We present a universal framework for constructing confidence sets based on sequential likelihood mixing. Building upon classical results from sequential analysis, we provide a unifying perspective on several recent lines of work, and establish fundamental connections between sequential mixing, Bayesian inference and regret inequalities from online estimation. The framework applies to any realizable family of likelihood functions and allows for non-i.i.d. data and anytime validity. Moreover, the framework seamlessly integrates standard approximate inference techniques, such as variational inference and sampling-based methods, and extends to misspecified model classes, while preserving provable coverage guarantees. We illustrate the power of the framework by deriving tighter confidence sequences for classical settings, including sequential linear regression and sparse estimation, with simplified proofs.

This article focuses on covariance estimation for multi-study data. Popular approaches employ factor-analytic terms with shared and study-specific loadings that decompose the variance into (i) a shared low-rank component, (ii) study-specific low-rank components, and (iii) a diagonal term capturing idiosyncratic variability. Our proposed methodology estimates the latent factors via spectral decompositions and infers the factor loadings via surrogate regression tasks, avoiding identifiability and computational issues of existing alternatives. Reliably inferring shared vs study-specific components requires novel developments that are of independent interest. The approximation error decreases as the sample size and the data dimension diverge, formalizing a blessing of dimensionality. Conditionally on the factors, loadings and residual error variances are inferred via conjugate normal-inverse gamma priors. The conditional posterior distribution of factor loadings has a simple product form across outcomes, facilitating parallelization. We show favorable asymptotic properties, including central limit theorems for point estimators and posterior contraction, and excellent empirical performance in simulations. The methods are applied to integrate three studies on gene associations among immune cells.

Adversarial robustness of machine learning models is critical to ensuring reliable performance under data perturbations. Recent progress has been on point estimators, and this paper considers distributional predictors. First, using the link between exponential families and Bregman divergences, we formulate an adversarial Bregman divergence loss as an adversarial negative log-likelihood. Using the geometric properties of Bregman divergences, we compute the adversarial perturbation for such models in closed-form. Second, under such losses, we introduce \emph{adversarially robust posteriors}, by exploiting the optimization-centric view of generalized Bayesian inference. Third, we derive the \emph{first} rigorous generalization certificates in the context of an adversarial extension of Bayesian linear regression by leveraging the PAC-Bayesian framework. Finally, experiments on real and synthetic datasets demonstrate the superior robustness of the derived adversarially robust posterior over Bayes posterior, and also validate our theoretical guarantees.

Conversational Product Search (CPS) is confined to simulated conversations due to the lack of real-world CPS datasets that reflect human-like language. Additionally, current conversational datasets are limited to support cross-market and multi-lingual usage. In this paper, we introduce a new CPS data collection protocol and present PSCon, a novel CPS dataset designed to assist product search via human-like conversations. The dataset is constructed using a coached human-to-human data collection protocol and supports two languages and dual markets. Also, the dataset enables thorough exploration of six subtasks of CPS: user intent detection, keyword extraction, system action prediction, question selection, item ranking, and response generation. Furthermore, we also offer an analysis of the dataset and propose a benchmark model on the proposed CPS dataset.

An important open question in AI is what simple and natural principle enables a machine to reason logically for meaningful abstraction with grounded symbols. This paper explores a conceptually new approach to combining probabilistic reasoning and predicative symbolic reasoning over data. We return to the era of reasoning with a full joint distribution before the advent of Bayesian networks. We then discuss that a full joint distribution over models of exponential size in propositional logic and of infinite size in predicate logic should be simply derived from a full joint distribution over data of linear size. We show that the same process is not only enough to generalise the logical consequence relation of predicate logic but also to provide a new perspective to rethink well-known limitations such as the undecidability of predicate logic, the symbol grounding problem and the principle of explosion. The reproducibility of this theoretical work is fully demonstrated by the included proofs.

In our increasingly interconnected world, Cyber-Physical Systems (CPS) play a crucial role in industries like healthcare, transportation, and manufacturing by combining physical processes with computing power. These systems, however, face many challenges, especially regarding security and system faults. Anomalies in CPS may indicate unexpected problems, from sensor malfunctions to cyber-attacks, and must be detected to prevent failures that can cause harm or disrupt services. This paper provides an overview of the different ways researchers have approached anomaly detection in CPS. We categorize and compare methods like machine learning, deep learning, mathematical models, invariant, and hybrid techniques. Our goal is to help readers understand the strengths and weaknesses of these methods and how they can be used to create safer, more reliable CPS. By identifying the gaps in current solutions, we aim to encourage future research that will make CPS more secure and adaptive in our increasingly automated world.

As machine learning-based prediction systems are increasingly used in high-stakes situations, it is important to understand how such predictive models will perform upon deployment. Distribution-free uncertainty quantification techniques such as conformal prediction provide guarantees about the loss black-box models will incur even when the details of the models are hidden. However, such methods are based on frequentist probability, which unduly limits their applicability. We revisit the central aspects of conformal prediction from a Bayesian perspective and thereby illuminate the shortcomings of frequentist guarantees. We propose a practical alternative based on Bayesian quadrature that provides interpretable guarantees and offers a richer representation of the likely range of losses to be observed at test time.

Inverse problems arise almost everywhere in science and engineering where we need to infer on a quantity from indirect observation. The cases of medical, biomedical, and industrial imaging systems are the typical examples. A very high overview of classification of the inverse problems method can be: i) Analytical, ii) Regularization, and iii) Bayesian inference methods. Even if there are straight links between them, we can say that the Bayesian inference based methods are the most powerful, as they give the possibility of accounting for prior knowledge and can account for errors and uncertainties in general. One of the main limitations stay in computational costs in particular for high dimensional imaging systems. Neural Networks (NN), and in particular Deep NNs (DNN), have been considered as a way to push farther this limit. Physics Informed Neural Networks (PINN) concept integrates physical laws with deep learning techniques to enhance the speed, accuracy and efficiency of the above mentioned problems. In this work, a new Bayesian framework for the concept of PINN (BPINN) is presented and discussed which includes the deterministic one if we use the Maximum A Posteriori (MAP) estimation framework. We consider two cases of supervised and unsupervised for training step, obtain the expressions of the posterior probability of the unknown variables, and deduce the posterior laws of the NN's parameters. We also discuss about the challenges of implementation of these methods in real applications.

Common sense suggests that when individuals explain why they believe something, we can arrive at more accurate conclusions than when they simply state what they believe. Yet, there is no known mechanism that provides incentives to elicit explanations for beliefs from agents. This likely stems from the fact that standard Bayesian models make assumptions (like conditional independence of signals) that preempt the need for explanations, in order to show efficient information aggregation. A natural justification for the value of explanations is that agents' beliefs tend to be drawn from overlapping sources of information, so agents' belief reports do not reveal all that needs to be known. Indeed, this work argues that rationales-explanations of an agent's private information-lead to more efficient aggregation by allowing agents to efficiently identify what information they share and what information is new. Building on this model of rationales, we present a novel 'deliberation mechanism' to elicit rationales from agents in which truthful reporting of beliefs and rationales is a perfect Bayesian equilibrium.

This project aims to compare various language classification procedures, procedures combining various Python language detection algorithms and metadata-based corpora extracted from manually-annotated articles sampled from the OpenAlex database. Following an analysis of precision and recall performance for each algorithm, corpus, and language as well as of processing speeds recorded for each algorithm and corpus type, overall procedure performance at the database level was simulated using probabilistic confusion matrices for each algorithm, corpus, and language as well as a probabilistic model of relative article language frequencies for the whole OpenAlex database. Results show that procedure performance strongly depends on the importance given to each of the measures implemented: for contexts where precision is preferred, using the LangID algorithm on the greedy corpus gives the best results; however, for all cases where recall is considered at least slightly more important than precision or as soon as processing times are given any kind of consideration, the procedure combining the FastSpell algorithm and the Titles corpus outperforms all other alternatives. Given the lack of truly multilingual, large-scale bibliographic databases, it is hoped that these results help confirm and foster the unparalleled potential of the OpenAlex database for cross-linguistic, bibliometric-based research and analysis.