Selecting cost-effective optimal sensor configurations for subsequent inference of parameters in black-box stochastic systems faces significant computational barriers. We propose a novel and robust approach, modelling the joint distribution over input parameters and solution with a joint energy-based model, trained on simulation data. Unlike existing simulation-based inference approaches, which must be tied to a specific set of point evaluations, we learn a functional representation of parameters and solution. This is used as a resolution-independent plug-and-play surrogate for the joint distribution, which can be conditioned over any set of points, permitting an efficient approach to sensor placement. We demonstrate the validity of our framework on a variety of stochastic problems, showing that our method provides highly informative sensor locations at a lower computational cost compared to conventional approaches.

Energy-based models (EBMs) offer a flexible framework for probabilistic modelling across various data domains. However, training EBMs on data in discrete or mixed state spaces poses significant challenges due to the lack of robust and fast sampling methods. In this work, we propose to train discrete EBMs with Energy Discrepancy, a loss function which only requires the evaluation of the energy function at data points and their perturbed counterparts, thus eliminating the need for Markov chain Monte Carlo. We introduce perturbations of the data distribution by simulating a diffusion process on the discrete state space endowed with a graph structure. This allows us to inform the choice of perturbation from the structure of the modelled discrete variable, while the continuous time parameter enables fine-grained control of the perturbation. Empirically, we demonstrate the efficacy of the proposed approaches in a wide range of applications, including the estimation of discrete densities with non-binary vocabulary and binary image modelling. We also introduce the first application of EBMs to tabular data sets with applications in synthetic data generation and calibrated classification.

Energy-based models are a simple yet powerful class of probabilistic models, but their widespread adoption has been limited by the computational burden of training them. We propose a novel loss function called Energy Discrepancy (ED) which does not rely on the computation of scores or expensive Markov chain Monte Carlo. We show that energy discrepancy approaches the explicit score matching and negative log-likelihood loss under different limits, effectively interpolating between both. Consequently, minimum energy discrepancy estimation overcomes the problem of nearsightedness encountered in score-based estimation methods, while also enjoying theoretical guarantees. Through numerical experiments, we demonstrate that ED learns low-dimensional data distributions faster and more accurately than explicit score matching or contrastive divergence. For high-dimensional image data, we describe how the manifold hypothesis puts limitations on our approach and demonstrate the effectiveness of energy discrepancy by training the energy-based model as a prior of a variational decoder model.

In this work, we present a general procedure for acoustic leak detection in water networks that satisfies multiple real-world constraints such as energy efficiency and ease of deployment. Based on recordings from seven contact microphones attached to the water supply network of a municipal suburb, we trained several shallow and deep anomaly detection models. Inspired by how human experts detect leaks using electronic sounding-sticks, we use these models to repeatedly listen for leaks over a predefined decision horizon. This way we avoid constant monitoring of the system. While we found the detection of leaks in close proximity to be a trivial task for almost all models, neural network based approaches achieve better results at the detection of distant leaks.

Notions of identity and of the self have long been studied in social psychology and sociology as key guiding elements of social interaction and coordination. In the AI of the future, these notions will also play a role in producing natural, socially appropriate artificially intelligent agents that encompass subtle and complex human social and affective skills. We propose here a Bayesian generalization of the sociological affect control theory of self as a theoretical foundation for socio-affectively skilled artificial agents. This theory posits that each human maintains an internal model of his or her deep sense of "self" that captures their emotional, psychological, and socio-cultural sense of being in the world. The "self" is then externalised as an identity within any given interpersonal and institutional situation, and this situational identity is the person's local (in space and time) representation of the self. Situational identities govern the actions of humans according to affect control theory. Humans will seek situations that allow them to enact identities consistent with their sense of self. This consistency is cumulative over time: if some parts of a person's self are not actualized regularly, the person will have a growing feeling of inauthenticity that they will seek to resolve. In our present generalisation, the self is represented as a probability distribution, allowing it to be multi-modal (a person can maintain multiple different identities), uncertain (a person can be unsure about who they really are), and learnable (agents can learn the identities and selves of other agents). We show how the Bayesian affect control theory of self can underpin artificial agents that are socially intelligent.

Affect Control Theory is a mathematical representation of the interactions between two persons, in which it is posited that people behave in a way so as to minimize the amount of deflection between their cultural emotional sentiments and the transient emotional sentiments that are created by each situation. Affect Control Theory presents a maximum likelihood solution in which optimal behaviours or identities can be predicted based on past interactions. Here, we formulate a probabilistic and decision theoretic model of the same underlying principles, and show this to be a generalisation of the basic theory. The model is more expressive than the original theory, as it can maintain multiple hypotheses about behaviours and identities simultaneously as a probability distribution. This allows the model to generate affectively believable interactions with people by learning about their identity and predicting their behaviours. We demonstrate this generalisation with a set of simulations. We then show how our model can be used as an emotional "plug-in" for systems that interact with humans. We demonstrate human-interactive capability by building a simple intelligent tutoring application and pilot-testing it in an experiment with 20 participants.

We use some results of Trnková to show first that subcoalgebras are always closed under finite intersections. Assuming that the type functor F is bounded, we obtain a concrete representation of the terminal F-coalgebra. We also provide several equivalent characterizations of boundedness.