability, and channel variability.