Encoding domain knowledge into the prior over the high-dimensional weight space is challenging in Bayesian neural networks. Two types of domain knowledge are commonly available in scientific applications: 1. feature sparsity (number of relevant features); 2. signal-to-noise ratio, quantified, for instance, as the proportion of variance explained (PVE). We show both types of domain knowledge can be encoded into the widely used Gaussian scale mixture priors with Automatic Relevance Determination. Specifically, we propose a new joint prior over the local (i.e., feature-specific) scale parameters to encode the knowledge about feature sparsity, and an algorithm to determine the global scale parameter (shared by all features) according to the PVE. Empirically, we show that the proposed informative prior improves prediction accuracy on publicly available datasets and in a genetics application.

Parameter estimation, statistical tests and confidence sets are the cornerstones of classical statistics that allow scientists to make inferences about the underlying process that generated the observed data. A key question is whether one can still construct hypothesis tests and confidence sets with proper coverage and high power in a so-called likelihood-free inference (LFI) setting; that is, a setting where the likelihood is not explicitly known but one can forward-simulate observable data according to a stochastic model. In this paper, we present $\texttt{ACORE}$ (Approximate Computation via Odds Ratio Estimation), a frequentist approach to LFI that first formulates the classical likelihood ratio test (LRT) as a parametrized classification problem, and then uses the equivalence of tests and confidence sets to build confidence regions for parameters of interest. We also present a goodness-of-fit procedure for checking whether the constructed tests and confidence regions are valid. $\texttt{ACORE}$ is based on the key observation that the LRT statistic, the rejection probability of the test, and the coverage of the confidence set are conditional distribution functions which often vary smoothly as a function of the parameters of interest. Hence, instead of relying solely on samples simulated at fixed parameter settings (as is the convention in standard Monte Carlo solutions), one can leverage machine learning tools and data simulated in the neighborhood of a parameter to improve estimates of quantities of interest. We demonstrate the efficacy of $\texttt{ACORE}$ with both theoretical and empirical results. Our implementation is available on Github.

Classifier calibration does not always go hand in hand with the classifier's ability to separate the classes. There are applications where good classifier calibration, i.e. the ability to produce accurate probability estimates, is more important than class separation. When the amount of data for training is limited, the traditional approach to improve calibration starts to crumble. In this article we show how generating more data for calibration is able to improve calibration algorithm performance in many cases where a classifier is not naturally producing well-calibrated outputs and the traditional approach fails. The proposed approach adds computational cost but considering that the main use case is with small data sets this extra computational cost stays insignificant and is comparable to other methods in prediction time. From the tested classifiers the largest improvement was detected with the random forest and naive Bayes classifiers. Therefore, the proposed approach can be recommended at least for those classifiers when the amount of data available for training is limited and good calibration is essential.

Real-world data often presents itself in the form of a network. Examples include social networks, citation networks, biological networks, and knowledge graphs. In their simplest form, networks represent real-life entities (e.g. people, papers, proteins, concepts) as nodes, and describe them in terms of their relations with other entities by means of edges between these nodes. This can be valuable for a range of purposes from the study of information diffusion to bibliographic analysis, bioinformatics research, and question-answering. The quality of networks is often problematic though, affecting downstream tasks. This paper focuses on the common problem where a node in the network in fact corresponds to multiple real-life entities. In particular, we introduce FONDUE, an algorithm based on network embedding for node disambiguation. Given a network, FONDUE identifies nodes that correspond to multiple entities, for subsequent splitting. Extensive experiments on twelve benchmark datasets demonstrate that FONDUE is substantially and uniformly more accurate for ambiguous node identification compared to the existing state-of-the-art, at a comparable computational cost, while less optimal for determining the best way to split ambiguous nodes.

The point estimates of ReLU classification networks---arguably the most widely used neural network architecture---have been shown to yield arbitrarily high confidence far away from the training data. This architecture, in conjunction with a maximum a posteriori estimation scheme, is thus not calibrated nor robust. Approximate Bayesian inference has been empirically demonstrated to improve predictive uncertainty in neural networks, although the theoretical analysis of such Bayesian approximations is limited. We theoretically analyze approximate Gaussian posterior distributions on the weights of ReLU networks and show that they fix the overconfidence problem. Furthermore, we show that even a simplistic, thus cheap, Bayesian approximation, also fixes these issues. This indicates that a sufficient condition for a calibrated uncertainty on a ReLU network is ``to be a bit Bayesian''. These theoretical results validate the usage of last-layer Bayesian approximation and motivate a range of a fidelity-cost trade-off. We further validate these findings empirically via various standard experiments using common deep ReLU networks and Laplace approximations.

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.

Thompson sampling is a methodology for multi-armed bandit problems that is known to enjoy favorable performance in both theory and practice. It does, however, have a significant limitation computationally, arising from the need for samples from posterior distributions at every iteration. We propose two Markov Chain Monte Carlo (MCMC) methods tailored to Thompson sampling to address this issue. We construct quickly converging Langevin algorithms to generate approximate samples that have accuracy guarantees, and we leverage novel posterior concentration rates to analyze the regret of the resulting approximate Thompson sampling algorithm. Further, we specify the necessary hyper-parameters for the MCMC procedure to guarantee optimal instance-dependent frequentist regret while having low computational complexity. In particular, our algorithms take advantage of both posterior concentration and a sample reuse mechanism to ensure that only a constant number of iterations and a constant amount of data is needed in each round. The resulting approximate Thompson sampling algorithm has logarithmic regret and its computational complexity does not scale with the time horizon of the algorithm.

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.