It enjoys model-free coverage guarantee regardless of the underlying distribution of the data.

Trustworthiness of generative language models (GLMs) is crucial in their deployment to critical decision making systems.

Methods for probability updating, of which Bayesian conditionalization is the most well-known and widely used, are modeling tools that aim to represent the process of modifying an initial epistemic state, typically represented by a prior probability function P, which is adjusted in light of new information. Notably, updating methods and conditional sentences seem to intuitively share a deep connection, as is evident in the case of conditionalization. The present work contributes to this line of research and aims at shedding new light on the relationship between updating methods and conditional connectives. Departing from previous literature that often focused on a specific type of conditional or a particular updating method, our goal is to prove general results concerning the connection between conditionals and their probabilities. This will allow us to characterize the probabilities of certain conditional connectives and to understand what class of updating procedures can be represented using specific conditional connectives. Broadly, we adopt a general perspective that encompasses a large class of conditionals and a wide range of updating methods, enabling us to prove some general results concerning their interrelation.

It enjoys model-free coverage guarantee regardless of the underlying distribution of the data.

Trustworthiness of generative language models (GLMs) is crucial in their deployment to critical decision making systems.

This paper uses category theory to develop an entirely new approach to approximate game theory. Game theory is the study of how different agents within a multi-agent system take decisions. At its core, game theory asks what an optimal decision is in a given scenario. Thus approximate game theory asks what is an approximately optimal decision in a given scenario. This is important in practice as -- just like in much of computing -- exact answers maybe too difficult to compute or even impossible to compute given inherent uncertainty in input. We consider first "Selection Functions" which are functions and develop a simple yet robust model of approximate equilibria. We develop the algebraic properties of approximation wrt selection functions and also relate approximation to the compositional structure of selection functions. We then repeat this process successfully for Open Games -- a more advanced model of game theory.

The stability rule for belief, advocated by Leitgeb [Annals of Pure and Applied Logic 164, 2013], is a rule for rational acceptance that captures categorical belief in terms of $\textit{probabilistically stable propositions}$: propositions to which the agent assigns resiliently high credence. The stability rule generates a class of $\textit{probabilistically stable belief revision}$ operators, which capture the dynamics of belief that result from an agent updating their credences through Bayesian conditioning while complying with the stability rule for their all-or-nothing beliefs. In this paper, we prove a representation theorem that yields a complete characterisation of such probabilistically stable revision operators and provides a `qualitative' selection function semantics for the (non-monotonic) logic of probabilistically stable belief revision. Drawing on the theory of comparative probability orders, this result gives necessary and sufficient conditions for a selection function to be representable as a strongest-stable-set operator on a finite probability space. The resulting logic of probabilistically stable belief revision exhibits strong monotonicity properties while failing the AGM belief revision postulates and satisfying only very weak forms of case reasoning. In showing the main theorem, we prove two results of independent interest to the theory of comparative probability: the first provides necessary and sufficient conditions for the joint representation of a pair of (respectively, strict and non-strict) comparative probability orders. The second result provides a method for axiomatising the logic of ratio comparisons of the form ``event $A$ is at least $k$ times more likely than event $B$''. In addition to these measurement-theoretic applications, we point out two applications of our main result to the theory of simple voting games and to revealed preference theory.

The focus of this study is to evaluate the effectiveness of Machine Learning (ML) methods for two-sample testing with right-censored observations. To achieve this, we develop several ML-based methods with varying architectures and implement them as two-sample tests. Each method is an ensemble (stacking) that combines predictions from classical two-sample tests. This paper presents the results of training the proposed ML methods, examines their statistical power compared to classical two-sample tests, analyzes the distribution of test statistics for the proposed methods when the null hypothesis is true, and evaluates the significance of the features incorporated into the proposed methods. All results from numerical experiments were obtained from a synthetic dataset generated using the Smirnov transform (Inverse Transform Sampling) and replicated multiple times through Monte Carlo simulation. To test the two-sample problem with right-censored observations, one can use the proposed two-sample methods. All necessary materials (source code, example scripts, dataset, and samples) are available on GitHub and Hugging Face.

Social media has emerged as a cornerstone of social movements, wielding significant influence in driving societal change. Simulating the response of the public and forecasting the potential impact has become increasingly important. However, existing methods for simulating such phenomena encounter challenges concerning their efficacy and efficiency in capturing the behaviors of social movement participants. In this paper, we introduce a hybrid framework HiSim for social media user simulation, wherein users are categorized into two types. Core users are driven by Large Language Models, while numerous ordinary users are modeled by deductive agent-based models. We further construct a Twitter-like environment to replicate their response dynamics following trigger events. Subsequently, we develop a multi-faceted benchmark SoMoSiMu-Bench for evaluation and conduct comprehensive experiments across real-world datasets. Experimental results demonstrate the effectiveness and flexibility of our method.

Image classifiers should be used with caution in the real world. Performance evaluated on a validation set may not reflect performance in the real world. In particular, classifiers may perform well for conditions that are frequently encountered during training, but poorly for other infrequent conditions. In this study, we hypothesize that recent advances in text-to-image generative models make them valuable for benchmarking computer vision models such as image classifiers: they can generate images conditioned by textual prompts that cause classifier failures, allowing failure conditions to be described with textual attributes. However, their generation cost becomes an issue when a large number of synthetic images need to be generated, which is the case when many different attribute combinations need to be tested. We propose an image classifier benchmarking method as an iterative process that alternates image generation, classifier evaluation, and attribute selection. This method efficiently explores the attributes that ultimately lead to poor behavior detection.