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.

Learning algorithms normally assume that there is at most one annotation or label per data point. However, in some scenarios, such as medical diagnosis and on-line collaboration,multiple annotations may be available. In either case, obtaining labels for data points can be expensive and time-consuming (in some circumstances ground-truth may not exist). Semi-supervised learning approaches have shown that utilizing the unlabeled data is often beneficial in these cases. This paper presents a probabilistic semi-supervised model and algorithm that allows for learning from both unlabeled and labeled data in the presence of multiple annotators. We assume that it is known what annotator labeled which data points. The proposed approach produces annotator models that allow us to provide (1) estimates of the true label and (2) annotator variable expertise for both labeled and unlabeled data. We provide numerical comparisons under various scenarios and with respect to standard semi-supervised learning. Experiments showed that the presented approach provides clear advantages over multi-annotator methods that do not use the unlabeled data and over methods that do not use multi-labeler information.

In this paper, we tackle the problem of online semi-supervised learning (SSL). When data arrive in a stream, the dual problems of computation and data storage arise for any SSL method. We propose a fast approximate online SSL algorithm that solves for the harmonic solution on an approximate graph. We show, both empirically and theoretically, that good behavior can be achieved by collapsing nearby points into a set of local "representative points" that minimize distortion. Moreover, we regularize the harmonic solution to achieve better stability properties. We apply our algorithm to face recognition and optical character recognition applications to show that we can take advantage of the manifold structure to outperform the previous methods. Unlike previous heuristic approaches, we show that our method yields provable performance bounds.

Recent reports have described that the equivalent sample size (ESS) in a Dirichlet prior plays an important role in learning Bayesian networks. This paper provides an asymptotic analysis of the marginal likelihood score for a Bayesian network. Results show that the ratio of the ESS and sample size determine the penalty of adding arcs in learning Bayesian networks. The number of arcs increases monotonically as the ESS increases; the number of arcs monotonically decreases as the ESS decreases. Furthermore, the marginal likelihood score provides a unified expression of various score metrics by changing prior knowledge.

We study the problem of learning Bayesian network structures from data. We develop an algorithm for finding the k-best Bayesian network structures. We propose to compute the posterior probabilities of hypotheses of interest by Bayesian model averaging over the k-best Bayesian networks. We present empirical results on structural discovery over several real and synthetic data sets and show that the method outperforms the model selection method and the state of-the-art MCMC methods.

Monte-Carlo Tree Search (MCTS) methods are drawing great interest after yielding breakthrough results in computer Go. This paper proposes a Bayesian approach to MCTS that is inspired by distributionfree approaches such as UCT [13], yet significantly differs in important respects. The Bayesian framework allows potentially much more accurate (Bayes-optimal) estimation of node values and node uncertainties from a limited number of simulation trials. We further propose propagating inference in the tree via fast analytic Gaussian approximation methods: this can make the overhead of Bayesian inference manageable in domains such as Go, while preserving high accuracy of expected-value estimates. We find substantial empirical outperformance of UCT in an idealized bandit-tree test environment, where we can obtain valuable insights by comparing with known ground truth. Additionally we rigorously prove on-policy and off-policy convergence of the proposed methods.

The explore-exploit dilemma is one of the central challenges in Reinforcement Learning (RL). Bayesian RL solves the dilemma by providing the agent with information in the form of a prior distribution over environments; however, full Bayesian planning is intractable. Planning with the mean MDP is a common myopic approximation of Bayesian planning. We derive a novel reward bonus that is a function of the posterior distribution over environments, which, when added to the reward in planning with the mean MDP, results in an agent which explores efficiently and effectively. Although our method is similar to existing methods when given an uninformative or unstructured prior, unlike existing methods, our method can exploit structured priors. We prove that our method results in a polynomial sample complexity and empirically demonstrate its advantages in a structured exploration task.