Bayes-adaptive planning offers a principled solution to the explorationexploitation trade-offunder model uncertainty. It finds the optimal policy in belief space, which explicitly accounts for the expected effect on future rewards of reductions in uncertainty. However, the Bayes-adaptive solution is typically intractable indomains with large or continuous state spaces. We present a tractable method for approximating the Bayes-adaptive solution by combining simulationbased searchwith a novel value function approximation technique that generalises appropriately over belief space. Our method outperforms prior approaches in both discrete bandit tasks and simple continuous navigation and control tasks.

Computing the partition function (i.e., the normalizing constant) of a given pairwise binary graphical model is NP-hard in general. As a result, the partition function is typically estimated by approximate inference algorithms such as belief propagation (BP) and tree-reweighted belief propagation (TRBP). The former provides reasonable estimates in practice but has convergence issues. The later has better convergence properties but typically provides poorer estimates. In this work, we propose a novel scheme that has better convergence properties than BP and provably provides better partition function estimates in many instances than TRBP. In particular, given an arbitrary pairwise binary graphical model, we construct a specific ``attractive'' 2-cover. We explore the properties of this special cover and show that it can be used to construct an algorithm with the desired properties.

Fluorescent calcium imaging provides a potentially powerful tool for inferring connectivity in neural circuits with up to thousands of neurons. However, a key challenge in using calcium imaging for connectivity detection is that current systems often have a temporal response and frame rate that can be orders of magnitude slower than the underlying neural spiking process. Bayesian inference based on expectation-maximization (EM) have been proposed to overcome these limitations, but they are often computationally demanding since the E-step in the EM procedure typically involves state estimation in a high-dimensional nonlinear dynamical system. In this work, we propose a computationally fast method for the state estimation based on a hybrid of loopy belief propagation and approximate message passing (AMP). The key insight is that a neural system as viewed through calcium imaging can be factorized into simple scalar dynamical systems for each neuron with linear interconnections between the neurons. Using the structure, the updates in the proposed hybrid AMP methodology can be computed by a set of one-dimensional state estimation procedures and linear transforms with the connectivity matrix. This yields a computationally scalable method for inferring connectivity of large neural circuits. Simulations of the method on realistic neural networks demonstrate good accuracy with computation times that are potentially significantly faster than current approaches based on Markov Chain Monte Carlo methods.

One of the most fundamental problems in causal inference is the estimation of a causal effect when variables are confounded. This is difficult in an observational study because one has no direct evidence that all confounders have been adjusted for. We introduce a novel approach for estimating causal effects that exploits observational conditional independencies to suggest ``weak'' paths in a unknown causal graph. The widely used faithfulness condition of Spirtes et al. is relaxed to allow for varying degrees of ``path cancellations'' that will imply conditional independencies but do not rule out the existence of confounding causal paths. The outcome is a posterior distribution over bounds on the average causal effect via a linear programming approach and Bayesian inference. We claim this approach should be used in regular practice to complement other default tools in observational studies.

Coverage functions are an important class of discrete functions that capture the law of diminishing returns arising naturally from applications in social network analysis, machine learning, and algorithmic game theory. In this paper, we propose anew problem of learning time-varying coverage functions, and develop a novel parametrization of these functions using random features. Based on the connection betweentime-varying coverage functions and counting processes, we also propose an efficient parameter learning algorithm based on likelihood maximization, andprovide a sample complexity analysis. We applied our algorithm to the influence function estimation problem in information diffusion in social networks, and show that with few assumptions about the diffusion processes, our algorithm is able to estimate influence significantly more accurately than existing approaches on both synthetic and real world data.

A determinantal point process (DPP) is a probabilistic model of set diversity compactly parameterized by a positive semi-definite kernel matrix. To fit a DPP to a given task, we would like to learn the entries of its kernel matrix by maximizing the log-likelihood of the available data. However, log-likelihood is non-convex in the entries of the kernel matrix, and this learning problem is conjectured to be NP-hard. Thus, previous work has instead focused on more restricted convex learning settings: learning only a single weight for each row of the kernel matrix, or learning weights for a linear combination of DPPs with fixed kernel matrices. In this work we propose a novel algorithm for learning the full kernel matrix. By changing the kernel parameterization from matrix entries to eigenvalues and eigenvectors, and then lower-bounding the likelihood in the manner of expectation-maximization algorithms, we obtain an effective optimization procedure. We test our method on a real-world product recommendation task, and achieve relative gains of up to 16.5% in test log-likelihood compared to the naive approach of maximizing likelihood by projected gradient ascent on the entries of the kernel matrix.

Sparse signal recovery addresses the problem of solving underdetermined linear inverse problems subject to a sparsity constraint. We propose a novel prior formulation, the structured spike and slab prior, which allows to incorporate a priori knowledge of the sparsity pattern by imposing a spatial Gaussian process on the spike and slab probabilities. Thus, prior information on the structure of the sparsity pattern can be encoded using generic covariance functions. Furthermore, we provide a Bayesian inference scheme for the proposed model based on the expectation propagation framework. Using numerical experiments on synthetic data, we demonstrate the benefits of the model.

Latent Dirichlet allocation (LDA) is a popular generative model of various objects such as texts and images, where an object is expressed as a mixture of latent topics. In this paper, we theoretically investigate variational Bayesian (VB) learning in LDA. More specifically, we analytically derive the leading term of the VB free energy under an asymptotic setup, and show that there exist transition thresholds in Dirichlet hyperparameters around which the sparsity-inducing behavior drastically changes. Then we further theoretically reveal the notable phenomenon that VB tends to induce weaker sparsity than MAP in the LDA model, which is opposed to other models. We experimentally demonstrate the practical validity of our asymptotic theory on real-world Last.FM music data.

Even though heterogeneous databases can be found in a broad variety of applications, there exists a lack of tools for estimating missing data in such databases. In this paper, we provide an efficient and robust table completion tool, based on a Bayesian nonparametric latent feature model. In particular, we propose a general observation model for the Indian buffet process (IBP) adapted to mixed continuous (real-valued and positive real-valued) and discrete (categorical, ordinal and count) observations. Then, we propose an inference algorithm that scales linearly with the number of observations. Finally, our experiments over five real databases show that the proposed approach provides more robust and accurate estimates than the standard IBP and the Bayesian probabilistic matrix factorization with Gaussian observations.

Dirichlet process mixture of Gaussians (DPMG) has been used in the literature for clustering and density estimation problems. However, many real-world data exhibit cluster distributions that cannot be captured by a single Gaussian. Modeling such data sets by DPMG creates several extraneous clusters even when clusters are relatively well-defined. Herein, we present the infinite mixture of infinite Gaussian mixtures (I2GMM) for more flexible modeling of data sets with skewed and multi-modal cluster distributions. Instead of using a single Gaussian for each cluster as in the standard DPMG model, the generative model of I2GMM uses a single DPMG for each cluster. The individual DPMGs are linked together through centering of their base distributions at the atoms of a higher level DP prior. Inference is performed by a collapsed Gibbs sampler that also enables partial parallelization. Experimental results on several artificial and real-world data sets suggest the proposed I2GMM model can predict clusters more accurately than existing variational Bayes and Gibbs sampler versions of DPMG.