Deep Boltzmann machines are in principle powerful models for extracting the hierarchical structure of data. Unfortunately, attempts to train layers jointly (without greedy layer-wise pretraining) have been largely unsuccessful. We propose a modification of the learning algorithm that initially recenters the output of the activation functions to zero. This modification leads to a better conditioned Hessian and thus makes learning easier. We test the algorithm on real data and demonstrate that our suggestion, the centered deep Boltzmann machine, learns a hierarchy of increasingly abstract representations and a better generative model of data.

It is known that fixed points of loopy belief propagation (BP) correspond to stationary points of the Bethe variational problem, where we minimize the Bethe free energy subject to normalization and marginalization constraints. Unfortunately, this does not entirely explain BP because BP is a dual rather than primal algorithm to solve the Bethe variational problem -- beliefs are infeasible before convergence. Thus, we have no better understanding of BP than as an algorithm to seek for a common zero of a system of non-linear functions, not explicitly related to each other. In this theoretical paper, we show that these functions are in fact explicitly related -- they are the partial derivatives of a single function of reparameterizations. That means, BP seeks for a stationary point of a single function, without any constraints. This function has a very natural form: it is a linear combination of local log-partition functions, exactly as the Bethe entropy is the same linear combination of local entropies.

Interactive applications incorporating high-data rate sensing and computer vision are becoming possible due to novel runtime systems and the use of parallel computation resources. To allow interactive use, such applications require careful tuning of multiple application parameters to meet required fidelity and latency bounds. This is a nontrivial task, often requiring expert knowledge, which becomes intractable as resources and application load characteristics change. This paper describes a method for automatic performance tuning that learns application characteristics and effects of tunable parameters online, and constructs models that are used to maximize fidelity for a given latency constraint. The paper shows that accurate latency models can be learned online, knowledge of application structure can be used to reduce the complexity of the learning task, and operating points can be found that achieve 90% of the optimal fidelity by exploring the parameter space only 3% of the time.

Gaussian processes (GP) are attractive building blocks for many probabilistic models. Their drawbacks, however, are the rapidly increasing inference time and memory requirement alongside increasing data. The problem can be alleviated with compactly supported (CS) covariance functions, which produce sparse covariance matrices that are fast in computations and cheap to store. CS functions have previously been used in GP regression but here the focus is in a classification problem. This brings new challenges since the posterior inference has to be done approximately. We utilize the expectation propagation algorithm and show how its standard implementation has to be modified to obtain computational benefits from the sparse covariance matrices. We study four CS covariance functions and show that they may lead to substantial speed up in the inference time compared to globally supported functions.

We propose a new method for estimating the intrinsic dimension of a dataset by applying the principle of regularized maximum likelihood to the distances between close neighbors. We propose a regularization scheme which is motivated by divergence minimization principles. We derive the estimator by a Poisson process approximation, argue about its convergence properties and apply it to a number of simulated and real datasets. We also show it has the best overall performance compared with two other intrinsic dimension estimators.

Multi-task learning is a learning paradigm which seeks to improve the generalization performance of a learning task with the help of some other related tasks. In this paper, we propose a regularization formulation for learning the relationships between tasks in multi-task learning. This formulation can be viewed as a novel generalization of the regularization framework for single-task learning. Besides modeling positive task correlation, our method, called multi-task relationship learning (MTRL), can also describe negative task correlation and identify outlier tasks based on the same underlying principle. Under this regularization framework, the objective function of MTRL is convex. For efficiency, we use an alternating method to learn the optimal model parameters for each task as well as the relationships between tasks. We study MTRL in the symmetric multi-task learning setting and then generalize it to the asymmetric setting as well. We also study the relationships between MTRL and some existing multi-task learning methods. Experiments conducted on a toy problem as well as several benchmark data sets demonstrate the effectiveness of MTRL.

In nonlinear latent variable models or dynamic models, if we consider the latent variables as confounders (common causes), the noise dependencies imply further relations between the observed variables. Such models are then closely related to causal discovery in the presence of nonlinear confounders, which is a challenging problem. However, generally in such models the observation noise is assumed to be independent across data dimensions, and consequently the noise dependencies are ignored. In this paper we focus on the Gaussian process latent variable model (GPLVM), from which we develop an extended model called invariant GPLVM (IGPLVM), which can adapt to arbitrary noise covariances. With the Gaussian process prior put on a particular transformation of the latent nonlinear functions, instead of the original ones, the algorithm for IGPLVM involves almost the same computational loads as that for the original GPLVM. Besides its potential application in causal discovery, IGPLVM has the advantage that its estimated latent nonlinear manifold is invariant to any nonsingular linear transformation of the data. Experimental results on both synthetic and realworld data show its encouraging performance in nonlinear manifold learning and causal discovery.

Separation of the sources and analysis of their connectivity have been an important topic in EEG/MEG analysis. To solve this problem in an automatic manner, we propose a two-layer model, in which the sources are conditionally uncorrelated from each other, but not independent; the dependence is caused by the causality in their time-varying variances (envelopes). The model is identified in two steps. We first propose a new source separation technique which takes into account the autocorrelations (which may be time-varying) and time-varying variances of the sources. The causality in the envelopes is then discovered by exploiting a special kind of multivariate GARCH (generalized autoregressive conditional heteroscedasticity) model. The resulting causal diagram gives the effective connectivity between the separated sources; in our experimental results on MEG data, sources with similar functions are grouped together, with negative influences between groups, and the groups are connected via some interesting sources.

Graphical models are widely used in scienti fic and engineering research to represent conditional independence structures between random variables. In many controlled experiments, environmental changes or external stimuli can often alter the conditional dependence between the random variables, and potentially produce significant structural changes in the corresponding graphical models. Therefore, it is of great importance to be able to detect such structural changes from data, so as to gain novel insights into where and how the structural changes take place and help the system adapt to the new environment. Here we report an effective learning strategy to extract structural changes in Gaussian graphical model using l1-regularization based convex optimization. We discuss the properties of the problem formulation and introduce an efficient implementation by the block coordinate descent algorithm. We demonstrate the principle of the approach on a numerical simulation experiment, and we then apply the algorithm to the modeling of gene regulatory networks under different conditions and obtain promising yet biologically plausible results.

Automatic image annotation (AIA) raises tremendous challenges to machine learning as it requires modeling of data that are both ambiguous in input and output, e.g., images containing multiple objects and labeled with multiple semantic tags. Even more challenging is that the number of candidate tags is usually huge (as large as the vocabulary size) yet each image is only related to a few of them. This paper presents a hybrid generative-discriminative classifier to simultaneously address the extreme data-ambiguity and overfitting-vulnerability issues in tasks such as AIA. Particularly: (1) an Exponential-Multinomial Mixture (EMM) model is established to capture both the input and output ambiguity and in the meanwhile to encourage prediction sparsity; and (2) the prediction ability of the EMM model is explicitly maximized through discriminative learning that integrates variational inference of graphical models and the pairwise formulation of ordinal regression. Experiments show that our approach achieves both superior annotation performance and better tag scalability.