Image clustering and visual codebook learning are two fundamental problems in computer vision and they are tightly related. On one hand, a good codebook can generate effective feature representations which largely affect clustering performance. On the other hand, class labels obtained from image clustering can serve as supervised information to guide codebook learning. Traditionally, these two processes are conducted separately and their correlation is generally ignored.In this paper, we propose a Double Layer Gaussian Mixture Model (DLGMM) to simultaneously perform image clustering and codebook learning. In DLGMM, two tasks are seamlessly coupled and can mutually promote each other. Cluster labels and codebook are jointly estimated to achieve the overall best performance. To incorporate the spatial coherence between neighboring visual patches, we propose a Spatially Coherent DLGMM which uses a Markov Random Field to encourage neighboring patches to share the same visual word label.We use variational inference to approximate the posterior of latent variables and learn model parameters.Experiments on two datasets demonstrate the effectiveness of two models.

To facilitate interaction with people, robots must not only recognize current actions, but also infer a person's intentions and future behavior. Recent advances in depth camera technology have significantly improved human motion tracking. However, the inherent high dimensionality of interacting with the physical world makes efficiently forecasting human intention and future behavior a challenging task. Predictive methods that estimate uncertainty are therefore critical for supporting appropriate robotic responses to the many ambiguities posed within the human-robot interaction setting. We address these two challenges, high dimensionality and uncertainty, by employing predictive inverse optimal control methods to estimate a probabilistic model of human motion trajectories. Our inverse optimal control formulation estimates quadratic cost functions that best rationalize observed trajectories framed as solutions to linear-quadratic regularization problems. The formulation calibrates its uncertainty from observed motion trajectories, and is efficient in high-dimensional state spaces with linear dynamics. We demonstrate its effectiveness on a task of anticipating the future trajectories, target locations and activity intentions of hand motions.

Most Relevant Explanation (MRE) is a new inference task in Bayesian networks that finds the most relevant partial instantiation of target variables as an explanation for given evidence by maximizing the Generalized Bayes Factor (GBF). No exact algorithm has been developed for solving MRE previously. This paper fills the void and introduces a breadth-first branch-and-bound MRE algorithm based on a novel upper bound on GBF. The bound is calculated by decomposing the computation of the score to a set of Markov blankets of subsets of evidence variables. Our empirical evaluations show that the proposed algorithm scales up exact MRE inference significantly.

The utilitarian solution criterion, which has been extensively studied in multi-agent decision making under uncertainty, aims to maximize the sum of individual utilities. However, as the utilitarian solution often discriminates against some agents, it is not desirable for many practical applications where agents have their own interests and fairness is expected. To address this issue, this paper introduces egalitarian solution criteria for sequential decision-making under uncertainty, which are based on the maximin principle. Motivated by different application domains, we propose four maximin fairness criteria and develop corresponding algorithms for computing their optimal policies. Furthermore, we analyze the connections between these criteria and discuss and compare their characteristics.

The main computational bottleneck in various sampling based and local-search based inference algorithms for Markov logic networks (e.g., Gibbs sampling, MC-SAT, MaxWalksat, etc.) is computing the number of groundings of a first-order formula that are true given a truth assignment to all of its ground atoms. We reduce this problem to the problem of counting the number of solutions of a constraint satisfaction problem (CSP) and show that during their execution, both sampling based and local-search based algorithms repeatedly solve dynamic versions of this counting problem. Deriving from the vast amount of literature on CSPs and graphical models, we propose an exact junction-tree based algorithm for computing the number of solutions of the dynamic CSP, analyze its properties, and show how it can be used to improve the computational complexity of Gibbs sampling and MaxWalksat. Empirical tests on a variety of benchmarks clearly show that our new approach is several orders of magnitude more scalable than existing approaches.

Lifted probabilistic inference algorithms have been successfully applied to a large number of symmetric graphical models. Unfortunately, the majority of real-world graphical models is asymmetric. This is even the case for relational representations when evidence is given. Therefore, more recent work in the community moved to making the models symmetric and then applying existing lifted inference algorithms. However, this approach has two shortcomings. First, all existing over-symmetric approximations require a relational representation such as Markov logic networks. Second, the induced symmetries often change the distribution significantly, making the computed probabilities highly biased. We present a framework for probabilistic sampling-based inference that only uses the induced approximate symmetries to propose steps in a Metropolis-Hastings style Markov chain. The framework, therefore, leads to improved probability estimates while remaining unbiased. Experiments demonstrate that the approach outperforms existing MCMC algorithms.

We consider the problem of, given a probabilistic model on a set of random variables, how to add a new variable that depends on the other variables, without changing the original distribution. In particular, we consider relational models (such as Markov logic networks (MLNs)), where we cannot directly define conditional probabilities. In relational models, there may be an unbounded number of parents in the grounding, and conditional distributions need to be defined in terms of aggregators. The question we ask is whether and when it is possible to represent conditional probabilities at all in various relational models. Some aggregators have been shown to be representable by MLNs, by adding auxiliary variables; however it was unknown whether they could be defined without auxiliary variables. For other aggregators, it was not known whether they can be represented by MLNs at all. We obtained surprisingly strong negative results on the capability of flexible undirected relational models such as MLNs to represent aggregators without affecting the original model's distribution. We provide a map of what aspects of the models, including the use of auxiliary variables and quantifiers, result in the ability to represent various aggregators. In addition, we provide proof techniques which can be used to facilitate future theoretic results on relational models, and demonstrate them on relational logistic regression (RLR).

Controlling for selection and confounding biases are two of the most challenging problems that appear in data analysis in the empirical sciences as well as in artificial intelligence tasks. The combination of previously studied methods for each of these biases in isolation is not directly applicable to certain non-trivial cases in which selection and confounding biases are simultaneously present. In this paper, we tackle these instances non-parametrically and in full generality. We provide graphical and algorithmic conditions for recoverability of interventional distributions for when selection and confounding biases are both present. Our treatment completely characterizes the class of causal effects that are recoverable in Markovian models, and is suffi- cient for Semi-Markovian models.

Many real-world Bayesian inference problems such as preference learning or trader valuation modeling in financial markets naturally use piecewise likelihoods. Unfortunately, exact closed-form inference in the underlying Bayesian graphical models is intractable in the general case and existing approximation techniques provide few guarantees on both approximation quality and efficiency. While (Markov Chain) Monte Carlo methods provide an attractive asymptotically unbiased approximation approach, rejection sampling and Metropolis-Hastings both prove inefficient in practice, and analytical derivation of Gibbs samplers require exponential space and time in the amount of data. In this work, we show how to transform problematic piecewise likelihoods into equivalent mixture models and then provide a blocked Gibbs sampling approach for this transformed model that achieves an exponential-to-linear reduction in space and time compared to a conventional Gibbs sampler. This enables fast, asymptotically unbiased Bayesian inference in a new expressive class of piecewise graphical models and empirically requires orders of magnitude less time than rejection, Metropolis-Hastings, and conventional Gibbs sampling methods to achieve the same level of accuracy.

Markov Decision Problems, MDPs offer an effective mechanism for planning under uncertainty. However, due to unavoidable uncertainty over models, it is difficult to obtain an exact specification of an MDP. We are interested in solving MDPs, where transition and reward functions are not exactly specified. Existing research has primarily focussed on computing infinite horizon stationary policies when optimizing robustness, regret and percentile based objectives. We focus specifically on finite horizon problems with a special emphasis on objectives that are separable over individual instantiations of model uncertainty (i.e., objectives that can be expressed as a sum over instantiations of model uncertainty): (a) First, we identify two separable objectives for uncertain MDPs: Average Value Maximization (AVM) and Confidence Probability Maximisation (CPM). (b) Second, we provide optimization based solutions to compute policies for uncertain MDPs with such objectives. In particular, we exploit the separability of AVM and CPM objectives by employing Lagrangian dual decomposition(LDD). (c) Finally, we demonstrate the utility of the LDD approach on a benchmark problem from the literature.