Infectious diseases, either emerging or long-lasting, place numerous people at risk and bring heavy public health burdens worldwide. In the process against infectious diseases, predicting the epidemic risk by modeling the disease transmission plays an essential role in assisting with preventing and controlling disease transmission in a more effective way. In this paper, we systematically describe how machine learning can play an essential role in quantitatively characterizing disease transmission patterns and accurately predicting infectious disease risks. First, we introduce the background and motivation of using machine learning for infectious disease risk prediction. Next, we describe the development and components of various machine learning models for infectious disease risk prediction. Specifically, existing models fall into three categories: Statistical prediction, data-driven machine learning, and epidemiology-inspired machine learning. Subsequently, we discuss challenges encountered when dealing with model inputs, designing task-oriented objectives, and conducting performance evaluation. Finally, we conclude with a discussion of open questions and future directions.

Variational inference has recently emerged as a popular alternative to the classical Markov chain Monte Carlo (MCMC) in large-scale Bayesian inference. The core idea is to trade statistical accuracy for computational efficiency. In this work, we study these statistical and computational trade-offs in variational inference via a case study in inferential model selection. Focusing on Gaussian inferential models (or variational approximating families) with diagonal plus low-rank precision matrices, we initiate a theoretical study of the trade-offs in two aspects, Bayesian posterior inference error and frequentist uncertainty quantification error. From the Bayesian posterior inference perspective, we characterize the error of the variational posterior relative to the exact posterior. We prove that, given a fixed computation budget, a lower-rank inferential model produces variational posteriors with a higher statistical approximation error, but a lower computational error; it reduces variance in stochastic optimization and, in turn, accelerates convergence. From the frequentist uncertainty quantification perspective, we consider the precision matrix of the variational posterior as an uncertainty estimate, which involves an additional statistical error originating from the sampling uncertainty of the data. As a consequence, for small datasets, the inferential model need not be full-rank to achieve optimal estimation error (even with unlimited computation budget).

Simulations using machine learning (ML) models and mechanistic models are often run to inform decision-making processes. Uncertainty estimates of simulation results are critical to the decision-making process because simulation results of specific scenarios may have wide, but unspecified, confidence bounds that may impact subsequent analyses and decisions. The objective of this work is to develop a protocol to assess uncertainties in predictions of machine learning and mechanistic simulation models. The protocol will outline an uncertainty quantification workflow that may be used to establish credible bounds of predictability on computed quantities of interest and to assess model sufficiency. The protocol identifies key sources of uncertainties in machine learning and mechanistic modeling, defines applicable methods of uncertainty propagation for these sources, and includes statistically rational estimators for output uncertainties. The work applies the protocol to test cases relevant to the gas distribution industry and presents learnings from its application. The paper concludes with a brief discussion outlining a pathway to the wider adoption of uncertainty quantification within the industry

Context: User intent modeling is a crucial process in Natural Language Processing that aims to identify the underlying purpose behind a user's request, enabling personalized responses. With a vast array of approaches introduced in the literature (over 13,000 papers in the last decade), understanding the related concepts and commonly used models in AI-based systems is essential. Method: We conducted a systematic literature review to gather data on models typically employed in designing conversational recommender systems. From the collected data, we developed a decision model to assist researchers in selecting the most suitable models for their systems. Additionally, we performed two case studies to evaluate the effectiveness of our proposed decision model. Results: Our study analyzed 59 distinct models and identified 74 commonly used features. We provided insights into potential model combinations, trends in model selection, quality concerns, evaluation measures, and frequently used datasets for training and evaluating these models. Contribution: Our study contributes practical insights and a comprehensive understanding of user intent modeling, empowering the development of more effective and personalized conversational recommender systems. With the Conversational Recommender System, researchers can perform a more systematic and efficient assessment of fitting intent modeling frameworks.

A physics-informed machine learning model, in the form of a multi-output Gaussian process, is formulated using the Euler-Bernoulli beam equation. Given appropriate datasets, the model can be used to regress the analytical value of the structure's bending stiffness, interpolate responses, and make probabilistic inferences on latent physical quantities. The developed model is applied on a numerically simulated cantilever beam, where the regressed bending stiffness is evaluated and the influence measurement noise on the prediction quality is investigated. Further, the regressed probabilistic stiffness distribution is used in a structural health monitoring context, where the Mahalanobis distance is employed to reason about the possible location and extent of damage in the structural system. To validate the developed framework, an experiment is conducted and measured heterogeneous datasets are used to update the assumed analytical structural model.

Probabilistic model checking is a technique for formal automated reasoning about software or hardware systems that operate in the context of uncertainty or stochasticity. It builds upon ideas and techniques from a diverse range of fields, from logic, automata and graph theory, to optimisation, numerical methods and control. In recent years, probabilistic model checking has also been extended to integrate ideas from game theory, notably using models such as stochastic games and solution concepts such as equilibria, to formally verify the interaction of multiple rational agents with distinct objectives. This provides a means to reason flexibly about agents acting in either an adversarial or a collaborative fashion, and opens up opportunities to tackle new problems within, for example, artificial intelligence, robotics and autonomous systems. In this paper, we summarise some of the advances in this area, and highlight applications for which they have already been used. We discuss how the strengths of probabilistic model checking apply, or have the potential to apply, to the multi-agent setting and outline some of the key challenges required to make further progress in this field.

The classical causal relations between a set of variables, some observed and some latent, can induce both equality constraints (typically conditional independences) as well as inequality constraints (Instrumental and Bell inequalities being prototypical examples) on their compatible distribution over the observed variables. Enumerating a causal structure's implied inequality constraints is generally far more difficult than enumerating its equalities. Furthermore, only inequality constraints ever admit violation by quantum correlations. For both those reasons, it is important to classify causal scenarios into those which impose inequality constraints versus those which do not. Here we develop methods for detecting such scenarios by appealing to d-separation, e-separation, and incompatible supports. Many (perhaps all?) scenarios with exclusively equality constraints can be detected via a condition articulated by Henson, Lal and Pusey (HLP). Considering all scenarios with up to 4 observed variables, which number in the thousands, we are able to resolve all but three causal scenarios, providing evidence that the HLP condition is, in fact, exhaustive.

We study the implementation of Automatic Differentiation Variational inference (ADVI) for Bayesian inference on regression models with bridge penalization. The bridge approach uses $\ell_{\alpha}$ norm, with $\alpha \in (0, +\infty)$ to define a penalization on large values of the regression coefficients, which includes the Lasso ($\alpha = 1$) and ridge $(\alpha = 2)$ penalizations as special cases. Full Bayesian inference seamlessly provides joint uncertainty estimates for all model parameters. Although MCMC aproaches are available for bridge regression, it can be slow for large dataset, specially in high dimensions. The ADVI implementation allows the use of small batches of data at each iteration (due to stochastic gradient based algorithms), therefore speeding up computational time in comparison with MCMC. We illustrate the approach on non-parametric regression models with B-splines, although the method works seamlessly for other choices of basis functions. A simulation study shows the main properties of the proposed method.

Despite their incredible performance, it is well reported that deep neural networks tend to be overoptimistic about their prediction confidence. Finding effective and efficient calibration methods for neural networks is therefore an important endeavour towards better uncertainty quantification in deep learning. In this manuscript, we introduce a novel calibration technique named expectation consistency (EC), consisting of a post-training rescaling of the last layer weights by enforcing that the average validation confidence coincides with the average proportion of correct labels. First, we show that the EC method achieves similar calibration performance to temperature scaling (TS) across different neural network architectures and data sets, all while requiring similar validation samples and computational resources. However, we argue that EC provides a principled method grounded on a Bayesian optimality principle known as the Nishimori identity. Next, we provide an asymptotic characterization of both TS and EC in a synthetic setting and show that their performance crucially depends on the target function. In particular, we discuss examples where EC significantly outperforms TS.

Computing the marginal likelihood (also called the Bayesian model evidence) is an important task in Bayesian model selection, providing a principled quantitative way to compare models. The learned harmonic mean estimator solves the exploding variance problem of the original harmonic mean estimation of the marginal likelihood. The learned harmonic mean estimator learns an importance sampling target distribution that approximates the optimal distribution. While the approximation need not be highly accurate, it is critical that the probability mass of the learned distribution is contained within the posterior in order to avoid the exploding variance problem. In previous work a bespoke optimization problem is introduced when training models in order to ensure this property is satisfied. In the current article we introduce the use of normalizing flows to represent the importance sampling target distribution. A flow-based model is trained on samples from the posterior by maximum likelihood estimation. Then, the probability density of the flow is concentrated by lowering the variance of the base distribution, i.e. by lowering its "temperature", ensuring its probability mass is contained within the posterior. This approach avoids the need for a bespoke optimisation problem and careful fine tuning of parameters, resulting in a more robust method. Moreover, the use of normalizing flows has the potential to scale to high dimensional settings. We present preliminary experiments demonstrating the effectiveness of the use of flows for the learned harmonic mean estimator. The harmonic code implementing the learned harmonic mean, which is publicly available, has been updated to now support normalizing flows.