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 ED approaches the explicit score matching and negative log-likelihood loss under different limits, effectively interpolating between both. Consequently, minimum ED 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.

The exploration-exploitation dilemma has been a central challenge in reinforcement learning (RL) with complex model classes. In this paper, we propose a new algorithm, Monotonic Q-Learning with Upper Confidence Bound (MQL-UCB) for RL with general function approximation. Our key algorithmic design includes (1) a general deterministic policy-switching strategy that achieves low switching cost, (2) a monotonic value function structure with carefully controlled function class complexity, and (3) a variance-weighted regression scheme that exploits historical trajectories with high data efficiency. MQL-UCB achieves minimax optimal regret of $\tilde{O}(d\sqrt{HK})$ when $K$ is sufficiently large and near-optimal policy switching cost of $\tilde{O}(dH)$, with $d$ being the eluder dimension of the function class, $H$ being the planning horizon, and $K$ being the number of episodes. Our work sheds light on designing provably sample-efficient and deployment-efficient Q-learning with nonlinear function approximation.

Car following (CF) models are fundamental to describing traffic dynamics. However, the CF behavior of human drivers is highly stochastic and nonlinear. As a result, identifying the "best" CF model has been challenging and controversial despite decades of research. Introduction of automated vehicles has further complicated this matter as their CF controllers remain proprietary, though their behavior appears different than human drivers. This paper develops a stochastic learning approach to integrate multiple CF models, rather than relying on a single model. The framework is based on approximate Bayesian computation that probabilistically concatenates a pool of CF models based on their relative likelihood of describing observed behavior. The approach, while data-driven, retains physical tractability and interpretability. Evaluation results using two datasets show that the proposed approach can better reproduce vehicle trajectories for both human-driven and automated vehicles than any single CF model considered.

Electroanatomical mapping is a technique used in cardiology to create a detailed 3D map of the electrical activity in the heart. It is useful for diagnosis, treatment planning and real time guidance in cardiac ablation procedures to treat arrhythmias like atrial fibrillation. A probabilistic machine learning model trained on a library of CT/MRI scans of the heart can be used during electroanatomical mapping to generate a patient-specific 3D model of the chamber being mapped. The use of probabilistic machine learning models under a Bayesian framework provides a way to quantify uncertainty in results and provide a natural framework of interpretability of the model. Here we introduce a Bayesian approach to surface reconstruction of cardiac chamber models from a sparse 3D point cloud data acquired during electroanatomical mapping. We show how probabilistic graphical models trained on segmented CT/MRI data can be used to generate cardiac chamber models from few acquired locations thereby reducing procedure time and x-ray exposure. We show how they provide insight into what the neural network learns from the segmented CT/MRI images used to train the network, which provides explainability to the resulting cardiac chamber models generated by the model.

Even after fine-tuning and reinforcement learning, large language models (LLMs) can be difficult, if not impossible, to control reliably with prompts alone. We propose a new inference-time approach to enforcing syntactic and semantic constraints on the outputs of LLMs, called sequential Monte Carlo (SMC) steering. The key idea is to specify language generation tasks as posterior inference problems in a class of discrete probabilistic sequence models, and replace standard decoding with sequential Monte Carlo inference. For a computational cost similar to that of beam search, SMC can steer LLMs to solve diverse tasks, including infilling, generation under syntactic constraints, and prompt intersection. To facilitate experimentation with SMC steering, we present a probabilistic programming library, LLaMPPL, for concisely specifying new generation tasks as language model probabilistic programs, and automating steering of LLaMA-family Transformers.

Computational models are powerful tools for understanding human cognition and behavior. They let us express our theories clearly and precisely, and offer predictions that can be subtle and often counter-intuitive. However, this same richness and ability to surprise means our scientific intuitions and traditional tools are ill-suited to designing experiments to test and compare these models. To avoid these pitfalls and realize the full potential of computational modeling, we require tools to design experiments that provide clear answers about what models explain human behavior and the auxiliary assumptions those models must make. Bayesian optimal experimental design (BOED) formalizes the search for optimal experimental designs by identifying experiments that are expected to yield informative data. In this work, we provide a tutorial on leveraging recent advances in BOED and machine learning to find optimal experiments for any kind of model that we can simulate data from, and show how by-products of this procedure allow for quick and straightforward evaluation of models and their parameters against real experimental data. As a case study, we consider theories of how people balance exploration and exploitation in multi-armed bandit decision-making tasks. We validate the presented approach using simulations and a real-world experiment. As compared to experimental designs commonly used in the literature, we show that our optimal designs more efficiently determine which of a set of models best account for individual human behavior, and more efficiently characterize behavior given a preferred model. At the same time, formalizing a scientific question such that it can be adequately addressed with BOED can be challenging and we discuss several potential caveats and pitfalls that practitioners should be aware of. We provide code and tutorial notebooks to replicate all analyses.

As the presence of outliers within observations may adversely affect the statistical inference, robust statistics has been developed for several decades (Huber and Ronchetti, 1981; Hampel et al., 1986; Maronna et al., 2006). Amongst many possible directions, the divergence-based approach, which estimates some parameters in probabilistic models by minimizing the divergence to underlying distributions, has drawn considerable attention owing to its compatibility with the probabilistically formulated problems. In particular, density power divergence (DPD), also known as β-divergence (Basu et al., 1998), extends the Kullback-Leibler divergence to enhance robustness against outliers. DPD has gained recognition as one of the most widely used divergences across disciplines. DPD finds applications in various fields, including blind source separation (Minami and Eguchi, 2002), matrix factorization (Tan and Févotte, 2012), signal processing (Basseville, 2013), Bayesian inference (Ghosh and Basu, 2016), variational inference (Futami et al., 2018), and more, contributing to the enhancement of robustness in these applications.

Multi-dimensional classification (MDC) can be employed in a range of applications where one needs to predict multiple class variables for each given instance. Many existing MDC methods suffer from at least one of inaccuracy, scalability, limited use to certain types of data, hardness of interpretation or lack of probabilistic (uncertainty) estimations. This paper is an attempt to address all these disadvantages simultaneously. We propose a formal framework for probabilistic MDC in which learning an optimal multi-dimensional classifier can be decomposed, without loss of generality, into learning a set of (smaller) single-variable multi-class probabilistic classifiers and a directed acyclic graph. Current and future developments of both probabilistic classification and graphical model learning can directly enhance our framework, which is flexible and provably optimal. A collection of experiments is conducted to highlight the usefulness of this MDC framework.

We propose an approach to do learning in Gaussian factor graphs. We treat all relevant quantities (inputs, outputs, parameters, latents) as random variables in a graphical model, and view both training and prediction as inference problems with different observed nodes. Our experiments show that these problems can be efficiently solved with belief propagation (BP), whose updates are inherently local, presenting exciting opportunities for distributed and asynchronous training. Our approach can be scaled to deep networks and provides a natural means to do continual learning: use the BP-estimated parameter marginals of the current task as parameter priors for the next. On a video denoising task we demonstrate the benefit of learnable parameters over a classical factor graph approach and we show encouraging performance of deep factor graphs for continual image classification on MNIST.

Effectively modeling phenomena present in highly nonlinear dynamical systems whilst also accurately quantifying uncertainty is a challenging task, which often requires problem-specific techniques. We outline the deep latent force model (DLFM), a domain-agnostic approach to tackling this problem, which consists of a deep Gaussian process architecture where the kernel at each layer is derived from an ordinary differential equation using the framework of process convolutions. Two distinct formulations of the DLFM are presented which utilise weight-space and variational inducing points-based Gaussian process approximations, both of which are amenable to doubly stochastic variational inference. We provide evidence that our model is capable of capturing highly nonlinear behaviour in real-world multivariate time series data. In addition, we find that our approach achieves comparable performance to a number of other probabilistic models on benchmark regression tasks. We also empirically assess the negative impact of the inducing points framework on the extrapolation capabilities of LFM-based models.