We consider log-supermodular models on binary variables, which are probabilistic models with negative log-densities which are submodular. These models provide probabilistic interpretations of common combinatorial optimization tasks such as image segmentation. In this paper, we focus primarily on parameter estimation in the models from known upper-bounds on the intractable log-partition function. We show that the bound based on separable optimization on the base polytope of the submodular function is always inferior to a bound based on ``perturb-and-MAP'' ideas. Then, to learn parameters, given that our approximation of the log-partition function is an expectation (over our own randomization), we use a stochastic subgradient technique to maximize a lower-bound on the log-likelihood. This can also be extended to conditional maximum likelihood. We illustrate our new results in a set of experiments in binary image denoising, where we highlight the flexibility of a probabilistic model to learn with missing data.

Neural Information Processing Systems http://nips.cc/

First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. UPDATE: I acknowledge that I have read the author rebuttal. The authors propose a method for learning a mapping from input messages to the output message in the context of expectation propagation. The method can be thought of as a sort of compilation step, where there is a one-time cost of closely approximating the true output messages using important sampling, after which a neural network is trained to reproduce the output messages in the context of future inference queries. First, the authors should be commended for attacking a difficult and interesting problem.

Technical quality: The math seems correct, though in general showing a few more intermediate steps in derivations would make the work of the reader easier (can push the proof to the supplement to make room). In the proof of Proposition 1 for instance, it would be nice to have more detail on how the final equality is obtained. The experiments compare to an SVM baseline, but not to the parameter learning done in [9]. Specifically, [9] does parameter learning for the spin glass model and shows that it achieves an error of 1.8% compared to an SVM's 8.2%. What is different about the learning done in this work (besides the use of a different probabilistic model)?

Parameter learning is a crucial task in the field of Statistical Relational Artificial Intelligence: given a probabilistic logic program and a set of observations in the form of interpretations, the goal is to learn the probabilities of the facts in the program such that the probabilities of the interpretations are maximized. In this paper, we propose two algorithms to solve such a task within the formalism of Probabilistic Answer Set Programming, both based on the extraction of symbolic equations representing the probabilities of the interpretations. The first solves the task using an off-the-shelf constrained optimization solver while the second is based on an implementation of the Expectation Maximization algorithm. Empirical results show that our proposals often outperform existing approaches based on projected answer set enumeration in terms of quality of the solution and in terms of execution time. The paper has been accepted at the ICLP2024 conference and is under consideration in Theory and Practice of Logic Programming (TPLP).

Wildland fires pose terrifying natural hazards, underscoring the urgent need to develop data-driven and physics-informed digital twins for wildfire prevention, monitoring, intervention, and response. In this direction of research, this work introduces a physics-informed neural network (PiNN) to learn the unknown parameters of an interpretable wildfire spreading model. The considered wildfire spreading model integrates fundamental physical laws articulated by key model parameters, essential for capturing the complex behavior of wildfires. The proposed machine learning approach leverages the theory of artificial neural networks with the physical constraints governing wildfire dynamics, such as the first principles of mass and energy conservation. Training of the PiNN for physics-informed parameter identification is realized using data of the temporal evolution of one- and two-dimensional (plane surface) fire fronts that have been obtained from a high-fidelity simulator of the wildfire spreading model under consideration. The parameter learning results demonstrate the remarkable predictive ability of the proposed PiNN in uncovering the unknown coefficients in both the one- and two-dimensional fire spreading scenarios. Additionally, this methodology exhibits robustness by identifying the same parameters in the presence of noisy data. The proposed framework is envisioned to be incorporated in a physics-informed digital twin for intelligent wildfire management and risk assessment.

Optimizing students' learning strategies is a crucial component in intelligent tutoring systems. Previous research has demonstrated the effectiveness of devising personalized learning strategies for students by modelling their learning processes through partially observable Markov decision process (POMDP). However, the research holds the assumption that the student population adheres to a uniform cognitive pattern. While this assumption simplifies the POMDP modelling process, it evidently deviates from a real-world scenario, thus reducing the precision of inducing individual students' learning strategies. In this article, we propose the homomorphic POMDP (H-POMDP) model to accommodate multiple cognitive patterns and present the parameter learning approach to automatically construct the H-POMDP model. Based on the H-POMDP model, we are able to represent different cognitive patterns from the data and induce more personalized learning strategies for individual students. We conduct experiments to show that, in comparison to the general POMDP approach, the H-POMDP model demonstrates better precision when modelling mixed data from multiple cognitive patterns. Moreover, the learning strategies derived from H-POMDPs exhibit better personalization in the performance evaluation.

We consider log-supermodular models on binary variables, which are probabilistic models with negative log-densities which are submodular. These models provide probabilistic interpretations of common combinatorial optimization tasks such as image segmentation. In this paper, we focus primarily on parameter estimation in the models from known upper-bounds on the intractable log-partition function. We show that the bound based on separable optimization on the base polytope of the submodular function is always inferior to a bound based on "perturb-and-MAP" ideas. Then, to learn parameters, given that our approximation of the log-partition function is an expectation (over our own randomization), we use a stochastic subgradient technique to maximize a lower-bound on the log-likelihood. This can also be extended to conditional maximum likelihood. We illustrate our new results in a set of experiments in binary image denoising, where we highlight the flexibility of a probabilistic model to learn with missing data.

This paper proposes and develops a physics-inspired neural network (PiNN) for learning the parameters of commercially implemented adaptive cruise control (ACC) systems in automotive industry. To emulate the core functionality of stock ACC systems, which have proprietary control logic and undisclosed parameters, the constant time-headway policy (CTHP) is adopted. Leveraging the multi-layer artificial neural networks as universal approximators, the developed PiNN serves as a surrogate model for the longitudinal dynamics of ACC-engaged vehicles, efficiently learning the unknown parameters of the CTHP. The ability of the PiNN to infer the unknown ACC parameters is meticulous evaluated using both synthetic and high-fidelity empirical data of space-gap and relative velocity involving ACC-engaged vehicles in platoon formation. The results have demonstrated the superior predictive ability of the proposed PiNN in learning the unknown design parameters of stock ACC systems from different car manufacturers. The set of ACC model parameters obtained from the PiNN revealed that the stock ACC systems of the considered vehicles in three experimental campaigns are neither $L_2$ nor $L_\infty$ string stable.

Federated learning makes it possible to train a machine learning model on decentralized data. Bayesian networks are probabilistic graphical models that have been widely used in artificial intelligence applications. Their popularity stems from the fact they can be built by combining existing expert knowledge with data and are highly interpretable, which makes them useful for decision support, e.g. in healthcare. While some research has been published on the federated learning of Bayesian networks, publications on Bayesian networks in a vertically partitioned or heterogeneous data setting (where different variables are located in different datasets) are limited, and suffer from important omissions, such as the handling of missing data. In this article, we propose a novel method called VertiBayes to train Bayesian networks (structure and parameters) on vertically partitioned data, which can handle missing values as well as an arbitrary number of parties. For structure learning we adapted the widely used K2 algorithm with a privacy-preserving scalar product protocol. For parameter learning, we use a two-step approach: first, we learn an intermediate model using maximum likelihood by treating missing values as a special value and then we train a model on synthetic data generated by the intermediate model using the EM algorithm. The privacy guarantees of our approach are equivalent to the ones provided by the privacy preserving scalar product protocol used. We experimentally show our approach produces models comparable to those learnt using traditional algorithms and we estimate the increase in complexity in terms of samples, network size, and complexity. Finally, we propose two alternative approaches to estimate the performance of the model using vertically partitioned data and we show in experiments that they lead to reasonably accurate estimates.