Many learning problems in real world applications involve rich datasets comprising multiple information modalities. In this work, we study co-regularized PLSA(coPLSA) as an efficient solution to probabilistic topic analysis of multi-modal data. In coPLSA, similarities between topic compositions of a data entity across different data modalities are measured with divergences between discrete probabilities, which are incorporated as a co-regularizer to augment individual PLSA models over each data modality. We derive efficient iterative learning algorithms for coPLSA with symmetric KL, L2 and L1 divergences as co-regularizers, in each case the essential optimization problem affords simple numerical solutions that entail only matrix arithmetic operations and numerical solution of 1D nonlinear equations. We evaluate the performance of the coPLSA algorithms on text/image cross-modal retrieval tasks, on which they show competitive performance with state-of-the-art methods.

In Supreme Court parlance and the political science literature, an ideal point positions a justice in a continuous space and can be interpreted as a quantification of the justice's policy preferences. We present an automated approach to infer such ideal points for justices of the US Supreme Court. This approach combines topic modeling over case opinions with the voting (and endorsing) behavior of justices. Furthermore, given a topic of interest, say the Fourth Amendment, the topic model can be optionally seeded with supervised information to steer the inference of ideal points. Application of this methodology over five years of cases provides interesting perspectives into the leaning of justices on crucial issues, coalitions underlying specific topics, and the role of swing justices in deciding the outcomes of cases.

Learning in deep models using Bayesian methods has generated significant attention recently. This is largely because of the feasibility of modern Bayesian methods to yield scalable learning and inference, while maintaining a measure of uncertainty in the model parameters. Stochastic gradient MCMC algorithms (SG-MCMC) are a family of diffusion-based sampling methods for large-scale Bayesian learning. In SG-MCMC, multivariate stochastic gradient thermostats (mSGNHT) augment each parameter of interest, with a momentum and a thermostat variable to maintain stationary distributions as target posterior distributions. As the number of variables in a continuous-time diffusion increases, its numerical approximation error becomes a practical bottleneck, so better use of a numerical integrator is desirable. To this end, we propose use of an efficient symmetric splitting integrator in mSGNHT, instead of the traditional Euler integrator. We demonstrate that the proposed scheme is more accurate, robust, and converges faster. These properties are demonstrated to be desirable in Bayesian deep learning. Extensive experiments on two canonical models and their deep extensions demonstrate that the proposed scheme improves general Bayesian posterior sampling, particularly for deep models.

Instead of using a uniform metric, instance specific distance learning methods assign multiple metrics for different localities, which take data heterogeneity into consideration. Therefore, they may improve the performance of distance based classifiers, e.g., kNN. Existing methods obtain multiple metrics of test data by either transductively assigning metrics for unlabeled instances or designing distance functions manually, which are with limited generalization ability. In this paper, we propose isMets (Instance Specific METric Subspace) framework which can automatically span the whole metric space in a generative manner and is able to inductively learn a specific metric subspace for each instance via inferring the expectation over the metric bases in a Bayesian manner. The whole framework can be solved with Variational Bayes (VB). Experiment on synthetic data shows that the learned results are with good interpretability. Moreover, comprehensive results on real world datasets validate the effectiveness and robustness of isMets.

Bayesian models provide a framework for probabilistic modelling of complex datasets. Many such models are computationally demanding, especially in the presence of large datasets. In sensor network applications, statistical (Bayesian) parameter estimation usually relies on decentralized algorithms, in which both data and computation are distributed across the nodes of the network. In this paper we propose a framework for decentralized Bayesian learning using Bregman Alternating Direction Method of Multipliers (B-ADMM). We demonstrate the utility of our framework, with Mean Field Variational Bayes (MFVB) as the primitive for distributed affine structure from motion (SfM).

Factor analysis aims to determine latent factors, or traits, which summarize a given data set. Inter-battery factor analysis extends this notion to multiple views of the data. In this paper we show how a nonlinear, nonparametric version of these models can be recovered through the Gaussian process latent variable model. This gives us a flexible formalism for multi-view learning where the latent variables can be used both for exploratory purposes and for learning representations that enable efficient inference for ambiguous estimation tasks. Learning is performed in a Bayesian manner through the formulation of a variational compression scheme which gives a rigorous lower bound on the log likelihood. Our Bayesian framework provides strong regularization during training, allowing the structure of the latent space to be determined efficiently and automatically. We demonstrate this by producing the first (to our knowledge) published results of learning from dozens of views, even when data is scarce. We further show experimental results on several different types of multi-view data sets and for different kinds of tasks, including exploratory data analysis, generation, ambiguity modelling through latent priors and classification.

Variational inference is a powerful tool for approximate inference, and it has been recently applied for representation learning with deep generative models. We develop the variational Gaussian process (VGP), a Bayesian nonparametric variational family, which adapts its shape to match complex posterior distributions. The VGP generates approximate posterior samples by generating latent inputs and warping them through random non-linear mappings; the distribution over random mappings is learned during inference, enabling the transformed outputs to adapt to varying complexity. We prove a universal approximation theorem for the VGP, demonstrating its representative power for learning any model. For inference we present a variational objective inspired by auto-encoders and perform black box inference over a wide class of models. The VGP achieves new state-of-the-art results for unsupervised learning, inferring models such as the deep latent Gaussian model and the recently proposed DRAW.

In magnetoencephalography (MEG) the conventional approach to source reconstruction is to solve the underdetermined inverse problem independently over time and space. Here we present how the conventional approach can be extended by regularizing the solution in space and time by a Gaussian process (Gaussian random field) model. Assuming a separable covariance function in space and time, the computational complexity of the proposed model becomes (without any further assumptions or restrictions) $\mathcal{O}(t^3 + n^3 + m^2n)$, where $t$ is the number of time steps, $m$ is the number of sources, and $n$ is the number of sensors. We apply the method to both simulated and empirical data, and demonstrate the efficiency and generality of our Bayesian source reconstruction approach which subsumes various classical approaches in the literature.

Time-varying mixture densities occur in many scenarios, for example, the distributions of keywords that appear in publications may evolve from year to year, video frame features associated with multiple targets may evolve in a sequence. Any models that realistically cater to this phenomenon must exhibit two important properties: the underlying mixture densities must have an unknown number of mixtures, and there must be some "smoothness" constraints in place for the adjacent mixture densities. The traditional Hierarchical Dirichlet Process (HDP) may be suited to the first property, but certainly not the second. This is due to how each random measure in the lower hierarchies is sampled independent of each other and hence does not facilitate any temporal correlations. To overcome such shortcomings, we proposed a new Smoothed Hierarchical Dirichlet Process (sHDP). The key novelty of this model is that we place a temporal constraint amongst the nearby discrete measures $\{G_j\}$ in the form of symmetric Kullback-Leibler (KL) Divergence with a fixed bound $B$. Although the constraint we place only involves a single scalar value, it nonetheless allows for flexibility in the corresponding successive measures. Remarkably, it also led us to infer the model within the stick-breaking process where the traditional Beta distribution used in stick-breaking is now replaced by a new constraint calculated from $B$. We present the inference algorithm and elaborate on its solutions. Our experiment using NIPS keywords has shown the desirable effect of the model.

As an automatic method of determining model complexity using the training data alone, Bayesian linear regression provides us a principled way to select hyperparameters. But one often needs approximation inference if distribution assumption is beyond Gaussian distribution. In this paper, we propose a Bayesian linear regression model with Student-t assumptions (BLRS), which can be inferred exactly. In this framework, both conjugate prior and expectation maximization (EM) algorithm are generalized. Meanwhile, we prove that the maximum likelihood solution is equivalent to the standard Bayesian linear regression with Gaussian assumptions (BLRG). The $q$-EM algorithm for BLRS is nearly identical to the EM algorithm for BLRG. It is showed that $q$-EM for BLRS can converge faster than EM for BLRG for the task of predicting online news popularity.