Training energy-based models (EBMs) on discrete spaces is challenging because sampling over such spaces can be difficult. We propose to train discrete EBMs with energy discrepancy (ED), a novel type of contrastive loss functional which only requires the evaluation of the energy function at data points and their perturbed counter parts, thus not relying on sampling strategies like Markov chain Monte Carlo (MCMC). Energy discrepancy offers theoretical guarantees for a broad class of perturbation processes of which we investigate three types: perturbations based on Bernoulli noise, based on deterministic transforms, and based on neighbourhood structures. We demonstrate their relative performance on lattice Ising models, binary synthetic data, and discrete image data sets.

Bayesian inference offers benefits over maximum likelihood, but it also comes with computational costs. Computing the posterior is typically intractable, as is marginalizing that posterior to form the posterior predictive distribution. In this paper, we present variational prediction, a technique for directly learning a variational approximation to the posterior predictive distribution using a variational bound. This approach can provide good predictive distributions without test time marginalization costs. We demonstrate Variational Prediction on an illustrative toy example.

Incorporating unstructured data into physical models is a challenging problem that is emerging in data assimilation. Traditional approaches focus on well-defined observation operators whose functional forms are typically assumed to be known. This prevents these methods from achieving a consistent model-data synthesis in configurations where the mapping from data-space to model-space is unknown. To address these shortcomings, in this paper we develop a physics-informed dynamical variational autoencoder ($\Phi$-DVAE) to embed diverse data streams into time-evolving physical systems described by differential equations. Our approach combines a standard, possibly nonlinear, filter for the latent state-space model and a VAE, to assimilate the unstructured data into the latent dynamical system. Unstructured data, in our example systems, comes in the form of video data and velocity field measurements, however the methodology is suitably generic to allow for arbitrary unknown observation operators. A variational Bayesian framework is used for the joint estimation of the encoding, latent states, and unknown system parameters. To demonstrate the method, we provide case studies with the Lorenz-63 ordinary differential equation, and the advection and Korteweg-de Vries partial differential equations. Our results, with synthetic data, show that $\Phi$-DVAE provides a data efficient dynamics encoding methodology which is competitive with standard approaches. Unknown parameters are recovered with uncertainty quantification, and unseen data are accurately predicted.

Despite the existence of numerous designs, significant research efforts, and successful applications in the field of control systems, the development of a reliable and secure controller that combines robust theoretical foundations with exceptional performance continues to present a formidable challenge. This challenge has captured the attention of researchers from diverse fields, including robotics [1] and healthcare [2], among others. In the context of control systems, safety is evaluated based on the system state. In this study, we focus on probabilistic safe control, wherein a safe controller is expected to prevent the system from entering hazardous states with an acceptable probability [3-5]. Due to the intricate nature of calculating the safe state space for a general dynamics-driven system, ensuring safety by designing or learning a safe controller is rather complex. Existing safe control strategies include model predictive control [6], reachability analysis [7], and control barrier function (CBF) method [8]. In our research, we build upon the CBF method, which ensures that the system state remains within safe regions by defining a forward invariant set. This set is a subset of the safe region and restricts the system state within its boundaries. Furthermore, we take into account the presence of uncertainty, which not only have a more significant impact on the system state than small disturbances [9], and does not have an analytical format as well [10].

In their seminal 1990 paper, Wasserman and Kadane establish an upper bound for the Bayes' posterior probability of a measurable set $A$, when the prior lies in a class of probability measures $\mathcal{P}$ and the likelihood is precise. They also give a sufficient condition for such upper bound to hold with equality. In this paper, we introduce a generalization of their result by additionally addressing uncertainty related to the likelihood. We give an upper bound for the posterior probability when both the prior and the likelihood belong to a set of probabilities. Furthermore, we give a sufficient condition for this upper bound to become an equality. This result is interesting on its own, and has the potential of being applied to various fields of engineering (e.g. model predictive control), machine learning, and artificial intelligence.

This paper presents a new approach to automatically discovering accurate models of complex time series data. Working within a Bayesian nonparametric prior over a symbolic space of Gaussian process time series models, we present a novel structure learning algorithm that integrates sequential Monte Carlo (SMC) and involutive MCMC for highly effective posterior inference. Our method can be used both in "online" settings, where new data is incorporated sequentially in time, and in "offline" settings, by using nested subsets of historical data to anneal the posterior. Empirical measurements on real-world time series show that our method can deliver 10x--100x runtime speedups over previous MCMC and greedy-search structure learning algorithms targeting the same model family. We use our method to perform the first large-scale evaluation of Gaussian process time series structure learning on a prominent benchmark of 1,428 econometric datasets. The results show that our method discovers sensible models that deliver more accurate point forecasts and interval forecasts over multiple horizons as compared to widely used statistical and neural baselines that struggle on this challenging data.

If much of the information is irrelevant, it's easy to To optimally coordinate with others in cooperative imagine how this could lead to significant increases in efficiency games, it is often crucial to have information for finding optimal policies. For example, this could about one's collaborators: successful driving requires allow a focused effort on few-shot or zero-shot adaptation to understanding which side of the road to co-players (Zand et al., 2022; Albrecht & Stone, 2017; Stone drive on. However, not every feature of collaborators et al., 2010; Hu et al., 2020) or more efficient DecPOMDP is strategically relevant: the fine-grained planning algorithms (Szer & Charpillet, 2006; Seuken & acceleration of drivers may be ignored while maintaining Zilberstein, 2007). In order to leverage these benefits, we optimal coordination. We show that there build the theory, data structures, and algorithms required to is a well-defined dichotomy between strategically distinguish between relevant and irrelevant information.

We formalize the problem of contextual optimization through the lens of Bayesian experimental design and propose CO-BED -- a general, model-agnostic framework for designing contextual experiments using information-theoretic principles. After formulating a suitable information-based objective, we employ black-box variational methods to simultaneously estimate it and optimize the designs in a single stochastic gradient scheme. In addition, to accommodate discrete actions within our framework, we propose leveraging continuous relaxation schemes, which can naturally be integrated into our variational objective. As a result, CO-BED provides a general and automated solution to a wide range of contextual optimization problems. We illustrate its effectiveness in a number of experiments, where CO-BED demonstrates competitive performance even when compared to bespoke, model-specific alternatives.

The dynamic vehicle dispatching problem corresponds to deciding which vehicles to assign to requests that arise stochastically over time and space. It emerges in diverse areas, such as in the assignment of trucks to loads to be transported; in emergency systems; and in ride-hailing services. In this paper, we model the problem as a semi-Markov decision process, which allows us to treat time as continuous. In this setting, decision epochs coincide with discrete events whose time intervals are random. We argue that an event-based approach substantially reduces the combinatorial complexity of the decision space and overcomes other limitations of discrete-time models often proposed in the literature. In order to test our approach, we develop a new discrete-event simulator and use double deep q-learning to train our decision agents. Numerical experiments are carried out in realistic scenarios using data from New York City. We compare the policies obtained through our approach with heuristic policies often used in practice. Results show that our policies exhibit better average waiting times, cancellation rates and total service times, with reduction in average waiting times of up to 50% relative to the other tested heuristic policies.

Applications that could benefit from automatic understanding of human-human conversations often come with challenges associated with private information in real-world data such as call center or clinical conversations. Working with protected data also increases costs of annotation, which limits technology development. To address these challenges, we propose DIALGEN, a human-in-the-loop semi-automated dialogue generation framework. DIALGEN uses a language model (ChatGPT) that can follow schema and style specifications to produce fluent conversational text, generating a complex conversation through iteratively generating subdialogues and using human feedback to correct inconsistencies or redirect the flow. In experiments on structured summarization of agent-client information gathering calls, framed as dialogue state tracking, we show that DIALGEN data enables significant improvement in model performance.