Bayesian Networks

Traditional neural networks have an impressive classification performance, but what they learn cannot be inspected, verified or extracted. Neural Logic Networks on the other hand have an interpretable structure that enables them to learn a logical mechanism relating the inputs and outputs with AND and OR operations. We generalize these networks with NOT operations and biases that take into account unobserved data and develop a rigorous logical and probabilistic modeling in terms of concept combinations to motivate their use. We also propose a novel factorized IF-THEN rule structure for the model as well as a modified learning algorithm. Our method improves the state-of-the-art in Boolean networks discovery and is able to learn relevant, interpretable rules in tabular classification, notably on examples from the medical and industrial fields where interpretability has tangible value.

Objective: Sparse Bayesian learning provides an effective framework to solve high-dimensional problems in brain signal decoding. However, conventional likelihoods regarding data distributions, such as Gaussian or Bernoulli, are potentially inadequate for handling the noisy recordings of brain activity. Hence, this work aims to formulate a robust sparse Bayesian learning framework to address noisy high-dimensional brain activity decoding. Methods: Motivated by the commendable robustness of the minimum error entropy learning criterion for addressing non-Gaussian signals, this study reformulated the sparse Bayesian learning framework under a generalized Bayesian paradigm, in which the model parameter is regulated with the minimum error entropy loss rather than a conventional likelihood function. Results: Our developed SBL-MEE algorithm was evaluated with two real-world brain decoding tasks of regression and classification scenarios, respectively. Experimental results demonstrated that our approach not only realizes superior brain decoding performance than existing methods, but also presents more physiologically interpretable decoder patterns. Conclusion: Although minimum error entropy is not constructed from an arbitrary probabilistic distribution, it is effective to establish noise-robust inference in sparse Bayesian learning method. Significance: This work provides a powerful tool to improve brain activity decoding capability, particularly regarding the noisy high-dimensional setting, thus promoting biomedical engineering applications such as brain-computer interface.

Reinforcement learning (RL) provides a principled framework for decision-making in partially observable environments, which can be modeled as Markov decision processes and compactly represented through dynamic decision Bayesian networks. Recent advances demonstrate that inference on sparse Bayesian networks can be accelerated using quantum rejection sampling combined with amplitude amplification, leading to a computational speedup in estimating acceptance probabilities. Building on this result, we introduce Quantum Bayesian Reinforcement Learning (QBRL), a hybrid quantum-classical look-ahead algorithm for model-based RL in partially observable environments. We present a rigorous, oracle-free time complexity analysis under fault-tolerant assumptions for the quantum device. Unlike standard treatments that assume a black-box oracle, we explicitly specify the inference process, allowing our bounds to more accurately reflect the true computational cost. We show that, for environments whose dynamics form a sparse Bayesian network, horizon-based near-optimal planning can be achieved sub-quadratically faster through quantum-enhanced belief updates. On the other hand, we show that there is no quantum speed-up for environments that are either fully observable, or characterized by Bayesian networks whose maximum in-degree is not small. Furthermore, we present numerical experiments benchmarking QBRL against its classical counterpart on simple yet illustrative decision-making tasks. Our results offer a detailed analysis of how the quantum computational advantage translates into decision-making performance, highlighting that the magnitude of the advantage can vary significantly across different deployment settings.

In this work, we evaluate the potential of Large Language Models (LLMs) in building Bayesian Networks (BNs) by approximating domain expert priors. LLMs have demonstrated potential as factual knowledge bases; however, their capability to generate probabilistic knowledge about real-world events remains understudied. We explore utilizing the probabilistic knowledge inherent in LLMs to derive probability estimates for statements regarding events and their relationships within a BN. Using LLMs in this context allows for the parameterization of BNs, enabling probabilistic modeling within specific domains. Our experiments on eighty publicly available Bayesian Networks, from healthcare to finance, demonstrate that querying LLMs about the conditional probabilities of events provides meaningful results when compared to baselines, including random and uniform distributions, as well as approaches based on next-token generation probabilities. We explore how these LLM-derived distributions can serve as expert priors to refine distributions extracted from data, especially when data is scarce. Overall, this work introduces a promising strategy for automatically constructing Bayesian Networks by combining probabilistic knowledge extracted from LLMs with real-world data. Additionally, we establish the first comprehensive baseline for assessing LLM performance in extracting probabilistic knowledge.

This paper proposes a hierarchical Bayesian multitask learning model that is applicable to the general multi-task binary classification learning problem where the model assumes a shared sparsity structure across different tasks. We derive a computationally efficient inference algorithm based on variational inference to approximate the posterior distribution. We demonstrate the potential of the new approach on various synthetic datasets and for predicting human health status based on microbiome profile. Our analysis incorporates data pooled from multiple microbiome studies, along with a comprehensive comparison with other benchmark methods. Results in synthetic datasets show that the proposed approach has superior support recovery property when the underlying regression coefficients share a common sparsity structure across different tasks. Our experiments on microbiome classification demonstrate the utility of the method in extracting informative taxa while providing well-calibrated predictions with uncertainty quantification and achieving competitive performance in terms of prediction metrics. Notably, despite the heterogeneity of the pooled datasets (e.g., different experimental objectives, laboratory setups, sequencing equipment, patient demographics), our method delivers robust results.

Analyzing the behavior of complex interdependent networks requires complete information about the network topology and the interdependent links across networks. For many applications such as critical infrastructure systems, understanding network interdependencies is crucial to anticipate cascading failures and plan for disruptions. However, data on the topology of individual networks are often publicly unavailable due to privacy and security concerns. Additionally, interdependent links are often only revealed in the aftermath of a disruption as a result of cascading failures. We propose a scalable nonparametric Bayesian approach to reconstruct the topology of interdependent infrastructure networks from observations of cascading failures. Metropolis-Hastings algorithm coupled with the infrastructure-dependent proposal are employed to increase the efficiency of sampling possible graphs. Results of reconstructing a synthetic system of interdependent infrastructure networks demonstrate that the proposed approach outperforms existing methods in both accuracy and computational time. We further apply this approach to reconstruct the topology of one synthetic and two real-world systems of interdependent infrastructure networks, including gas-power-water networks in Shelby County, TN, USA, and an interdependent system of power-water networks in Italy, to demonstrate the general applicability of the approach.