Probabilistic programming is emerging as a popular and effective means of probabilistic modeling and an alternative to probabilistic graphical models. Probabilistic programs provide greater expressivity and flexibility in modeling probabilistic systems than graphical models, but this flexibility comes at a cost: there remains a significant disparity in performance between specialized Bayesian network solvers and probabilistic program inference algorithms. In this work we present a program analysis and associated optimization, flip-hoisting, that collapses repetitious parameters in discrete probabilistic programs to improve inference performance. flip-hoisting generalizes parameter sharing - a well-known important optimization from discrete graphical models - to probabilistic programs. We implement flip-hoisting in an existing probabilistic programming language and show empirically that it significantly improves inference performance, narrowing the gap between the performances of probabilistic programs and probabilistic graphical models.

Lifted inference allows to perform inference in polynomial time w.r.t. domain sizes. For a lifted algorithm, completeness investigates model classes for which the algorithm is guaranteed to compute a lifted solution. We contribute, to the best of our knowledge, the first completeness and complexity analysis for a temporal lifted algorithm, the so-called lifted dynamic junction tree algorithm (LDJT). To treat time as a first class citizen, LDJT introduces some constraints. Given these constraints, we analyse the classes of liftable models. Further, we show that LDJT has many advantages from a complexity point of view compared to a propositional temporal inference algorithm w.r.t. domain sizes. Therefore, LDJT advances the number of models for which inference tasks can be solved in reasonable time not only from a practically point of view, but also from a theoretical point of view.

Graphs from complex systems often share a partial underlying structure across domains while retaining individual features. Thus, identifying common structures can shed light on the underlying signal, for instance, when applied to scientific discoveries or clinical diagnoses. Furthermore, growing evidence shows that the shared structure across domains boosts the estimation power of graphs, particularly for high-dimensional data. However, building a joint estimator to extract the common structure may be more complicated than it seems, most often due to data heterogeneity across sources. This manuscript surveys recent work on statistical inference of joint Gaussian graphical models, identifying model structures that fit various data generation processes. Simulations under different data generation processes are implemented with detailed discussions on the choice of models.

Data-efficient learning algorithms are essential in many practical applications for which data collection and labeling is expensive or infeasible, e.g., for autonomous cars. To address this problem, meta-learning infers an inductive bias from a set of meta-training tasks in order to learn new, but related, task using a small number of samples. Most studies assume the meta-learner to have access to labeled data sets from a large number of tasks. In practice, one may have available only unlabeled data sets from the tasks, requiring a costly labeling procedure to be carried out before use in standard meta-learning schemes. To decrease the number of labeling requests for meta-training tasks, this paper introduces an information-theoretic active task selection mechanism which quantifies the epistemic uncertainty via disagreements among the predictions obtained under different inductive biases. We detail an instantiation for nonparametric methods based on Gaussian Process Regression, and report its empirical performance results that compare favourably against existing heuristic acquisition mechanisms.

To achieve sample efficiency in reinforcement learning (RL), it necessitates efficiently exploring the underlying environment. Under the offline setting, addressing the exploration challenge lies in collecting an offline dataset with sufficient coverage. Motivated by such a challenge, we study the reward-free RL problem, where an agent aims to thoroughly explore the environment without any pre-specified reward function. Then, given any extrinsic reward, the agent computes the policy via a planning algorithm with offline data collected in the exploration phase. Moreover, we tackle this problem under the context of function approximation, leveraging powerful function approximators. Specifically, we propose to explore via an optimistic variant of the value-iteration algorithm incorporating kernel and neural function approximations, where we adopt the associated exploration bonus as the exploration reward. Moreover, we design exploration and planning algorithms for both single-agent MDPs and zero-sum Markov games and prove that our methods can achieve $\widetilde{\mathcal{O}}(1 /\varepsilon^2)$ sample complexity for generating a $\varepsilon$-suboptimal policy or $\varepsilon$-approximate Nash equilibrium when given an arbitrary extrinsic reward. To the best of our knowledge, we establish the first provably efficient reward-free RL algorithm with kernel and neural function approximators.

The past decade has witnessed a surge of interest in practical techniques for projected model counting. Despite significant advancements, however, performance scaling remains the Achilles' heel of this field. A key idea used in modern counters is to count models projected on an \emph{independent support} that is often a small subset of the projection set, i.e. original set of variables on which we wanted to project. While this idea has been effective in scaling performance, the question of whether it can benefit to count models projected on variables beyond the projection set, has not been explored. In this paper, we study this question and show that contrary to intuition, it can be beneficial to project on variables beyond the projection set. In applications such as verification of binarized neural networks, quantification of information flow, reliability of power grids etc., a good upper bound of the projected model count often suffices. We show that in several such cases, we can identify a set of variables, called upper bound support (UBS), that is not necessarily a subset of the projection set, and yet counting models projected on UBS guarantees an upper bound of the true projected model count. Theoretically, a UBS can be exponentially smaller than the smallest independent support. Our experiments show that even otherwise, UBS-based projected counting can be more efficient than independent support-based projected counting, while yielding bounds of very high quality. Based on extensive experiments, we find that UBS-based projected counting can solve many problem instances that are beyond the reach of a state-of-the-art independent support-based projected model counter.

Statistical Relational Learning (SRL) models have attracted significant attention due to their ability to model complex data while handling uncertainty. However, most of these models have been limited to discrete domains due to their limited potential functions. We introduce Relational Neural Markov Random Fields (RN-MRFs) which allow for handling of complex relational hybrid domains. The key advantage of our model is that it makes minimal data distributional assumptions and can seamlessly allow for human knowledge through potentials or relational rules. We propose a maximum pseudolikelihood estimation-based learning algorithm with importance sampling for training the neural potential parameters. Our empirical evaluations across diverse domains such as image processing and relational object mapping, clearly demonstrate its effectiveness against non-neural counterparts.

Detecting out-of-distribution (OOD) samples is vital for developing machine learning based models for critical safety systems. Common approaches for OOD detection assume access to some OOD samples during training which may not be available in a real-life scenario. Instead, we utilize the {\em predictive normalized maximum likelihood} (pNML) learner, in which no assumptions are made on the tested input. We derive an explicit expression of the pNML and its generalization error, denoted as the {\em regret}, for a single layer neural network (NN). We show that this learner generalizes well when (i) the test vector resides in a subspace spanned by the eigenvectors associated with the large eigenvalues of the empirical correlation matrix of the training data, or (ii) the test sample is far from the decision boundary. Furthermore, we describe how to efficiently apply the derived pNML regret to any pretrained deep NN, by employing the explicit pNML for the last layer, followed by the softmax function. Applying the derived regret to deep NN requires neither additional tunable parameters nor extra data. We extensively evaluate our approach on 74 OOD detection benchmarks using DenseNet-100, ResNet-34, and WideResNet-40 models trained with CIFAR-100, CIFAR-10, SVHN, and ImageNet-30 showing a significant improvement of up to 15.6\% over recent leading methods.

In the age of digital interaction, person-to-person relationships existing on social media may be different from the very same interactions that exist offline. Examining potential or spurious relationships between members in a social network is a fertile area of research for computer scientists -- here we examine how relationships can be predicted between two unconnected people in a social network by using area under Precison-Recall curve and ROC. Modeling the social network as a signed graph, we compare Triadic model,Latent Information model and Sentiment model and use them to predict peer to peer interactions, first using a plain signed network, and second using a signed network with comments as context. We see that our models are much better than random model and could complement each other in different cases.

Sampling and Variational Inference (VI) are two large families of methods for approximate inference with complementary strengths. Sampling methods excel at approximating arbitrary probability distributions, but can be inefficient. VI methods are efficient, but can fail when probability distributions are complex. Here, we develop a framework for constructing intermediate algorithms that balance the strengths of both sampling and VI. Both approximate a probability distribution using a mixture of simple component distributions: in sampling, each component is a delta-function and is chosen stochastically, while in standard VI a single component is chosen to minimize divergence. We show that sampling and VI emerge as special cases of an optimization problem over a mixing distribution, and intermediate approximations arise by varying a single parameter. We then derive closed-form sampling dynamics over variational parameters that stochastically build a mixture. Finally, we discuss how to select the optimal compromise between sampling and VI given a computational budget. This work is a first step towards a highly flexible yet simple family of inference methods that combines the complementary strengths of sampling and VI.