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.

Uncertainty is omnipresent when we perceive or interact with our environment, and the Bayesian framework provides computational methods for dealing with it. Mathematical models for Bayesian decision making typically require datastructures that are hard to implement in neural networks. This article shows that even the simplest and experimentally best supported type of synaptic plasticity, Hebbian learning, in combination with a sparse, redundant neural code, can in principle learn to infer optimal Bayesian decisions. We present a concrete Hebbian learning rule operating on log-probability ratios. Modulated by reward-signals, this Hebbian plasticity rule also provides a new perspective for understanding how Bayesian inference could support fast reinforcement learning in the brain.

Many graphical models, such as Markov Logic Networks (MLNs) with evidence, possess highly symmetric substructures but no exact symmetries. Unfortunately, there are few principled methods that exploit these symmetric substructures to perform efficient approximate inference. In this paper, we present a lifted variant of the Weighted Mini-Bucket elimination algorithm which provides a principled way to (i) exploit the highly symmetric substructure of MLN models, and (ii) incorporate high-order inference terms which are necessary for high quality approximate inference. Our method has significant control over the accuracy-time trade-off of the approximation, allowing us to generate any-time approximations. Experimental results demonstrate the utility of this class of approximations, especially in models with strong repulsive potentials.

In recent years, a rapidly increasing number of applications in practice requires solving non-convex objectives, like training neural networks, learning graphical models, maximum likelihood estimation etc. Though simple heuristics such as gradient descent with very few modifications tend to work well, theoretical understanding is very weak. We consider possibly the most natural class of non-convex functions where one could hope to obtain provable guarantees: functions that are approximately convex'', i.e. functions $\tf: \Real d \to \Real$ for which there exists a \emph{convex function} $f$ such that for all $x$, $ \tf(x) - f(x) \le \errnoise$ for a fixed value $\errnoise$. It is quite natural to conjecture that for fixed $\err$, the problem gets harder for larger $\errnoise$, however, the exact dependency of $\err$ and $\errnoise$ is not known. In this paper, we strengthen the known \emph{information theoretic} lower bounds on the trade-off between $\err$ and $\errnoise$ substantially, and exhibit an algorithm that matches these lower bounds for a large class of convex bodies.

Stochastic variational inference (SVI) uses stochastic optimization to scale up Bayesian computation to massive data. We present an alternative perspective on SVI as approximate parallel coordinate ascent. SVI trades-off bias and variance to step close to the unknown true coordinate optimum given by batch variational Bayes (VB). We define a model to automate this process. As a consequence of this construction, we update the variational parameters using Bayes rule, rather than a hand-crafted optimization schedule.

We present a new algorithmic approach for the task of finding a chordal Markov network structure that maximizes a given scoring function. The algorithm is based on branch and bound and integrates dynamic programming for both domain pruning and for obtaining strong bounds for search-space pruning. Empirically, we show that the approach dominates in terms of running times a recent integer programming approach (and thereby also a recent constraint optimization approach) for the problem. Papers published at the Neural Information Processing Systems Conference.

In this paper, we prove that every multivariate polynomial with even degree can be decomposed into a sum of convex and concave polynomials. Motivated by this property, we exploit the concave-convex procedure to perform inference on continuous Markov random fields with polynomial potentials. In particular, we show that the concave-convex decomposition of polynomials can be expressed as a sum-of-squares optimization, which can be efficiently solved via semidefinite programming. We demonstrate the effectiveness of our approach in the context of 3D reconstruction, shape from shading and image denoising, and show that our approach significantly outperforms existing approaches in terms of efficiency as well as the quality of the retrieved solution. Papers published at the Neural Information Processing Systems Conference.

Both learning and inference tasks on Bayesian networks are NP-hard in general. Bounded tree-width Bayesian networks have recently received a lot of attention as a way to circumvent this complexity issue; however, while inference on bounded tree-width networks is tractable, the learning problem remains NP-hard even for tree-width 2. In this paper, we propose bounded vertex cover number Bayesian networks as an alternative to bounded tree-width networks. In particular, we show that both inference and learning can be done in polynomial time for any fixed vertex cover number bound $k$, in contrast to the general and bounded tree-width cases; on the other hand, we also show that learning problem is W[1]-hard in parameter $k$. Furthermore, we give an alternative way to learn bounded vertex cover number Bayesian networks using integer linear programming (ILP), and show this is feasible in practice. Papers published at the Neural Information Processing Systems Conference.

We introduce the Locally Linear Latent Variable Model (LL-LVM), a probabilistic model for non-linear manifold discovery that describes a joint distribution over observations, their manifold coordinates and locally linear maps conditioned on a set of neighbourhood relationships. The model allows straightforward variational optimisation of the posterior distribution on coordinates and locally linear maps from the latent space to the observation space given the data. Thus, the LL-LVM encapsulates the local-geometry preserving intuitions that underlie non-probabilistic methods such as locally linear embedding (LLE). Its probabilistic semantics make it easy to evaluate the quality of hypothesised neighbourhood relationships, select the intrinsic dimensionality of the manifold, construct out-of-sample extensions and to combine the manifold model with additional probabilistic models that capture the structure of coordinates within the manifold. Papers published at the Neural Information Processing Systems Conference.

Reliably recovering 3D human pose from monocular video requires constraints that bias the estimates towards typical human poses and motions. We define priors for people tracking using a Laplacian Eigenmaps Latent Variable Model (LELVM). LELVM is a probabilistic dimensionality reduction model that naturally combines the advantages of latent variable models---definining a multimodal probability density for latent and observed variables, and globally differentiable nonlinear mappings for reconstruction and dimensionality reduction---with those of spectral manifold learning methods---no local optima, ability to unfold highly nonlinear manifolds, and good practical scaling to latent spaces of high dimension. LELVM is computationally efficient, simple to learn from sparse training data, and compatible with standard probabilistic trackers such as particle filters. We analyze the performance of a LELVM-based probabilistic sigma point mixture tracker in several real and synthetic human motion sequences and demonstrate that LELVM provides sufficient constraints for robust operation in the presence of missing, noisy and ambiguous image measurements.