We introduce the first temporal-difference learning algorithms that converge with smooth value function approximators, such as neural networks. Conventional temporal-difference (TD) methods, such as TD($\lambda$), Q-learning and Sarsa have been used successfully with function approximation in many applications. However, it is well known that off-policy sampling, as well as nonlinear function approximation, can cause these algorithms to become unstable (i.e., the parameters of the approximator may diverge). Sutton et al (2009a,b) solved the problem of off-policy learning with linear TD algorithms by introducing a new objective function, related to the Bellman-error, and algorithms that perform stochastic gradient-descent on this function. In this paper, we generalize their work to nonlinear function approximation. We present a Bellman error objective function and two gradient-descent TD algorithms that optimize it. We prove the asymptotic almost-sure convergence of both algorithms for any finite Markov decision process and any smooth value function approximator, under usual stochastic approximation conditions. The computational complexity per iteration scales linearly with the number of parameters of the approximator. The algorithms are incremental and are guaranteed to converge to locally optimal solutions.

Imaging techniques such as optical imaging of intrinsic signals, 2-photon calcium imaging and voltage sensitive dye imaging can be used to measure the functional organization of visual cortex across different spatial scales. Here, we present Bayesian methods based on Gaussian processes for extracting topographic maps from functional imaging data. In particular, we focus on the estimation of orientation preference maps (OPMs) from intrinsic signal imaging data. We model the underlying map as a bivariate Gaussian process, with a prior covariance function that reflects known properties of OPMs, and a noise covariance adjusted to the data. The posterior mean can be interpreted as an optimally smoothed estimate of the map, and can be used for model based interpolations of the map from sparse measurements. By sampling from the posterior distribution, we can get error bars on statistical properties such as preferred orientations, pinwheel locations or -counts. Finally, the use of an explicit probabilistic model facilitates interpretation of parameters and provides the basis for decoding studies. We demonstrate our model both on simulated data and on intrinsic signaling data from ferret visual cortex.

We present a probabilistic factor analysis model which can be used for studying spatiotemporal datasets. The spatial and temporal structure is modeled by using Gaussian process priors both for the loading matrix and the factors. The posterior distributions are approximated using the variational Bayesian framework. High computational cost of Gaussian process modeling is reduced by using sparse approximations. Themodel is used to compute the reconstructions of the global sea surface temperatures from a historical dataset. The results suggest that the proposed model can outperform the state-of-the-art reconstruction systems.

In recent years, deep learning approaches have gained significant interest as a way of building hierarchical representations from unlabeled data. However, to our knowledge, these deep learning approaches have not been extensively studied for auditory data. In this paper, we apply convolutional deep belief networks to audio data and empirically evaluate them on various audio classification tasks. For the case of speech data, we show that the learned features correspond to phones/phonemes. In addition, our feature representations trained from unlabeled audio data show very good performance for multiple audio classification tasks. We hope that this paper will inspire more research on deep learning approaches applied to a wide range of audio recognition tasks.

The problem of approximating a given probability distribution using a simpler distribution plays an important role in several areas of machine learning, e.g. variational inference and classification. Within this context, we consider the task of learning a mixture of tree distributions. Although mixtures of trees can be learned by minimizing the KL-divergence using an EM algorithm, its success depends heavily on the initialization. We propose an efficient strategy for obtaining a good initial set of trees that attempts to cover the entire observed distribution by minimizing the $\alpha$-divergence with $\alpha = \infty$. We formulate the problem using the fractional covering framework and present a convergent sequential algorithm that only relies on solving a convex program at each iteration. Compared to previous methods, our approach results in a significantly smaller mixture of trees that provides similar or better accuracies. We demonstrate the usefulness of our approach by learning pictorial structures for face recognition.

Most of existing methods for DNA motif discovery consider only a single set of sequences to find an over-represented motif. In contrast, we consider multiple sets of sequences where we group sets associated with the same motif into a cluster, assuming that each set involves a single motif. Clustering sets of sequences yields clusters of coherent motifs, improving signal-to-noise ratio or enabling us to identify multiple motifs. We present a probabilistic model for DNA motif discovery where we identify multiple motifs through searching for patterns which are shared across multiple sets of sequences. Our model infers cluster-indicating latent variables and learns motifs simultaneously, where these two tasks interact with each other. We show that our model can handle various motif discovery problems, depending on how to construct multiple sets of sequences. Experiments on three different problems for discovering DNA motifs emphasize the useful behavior and confirm the substantial gains over existing methods where only single set of sequences is considered.

The Minimum Description Length (MDL) principle selects the model that has the shortest code for data plus model. We show that for a countable class of models, MDL predictions are close to the true distribution in a strong sense. The result is completely general. No independence, ergodicity, stationarity, identifiability, or other assumption on the model class need to be made. More formally, we show that for any countable class of models, the distributions selected by MDL (or MAP) asymptotically predict (merge with) the true measure in the class in total variation distance.

Locality information is crucial in datasets where each variable corresponds to a measurement in a manifold (silhouettes, motion trajectories, 2D and 3D images). Although these datasets are typically under-sampled and high-dimensional, they often need to be represented with low-complexity statistical models, which are comprised of only the important probabilistic dependencies in the datasets. Most methods attempt to reduce model complexity by enforcing structure sparseness. However, sparseness cannot describe inherent regularities in the structure. Hence, in this paper we first propose a new class of Gaussian graphical models which, together with sparseness, imposes local constancy through ${\ell}_1$-norm penalization. Second, we propose an efficient algorithm which decomposes the strictly convex maximum likelihood estimation into a sequence of problems with closed form solutions. Through synthetic experiments, we evaluate the closeness of the recovered models to the ground truth. We also test the generalization performance of our method in a wide range of complex real-world datasets and demonstrate that it can capture useful structures such as the rotation and shrinking of a beating heart, motion correlations between body parts during walking and functional interactions of brain regions. Our method outperforms the state-of-the-art structure learning techniques for Gaussian graphical models both for small and large datasets.

In this paper we present a novel approach to learn directed acyclic graphs (DAG) and factor models within the same framework while also allowing for model comparison between them. For this purpose, we exploit the connection between factor models and DAGs to propose Bayesian hierarchies based on spike and slab priors to promote sparsity, heavy-tailed priors to ensure identifiability and predictive densities to perform the model comparison. We require identifiability to be able to produce variable orderings leading to valid DAGs and sparsity to learn the structures. The effectiveness of our approach is demonstrated through extensive experiments on artificial and biological data showing that our approach outperform a number of state of the art methods.

Existing models of categorization typically represent to-be-classified items as points in a multidimensional space. While from a mathematical point of view, an infinite number of basis sets can be used to represent points in this space, the choice of basis set is psychologically crucial. People generally choose the same basis dimensions, and have a strong preference to generalize along the axes of these dimensions, but not diagonally". What makes some choices of dimension special? We explore the idea that the dimensions used by people echo the natural variation in the environment. Specifically, we present a rational model that does not assume dimensions, but learns the same type of dimensional generalizations that people display. This bias is shaped by exposing the model to many categories with a structure hypothesized to be like those which children encounter. Our model can be viewed as a type of transformed Dirichlet process mixture model, where it is the learning of the base distribution of the Dirichlet process which allows dimensional generalization.The learning behaviour of our model captures the developmental shift from roughly "isotropic" for children to the axis-aligned generalization that adults show."