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Event sequences are widely available across application domains and there is a long history of models for representing and analyzing such datasets. Summary Markov models are a recent addition to the literature that help identify the subset of event types that influence event types of interest to a user. In this paper, we introduce logical summary Markov models, which are a family of models for event sequences that enable interpretable predictions through logical rules that relate historical predicates to the probability of observing an event type at any arbitrary position in the sequence. We illustrate their connection to prior parametric summary Markov models as well as probabilistic logic programs, and propose new models from this family along with efficient greedy search algorithms for learning them from data. The proposed models outperform relevant baselines on most datasets in an empirical investigation on a probabilistic prediction task. We also compare the number of influencers that various logical summary Markov models learn on real-world datasets, and conduct a brief exploratory qualitative study to gauge the promise of such symbolic models around guiding large language models for predicting societal events.

We study the computational complexity of counterfactual reasoning in relation to the complexity of associational and interventional reasoning on structural causal models (SCMs). We show that counterfactual reasoning is no harder than associational or interventional reasoning on fully specified SCMs in the context of two computational frameworks. The first framework is based on the notion of treewidth and includes the classical variable elimination and jointree algorithms. The second framework is based on the more recent and refined notion of causal treewidth which is directed towards models with functional dependencies such as SCMs. Our results are constructive and based on bounding the (causal) treewidth of twin networks---used in standard counterfactual reasoning that contemplates two worlds, real and imaginary---to the (causal) treewidth of the underlying SCM structure. In particular, we show that the latter (causal) treewidth is no more than twice the former plus one. Hence, if associational or interventional reasoning is tractable on a fully specified SCM then counterfactual reasoning is tractable too. We extend our results to general counterfactual reasoning that requires contemplating more than two worlds and discuss applications of our results to counterfactual reasoning with partially specified SCMs that are coupled with data. We finally present empirical results that measure the gap between the complexities of counterfactual reasoning and associational/interventional reasoning on random SCMs.

Graph convolutional networks (GCN) are viewed as one of the most popular representations among the variants of graph neural networks over graph data and have shown powerful performance in empirical experiments. That l2-based graph smoothing enforces the global smoothness of GCN, while (soft) l1-based sparse graph learning tends to promote signal sparsity to trade for discontinuity. This paper aims to quantify the trade-off of GCN between smoothness and sparsity, with the help of a general lp-regularized (1 Keywords: Uncertainty in AI: UAI: Graphical models

The Logical Credal Network or LCN is a recent probabilistic logic designed for effective aggregation and reasoning over multiple sources of imprecise knowledge. An LCN specifies a set of probability distributions over all interpretations of a set of logical formulas for which marginal and conditional probability bounds on their truth values are known. Inference in LCNs involves the exact solution of a non-convex non-linear program defined over an exponentially large number of non-negative real valued variables and, therefore, is limited to relatively small problems. In this paper, we present ARIEL -- a novel iterative message-passing scheme for approximate inference in LCNs. Inspired by classical belief propagation for graphical models, our method propagates messages that involve solving considerably smaller local non-linear programs. Experiments on several classes of LCNs demonstrate clearly that ARIEL yields high quality solutions compared with exact inference and scales to much larger problems than previously considered.

Learning causal structure among event types from discrete-time event sequences is a particularly important but challenging task. Existing methods, such as the multivariate Hawkes processes based methods, mostly boil down to learning the so-called Granger causality which assumes that the cause event happens strictly prior to its effect event. Such an assumption is often untenable beyond applications, especially when dealing with discrete-time event sequences in low-resolution; and typical discrete Hawkes processes mainly suffer from identifiability issues raised by the instantaneous effect, i.e., the causal relationship that occurred simultaneously due to the low-resolution data will not be captured by Granger causality. In this work, we propose Structure Hawkes Processes (SHPs) that leverage the instantaneous effect for learning the causal structure among events type in discrete-time event sequence. The proposed method is featured with the Expectation-Maximization of the likelihood function and a sparse optimization scheme. Theoretical results show that the instantaneous effect is a blessing rather than a curse, and the causal structure is identifiable under the existence of the instantaneous effect. Experiments on synthetic and real-world data verify the effectiveness of the proposed method.

For effective decision support in scenarios with conflicting objectives, sets of potentially optimal solutions can be presented to the decision maker. We explore both what policies these sets should contain and how such sets can be computed efficiently. With this in mind, we take a distributional approach and introduce a novel dominance criterion relating return distributions of policies directly. Based on this criterion, we present the distributional undominated set and show that it contains optimal policies otherwise ignored by the Pareto front. In addition, we propose the convex distributional undominated set and prove that it comprises all policies that maximise expected utility for multivariate risk-averse decision makers. We propose a novel algorithm to learn the distributional undominated set and further contribute pruning operators to reduce the set to the convex distributional undominated set. Through experiments, we demonstrate the feasibility and effectiveness of these methods, making this a valuable new approach for decision support in real-world problems.

This paper addresses the ε-close parameter tuning problem for Bayesian networks (BNs): find a minimal ε-close amendment of probability entries in a given set of (rows in) conditional probability tables that make a given quantitative constraint on the BN valid. Based on the state-of-the-art “region verification” techniques for parametric Markov chains, we propose an algorithm whose capabilities go beyond any existing techniques. Our experiments show that ε-close tuning of large BN benchmarks with up to eight parameters is feasible. In particular, by allowing (i) varied parameters in multiple CPTs and (ii) inter-CPT parameter dependencies, we treat subclasses of parametric BNs that have received scant attention so far.

We study formal languages which are capable of fully expressing quantitative probabilistic reasoning and do-calculus reasoning for causal effects, from a computational complexity perspective. We focus on satisfiability problems whose instance formulas allow expressing many tasks in probabilistic and causal inference. The main contribution of this work is establishing the exact computational complexity of these satisfiability problems. We introduce a new natural complexity class, named succ∃R, which can be viewed as a succinct variant of the well-studied class ∃R, and show that these problems are complete for succ∃R. Our results imply even stronger limitations on the use of algorithmic methods for reasoning about probabilities and causality than previous state-of-the-art results that rely only on the NP- or ∃R-completeness of the satisfiability problems for some restricted languages.

Safe Reinforcement learning (Safe RL) aims at learning optimal policies while staying safe. A popular solution to Safe RL is shielding, which uses a logical safety specification to prevent an RL agent from taking unsafe actions. However, traditional shielding techniques are difficult to integrate with continuous, end-to-end deep RL methods. To this end, we introduce Probabilistic Logic Policy Gradient (PLPG). PLPG is a model-based Safe RL technique that uses probabilistic logic programming to model logical safety constraints as differentiable functions. Therefore, PLPG can be seamlessly applied to any policy gradient algorithm while still providing the same convergence guarantees. In our experiments, we show that PLPG learns safer and more rewarding policies compared to other state-of-the-art shielding techniques.

Structural causal models provide a formalism to express causal relations between variables of interest. Models and variables can represent a system at different levels of abstraction, whereby relations may be coarsened and refined according to the need of a modeller. However, switching between different levels of abstraction requires evaluating a trade-off between the consistency and the information loss among different models. In this paper we introduce a family of interventional measures that an agent may use to evaluate such a trade-off. We consider four measures suited for different tasks, analyze their properties, and propose algorithms to evaluate and learn causal abstractions. Finally, we illustrate the flexibility of our setup by empirically showing how different measures and algorithmic choices may lead to different abstractions.

In this paper, we introduce Max Markov Chain (MMC), a novel model for sequential data with sparse correlations among the state variables. It may also be viewed as a special class of approximate models for High-order Markov Chains (HMCs). MMC is desirable for domains where the sparse correlations are long-term and vary in their temporal stretches. Although generally intractable, parameter optimization for MMC can be solved analytically. However, based on this result, we derive an approximate solution that is highly efficient empirically. When compared with HMC and approximate HMC models, MMC combines better sample efficiency, model parsimony, and an outstanding computational advantage. Such a quality allows MMC to scale to large domains where the competing models would struggle to perform. We compare MMC with several baselines with synthetic and real-world datasets to demonstrate MMC as a valuable alternative for stochastic modeling.