Latent variable models for network data extract a summary of the relational structure underlying an observed network. The simplest possible models subdivide nodes of the network into clusters; the probability of a link between any two nodes then depends only on their cluster assignment. Currently available models can be classified by whether clusters are disjoint or are allowed to overlap. These models can explain a "flat" clustering structure. Hierarchical Bayesian models provide a natural approach to capture more complex dependencies. We propose a model in which objects are characterised by a latent feature vector. Each feature is itself partitioned into disjoint groups (subclusters), corresponding to a second layer of hierarchy. In experimental comparisons, the model achieves significantly improved predictive performance on social and biological link prediction tasks. The results indicate that models with a single layer hierarchy over-simplify real networks.

In this paper we address the following question: Can we approximately sample from a Bayesian posterior distribution if we are only allowed to touch a small mini-batch of data-items for every sample we generate?. An algorithm based on the Langevin equation with stochastic gradients (SGLD) was previously proposed to solve this, but its mixing rate was slow. By leveraging the Bayesian Central Limit Theorem, we extend the SGLD algorithm so that at high mixing rates it will sample from a normal approximation of the posterior, while for slow mixing rates it will mimic the behavior of SGLD with a pre-conditioner matrix. As a bonus, the proposed algorithm is reminiscent of Fisher scoring (with stochastic gradients) and as such an efficient optimizer during burn-in.

Discriminative linear models are a popular tool in machine learning. These can be generally divided into two types: The first is linear classifiers, such as support vector machines, which are well studied and provide state-of-the-art results. One shortcoming of these models is that their output (known as the 'margin') is not calibrated, and cannot be translated naturally into a distribution over the labels. Thus, it is difficult to incorporate such models as components of larger systems, unlike probabilistic based approaches. The second type of approach constructs class conditional distributions using a nonlinearity (e.g. log-linear models), but is occasionally worse in terms of classification error. We propose a supervised learning method which combines the best of both approaches. Specifically, our method provides a distribution over the labels, which is a linear function of the model parameters. As a consequence, differences between probabilities are linear functions, a property which most probabilistic models (e.g. log-linear) do not have. Our model assumes that classes correspond to linear subspaces (rather than to half spaces). Using a relaxed projection operator, we construct a measure which evaluates the degree to which a given vector 'belongs' to a subspace, resulting in a distribution over labels. Interestingly, this view is closely related to similar concepts in quantum detection theory. The resulting models can be trained either to maximize the margin or to optimize average likelihood measures. The corresponding optimization problems are semidefinite programs which can be solved efficiently. We illustrate the performance of our algorithm on real world datasets, and show that it outperforms 2nd order kernel methods.

Most existing approaches to clustering gene expression time course data treat the different time points as independent dimensions and are invariant to permutations, such as reversal, of the experimental time course. Approaches utilizing HMMs have been shown to be helpful in this regard, but are hampered by having to choose model architectures with appropriate complexities. Here we propose for a clustering application an HMM with a countably infinite state space; inference in this model is possible by recasting it in the hierarchical Dirichlet process (HDP) framework (Teh et al. 2006), and hence we call it the HDP-HMM. We show that the infinite model outperforms model selection methods over finite models, and traditional time-independent methods, as measured by a variety of external and internal indices for clustering on two large publicly available data sets. Moreover, we show that the infinite models utilize more hidden states and employ richer architectures (e.g. state-to-state transitions) without the damaging effects of overfitting.

Latent feature models are attractive for image modeling, since images generally contain multiple objects. However, many latent feature models ignore that objects can appear at different locations or require pre-segmentation of images. While the transformed Indian buffet process (tIBP) provides a method for modeling transformation-invariant features in unsegmented binary images, its current form is inappropriate for real images because of its computational cost and modeling assumptions. We combine the tIBP with likelihoods appropriate for real images and develop an efficient inference, using the cross-correlation between images and features, that is theoretically and empirically faster than existing inference techniques. Our method discovers reasonable components and achieve effective image reconstruction in natural images.

In this paper we propose a unified framework for structured prediction with latent variables which includes hidden conditional random fields and latent structured support vector machines as special cases. We describe a local entropy approximation for this general formulation using duality, and derive an efficient message passing algorithm that is guaranteed to converge. We demonstrate its effectiveness in the tasks of image segmentation as well as 3D indoor scene understanding from single images, showing that our approach is superior to latent structured support vector machines and hidden conditional random fields.

Managing risk in dynamic decision problems is of cardinal importance in many fields such as finance and process control. The most common approach to defining risk is through various variance related criteria such as the Sharpe Ratio or the standard deviation adjusted reward. It is known that optimizing many of the variance related risk criteria is NP-hard. In this paper we devise a framework for local policy gradient style algorithms for reinforcement learning for variance related criteria. Our starting point is a new formula for the variance of the cost-to-go in episodic tasks. Using this formula we develop policy gradient algorithms for criteria that involve both the expected cost and the variance of the cost. We prove the convergence of these algorithms to local minima and demonstrate their applicability in a portfolio planning problem.

In this paper, we present a novel framework incorporating a combination of sparse models in different domains. We posit the observed data as generated from a linear combination of a sparse Gaussian Markov model (with a sparse precision matrix) and a sparse Gaussian independence model (with a sparse covariance matrix). We provide efficient methods for decomposition of the data into two domains, \viz Markov and independence domains. We characterize a set of sufficient conditions for identifiability and model consistency. Our decomposition method is based on a simple modification of the popular $\ell_1$-penalized maximum-likelihood estimator ($\ell_1$-MLE). We establish that our estimator is consistent in both the domains, i.e., it successfully recovers the supports of both Markov and independence models, when the number of samples $n$ scales as $n = \Omega(d^2 \log p)$, where $p$ is the number of variables and $d$ is the maximum node degree in the Markov model. Our conditions for recovery are comparable to those of $\ell_1$-MLE for consistent estimation of a sparse Markov model, and thus, we guarantee successful high-dimensional estimation of a richer class of models under comparable conditions. Our experiments validate these results and also demonstrate that our models have better inference accuracy under simple algorithms such as loopy belief propagation.

As data sets grow in size, the ability of learning methods to find structure in them is increasingly hampered by the time needed to search the large spaces of possibilities and generate a score for each that takes all of the observed data into account. For instance, Bayesian networks, the model chosen in this paper, have a super-exponentially large search space for a fixed number of variables. One possible method to alleviate this problem is to use a proxy, such as a Gaussian Process regressor, in place of the true scoring function, training it on a selection of sampled networks. We prove here that the use of such a proxy is well-founded, as we can bound the smoothness of a commonly-used scoring function for Bayesian network structure learning. We show here that, compared to an identical search strategy using the network?s exact scores, our proxy-based search is able to get equivalent or better scores on a number of data sets in a fraction of the time.

Nonparametric Bayesian approaches to clustering, information retrieval, language modeling and object recognition have recently shown great promise as a new paradigm for unsupervised data analysis. Most contributions have focused on the Dirichlet process mixture models or extensions thereof for which efficient Gibbs samplers exist. In this paper we explore Gibbs samplers for infinite complexity mixture models in the stick breaking representation. The advantage of this representation is improved modeling flexibility. For instance, one can design the prior distribution over cluster sizes or couple multiple infinite mixture models (e.g. over time) at the level of their parameters (i.e. the dependent Dirichlet process model). However, Gibbs samplers for infinite mixture models (as recently introduced in the statistics literature) seem to mix poorly over cluster labels. Among others issues, this can have the adverse effect that labels for the same cluster in coupled mixture models are mixed up. We introduce additional moves in these samplers to improve mixing over cluster labels and to bring clusters into correspondence. An application to modeling of storm trajectories is used to illustrate these ideas.