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Over the past few years, insights from computer science, statistical physics, and information theory have revealed phase transitions in a wide array of high-dimensional statistical problems at two distinct thresholds: One is the…
The bottleneck in the quantitative analysis of Markov chains and Markov decision processes against specifications given in LTL or as some form of nondeterministic B\"uchi automata is the inclusion of a determinisation step of the automaton…
Motivated by the success of bounded model checking framework for finite state machines, Ouaknine and Worrell proposed a time-bounded theory of real-time verification by claiming that restriction to bounded-time recovers decidability for…
Mathematical modelling allows us to concisely describe fundamental principles in biology. Analysis of models can help to both explain known phenomena, and predict the existence of new, unseen behaviours. Model analysis is often a complex…
In scientific inference problems, the underlying statistical modeling assumptions have a crucial impact on the end results. There exist, however, only a few automatic means for validating these fundamental modelling assumptions. The…
Statistics is sometimes described as the science of reasoning under uncertainty. Statistical models provide one view of this uncertainty, but what is frequently neglected is the 'invisible' portion of uncertainty: that assumed not to exist…
To solve a real-world problem, the modeler usually needs to make a trade-off between model complexity and usefulness. This is also true for robust optimization, where a wide range of models for uncertainty, so-called uncertainty sets, have…
In this paper we consider a fragment of the first-order theory of the real numbers that includes systems of equations of continuous functions in bounded domains, and for which all functions are computable in the sense that it is possible to…
We describe a general technique that yields the first {\em Statistical Query lower bounds} for a range of fundamental high-dimensional learning problems involving Gaussian distributions. Our main results are for the problems of (1) learning…
Many embedded and real-time systems have a inherent probabilistic behaviour (sensors data, unreliable hardware,...). In that context, it is crucial to evaluate system properties such as "the probability that a particular hardware fails".…
Recently there has been a great attention from the scientific community towards the use of the model-checking technique as a tool for test generation in the simulation field. This paper aims to provide a useful mean to get more insights…
In survival analysis, estimating the fraction of 'immune' or 'cured' subjects who will never experience the event of interest, requires a sufficiently long follow-up period. A few statistical tests have been proposed to test the assumption…
In a seminal paper from 1985, Sistla and Clarke showed that the model-checking problem for Linear Temporal Logic (LTL) is either NP-complete or PSPACE-complete, depending on the set of temporal operators used. If, in contrast, the set of…
Low-rank matrix completion concerns the problem of estimating unobserved entries in a matrix using a sparse set of observed entries. We consider the non-uniform setting where the observed entries are sampled with highly varying…
Concolic testing is a popular dynamic validation technique that can be used for both model checking and automatic test case generation. We have recently introduced concolic testing in the context of logic programming. In contrast to…
This paper is concerned with the sample efficiency of reinforcement learning, assuming access to a generative model (or simulator). We first consider $\gamma$-discounted infinite-horizon Markov decision processes (MDPs) with state space…
Fluid models are a popular formalism in the quantitative modeling of biochemical systems and analytical performance models. The main idea is to approximate a large-scale Markov chain by a compact set of ordinary differential equations…
Boolean satisfiability ({\SAT}) has played a key role in diverse areas spanning testing, formal verification, planning, optimization, inferencing and the like. Apart from the classical problem of checking boolean satisfiability, the…
According to recent results, convergence in a prespecified or prescribed finite time can be achieved under extreme model uncertainty if control is applied continuously over time. This paper shows that this extreme amount of uncertainty…
Accurately quantifying a large language model's (LLM) predictive uncertainty is crucial for judging the reliability of its answers. While most existing research focuses on short, directly answerable questions with closed-form outputs (e.g.,…