We address the problem of finding a minimal separator in an Andersson-Madigan-Perlman chain graph (AMP CG), namely, finding a set Z of nodes that separate a given non-adjacent pair of nodes such that no proper subset of Z separates that pair. We analyze several versions of this problem and offer polynomial-time algorithms for each. These include finding a minimal separator from a restricted set of nodes, finding a minimal separator for two given disjoint sets, and testing whether a given separator is minimal. We provide an extension of the decomposition approach for learning Bayesian networks (BNs) proposed by (Xie et. al.) to learn AMP CGs, which include BNs as a special case, under the faithfulness assumption and prove its correctness using the minimal separator results. The advantages of this decomposition approach hold in the more general setting: reduced complexity and increased power of computational independence tests. In addition, we show that the PC-like algorithm is order-dependent, in the sense that the output can depend on the order in which the variables are given. We propose two modifications of the PC-like algorithm that remove part or all of this order-dependence. Simulations under a variety of settings demonstrate the competitive performance of our decomposition-based method, called LCD-AMP, in comparison with the (modified version of) PC-like algorithm. In fact, the decomposition-based algorithm usually outperforms the PC-like algorithm. We empirically show that the results of both algorithms are more accurate and stable when the sample size is reasonably large and the underlying graph is sparse.

Robotic agents should be able to learn from sub-symbolic sensor data, and at the same time, be able to reason about objects and communicate with humans on a symbolic level. This raises the question of how to overcome the gap between symbolic and sub-symbolic artificial intelligence. We propose a semantic world modeling approach based on bottom-up object anchoring using an object-centered representation of the world. Perceptual anchoring processes continuous perceptual sensor data and maintains a correspondence to a symbolic representation. We extend the definitions of anchoring to handle multi-modal probability distributions and we couple the resulting symbol anchoring system to a probabilistic logic reasoner for performing inference. Furthermore, we use statistical relational learning to enable the anchoring framework to learn symbolic knowledge in the form of a set of probabilistic logic rules of the world from noisy and sub-symbolic sensor input. The resulting framework, which combines perceptual anchoring and statistical relational learning, is able to maintain a semantic world model of all the objects that have been perceived over time, while still exploiting the expressiveness of logical rules to reason about the state of objects which are not directly observed through sensory input data. To validate our approach we demonstrate, on the one hand, the ability of our system to perform probabilistic reasoning over multi-modal probability distributions, and on the other hand, the learning of probabilistic logical rules from anchored objects produced by perceptual observations. The learned logical rules are, subsequently, used to assess our proposed probabilistic anchoring procedure. We demonstrate our system in a setting involving object interactions where object occlusions arise and where probabilistic inference is needed to correctly anchor objects.

Statistical Relational Learning [Getoor and Taskar, 2007] (SRL) is concerned with learning probabilistic models from relational data such as, for instance, knowledge graphs, biological or social networks, structures of molecules etc. Markov Logic Networks [Richardson and Domingos, 2006] (MLNs) are among the most prominent SRL systems and in this paper we are interested in their expressivity. Informally, expressivity measures the "amount" of distributions that can be modelled by a given class of probabilistic models. An MLN is given by a set of weighted first-order logic formulas and it defines a distribution on possible worlds over a given domain. Here we study expressivity of MLNs in a setting where we first fix the first-order logic formulas defining the MLN and then vary their weights. Since it is not even clear what expressivity should mean in this context, our first contribution in this paper is a formal framework for studying expressivity of MLNs. The main reason for studying expressivity of MLNs in the setting where one first fixes the formulas is computational complexity of inference because its complexity usually depends mostly on the formulas and not so much on their weights.

Causal effect estimation from observational data is a crucial but challenging task. Currently, only a limited number of data-driven causal effect estimation methods are available. These methods either only provide a bound estimation of the causal effect of a treatment on the outcome, or have impractical assumptions on the data or low efficiency although providing a unique estimation of the causal effect. In this paper, we identify a practical problem setting and propose an approach to achieving unique causal effect estimation from data with hidden variables under this setting. For the approach, we develop the theorems to support the discovery of the proper covariate sets for confounding adjustment (adjustment sets). Based on the theorems, two algorithms are presented for finding the proper adjustment sets from data with hidden variables to obtain unbiased and unique causal effect estimation. Experiments with benchmark Bayesian networks and real-world datasets have demonstrated the efficiency and effectiveness of the proposed algorithms, indicating the practicability of the identified problem setting and the potential of the approach in real-world applications.

The recent development of online recommender systems has a focus on collaborative ranking from implicit feedback, such as user clicks and purchases. Different from explicit ratings, which reflect graded user preferences, the implicit feedback only generates positive and unobserved labels. While considerable efforts have been made in this direction, the well-known pairwise and listwise approaches have still been limited by various challenges. Specifically, for the pairwise approaches, the assumption of independent pairwise preference is not always held in practice. Also, the listwise approaches cannot efficiently accommodate "ties" due to the precondition of the entire list permutation. To this end, in this paper, we propose a novel setwise Bayesian approach for collaborative ranking, namely SetRank, to inherently accommodate the characteristics of implicit feedback in recommender system. Specifically, SetRank aims at maximizing the posterior probability of novel setwise preference comparisons and can be implemented with matrix factorization and neural networks. Meanwhile, we also present the theoretical analysis of SetRank to show that the bound of excess risk can be proportional to $\sqrt{M/N}$, where $M$ and $N$ are the numbers of items and users, respectively. Finally, extensive experiments on four real-world datasets clearly validate the superiority of SetRank compared with various state-of-the-art baselines.

We present an implementation of a probabilistic first-order logic called TensorLog, in which classes of logical queries are compiled into differentiable functions in a neural-network infrastructure such as Tensorflow or Theano. This leads to a close integration of probabilistic logical reasoning with deep-learning infrastructure: in particular, it enables high-performance deep learning frameworks to be used for tuning the parameters of a probabilistic logic. The integration with these frameworks enables use of GPU-based parallel processors for inference and learning, making TensorLog the first highly parallellizable probabilistic logic. Experimental results show that TensorLog scales to problems involving hundreds of thousands of knowledge-base triples and tens of thousands of examples.

We introduce a framework for inference in general state-space hidden Markov models (HMMs) under likelihood misspecification. In particular, we leverage the loss-theoretic perspective of generalized Bayesian inference (GBI) to define generalized filtering recursions in HMMs, that can tackle the problem of inference under model misspecification. In doing so, we arrive at principled procedures for robust inference against observation contamination through the $\beta$-divergence. Operationalizing the proposed framework is made possible via sequential Monte Carlo methods (SMC). The standard particle methods, and their associated convergence results, are readily generalized to the new setting. We demonstrate our approach to object tracking and Gaussian process regression problems, and observe improved performance over standard filtering algorithms.

This paper will discuss the role of an artificially-intelligent computer system as critique-based, implicitorganizational, and an inherently necessary device, deployed in synchrony with parallel governmental policy, as a genuine means of capturing nation-population complexity in quantitative form, public contentment in societal-cooperative economic groups, regulatory proposition, and governance-effectiveness domains. It will discuss a solution involving a well-known algorithm and proffer an improved mechanism for knowledgerepresentation, thereby increasing range of utility, scope of influence (in terms of differentiating class sectors) and operational efficiency. It will finish with a discussion of these and other historical implications. Introduction The world created by humans to manage their daily affairs is growing in complexity beyond the comprehension capability of the vast majority of them. The political classes are vulnerable to implementation of policy that proves incorrect and damages the credibility of the state over the long term.

Deep reinforcement learning is successful in decision making for sophisticated games, such as Atari, Go, etc. However, real-world decision making often requires reasoning with partial information extracted from complex visual observations. This paper presents Discriminative Particle Filter Reinforcement Learning (DPFRL), a new reinforcement learning framework for complex partial observations. DPFRL encodes a differentiable particle filter in the neural network policy for explicit reasoning with partial observations over time. The particle filter maintains a belief using learned discriminative update, which is trained end-to-end for decision making. We show that using the discriminative update instead of standard generative models results in significantly improved performance, especially for tasks with complex visual observations, because they circumvent the difficulty of modeling complex observations that are irrelevant to decision making. In addition, to extract features from the particle belief, we propose a new type of belief feature based on the moment generating function. DPFRL outperforms state-of-the-art POMDP RL models in Flickering Atari Games, an existing POMDP RL benchmark, and in Natural Flickering Atari Games, a new, more challenging POMDP RL benchmark introduced in this paper. Further, DPFRL performs well for visual navigation with real-world data in the Habitat environment.

Bayes' theorem is one of the most important formulae in the field of mathematical statistics and probability, used to calculate the chances of a particular event occurring based on relevant existing information. Bayesian inference meanwhile leverages Bayes' theorem to update the probability of a hypothesis as additional data becomes available. New York University Assistant Professor Andrew Gordon Wilson addressed this question in his recent paper The Case for Bayesian Deep Learning. Paper Abstract: The key distinguishing property of a Bayesian approach is marginalization instead of optimization, not the prior, or Bayes rule. Bayesian inference is especially compelling for deep neural networks.