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.

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.

The Indian Buffet Process is a versatile statistical tool for modeling distributions over binary matrices. We provide an efficient spectral algorithm as an alternative to costly Variational Bayes and sampling-based algorithms. We derive a novel tensorial characterization of the moments of the Indian Buffet Process proper and for two of its applications. We give a computationally efficient iterative inference algorithm, concentration of measure bounds, and reconstruction guarantees. Our algorithm provides superior accuracy and cheaper computation than comparable Variational Bayesian approach on a number of reference problems.

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.

This paper studies the following problem: given samples from a high dimensional discrete distribution, we want to estimate the leading $(\delta,\rho)$-modes of the underlying distributions. A point is defined to be a $(\delta,\rho)$-mode if it is a local optimum of the density within a $\delta$-neighborhood under metric $\rho$. As we increase the ``scale'' parameter $\delta$, the neighborhood size increases and the total number of modes monotonically decreases. The sequence of the $(\delta,\rho)$-modes reveal intrinsic topographical information of the underlying distributions. Though the mode finding problem is generally intractable in high dimensions, this paper unveils that, if the distribution can be approximated well by a tree graphical model, mode characterization is significantly easier. An efficient algorithm with provable theoretical guarantees is proposed and is applied to applications like data analysis and multiple predictions.

We develop a new exponential family probabilistic model for permutations that can capture hierarchical structure, and that has the well known Mallows and generalized Mallows models as subclasses. We describe how one can do parameter estimation and propose an approach to structure search for this class of models. We provide experimental evidence that this added flexibility both improves predictive performance and enables a deeper understanding of collections of permutations.

The Generic Viewpoint Assumption (GVA) states that the position of the viewer or the light in a scene is not special. Thus, any estimated parameters from an observation should be stable under small perturbations such as object, viewpoint or light positions. The GVA has been analyzed and quantified in previous works, but has not been put to practical use in actual vision tasks. In this paper, we show how to utilize the GVA to estimate shape and illumination from a single shading image, without the use of other priors. We propose a novel linearized Spherical Harmonics (SH) shading model which enables us to obtain a computationally efficient form of the GVA term. Together with a data term, we build a model whose unknowns are shape and SH illumination. The model parameters are estimated using the Alternating Direction Method of Multipliers embedded in a multi-scale estimation framework. In this prior-free framework, we obtain competitive shape and illumination estimation results under a variety of models and lighting conditions, requiring fewer assumptions than competing methods.

This paper is concerned with compressive sensing of signals drawn from a Gaussian mixture model (GMM) with sparse precision matrices. Previous work has shown: (i) a signal drawn from a given GMM can be perfectly reconstructed from r noise-free measurements if the (dominant) rank of each covariance matrix is less than r; (ii) a sparse Gaussian graphical model can be efficiently estimated from fully-observed training signals using graphical lasso. This paper addresses a problem more challenging than both (i) and (ii), by assuming that the GMM is unknown and each signal is only partially observed through incomplete linear measurements. Under these challenging assumptions, we develop a hierarchical Bayesian method to simultaneously estimate the GMM and recover the signals using solely the incomplete measurements and a Bayesian shrinkage prior that promotes sparsity of the Gaussian precision matrices. In addition, we provide theoretical performance bounds to relate the reconstruction error to the number of signals for which measurements are available, the sparsity level of precision matrices, and the “incompleteness” of measurements. The proposed method is demonstrated extensively on compressive sensing of imagery and video, and the results with simulated and hardware-acquired real measurements show significant performance improvement over state-of-the-art methods.

The idea that animals might use information-driven planning to explore an unknown environment and build an internal model of it has been proposed for quite some time. Recent work has demonstrated that agents using this principle can efficiently learn models of probabilistic environments with discrete, bounded state spaces. However, animals and robots are commonly confronted with unbounded environments. To address this more challenging situation, we study information-based learning strategies of agents in unbounded state spaces using non-parametric Bayesian models. Specifically, we demonstrate that the Chinese Restaurant Process (CRP) model is able to solve this problem and that an Empirical Bayes version is able to efficiently explore bounded and unbounded worlds by relying on little prior information.

Video summarization is a challenging problem with great application potential. Whereas prior approaches, largely unsupervised in nature, focus on sampling useful frames and assembling them as summaries, we consider video summarization as a supervised subset selection problem. Our idea is to teach the system to learn from human-created summaries how to select informative and diverse subsets, so as to best meet evaluation metrics derived from human-perceived quality. To this end, we propose the sequential determinantal point process (seqDPP), a probabilistic model for diverse sequential subset selection. Our novel seqDPP heeds the inherent sequential structures in video data, thus overcoming the deficiency of the standard DPP, which treats video frames as randomly permutable items. Meanwhile, seqDPP retains the power of modeling diverse subsets, essential for summarization. Our extensive results of summarizing videos from 3 datasets demonstrate the superior performance of our method, compared to not only existing unsupervised methods but also naive applications of the standard DPP model.