Related papers: Game-theoretic statistics and safe anytime-valid i…
Statistical hypothesis tests typically use prespecified sample sizes, yet data often arrive sequentially. Interim analyses invalidate classical error guarantees, while existing sequential methods require rigid testing preschedules or incur…
Shafer (2021) offers a betting perspective on statistical testing which may be useful for foundational debates, given that disputes over such testing continue to be intense. To be helpful for researchers, however, this perspective will need…
We consider a variant of continuous-state partially-observable stochastic games with neural perception mechanisms and an asymmetric information structure. One agent has partial information, with the observation function implemented as a…
Explainable artificial intelligence (XAI) is essential for trustworthy machine learning (ML), particularly in high-stakes domains such as healthcare and finance. Shapley value (SV) methods provide a principled framework for feature…
We propose a sequential, anytime-valid method to test the conditional independence of a response $Y$ and a predictor $X$ given a random vector $Z$. The proposed test is based on e-statistics and test martingales, which generalize likelihood…
Automated verification techniques for stochastic games allow formal reasoning about systems that feature competitive or collaborative behaviour among rational agents in uncertain or probabilistic settings. Existing tools and techniques…
We consider the general model of zero-sum repeated games (or stochastic games with signals), and assume that one of the players is fully informed and controls the transitions of the state variable. We prove the existence of the uniform…
Algorithmic analysis of Markov decision processes (MDP) and stochastic games (SG) in practice relies on value-iteration (VI) algorithms. Since basic VI does not provide guarantees on the precision of the result, variants of VI have been…
While value iteration (VI) is a standard solution approach to simple stochastic games (SSGs), it suffered from the lack of a stopping criterion. Recently, several solutions have appeared, among them also "optimistic" VI (OVI). However, OVI…
We use martingale and stochastic analysis techniques to study a continuous-time optimal stopping problem, in which the decision maker uses a dynamic convex risk measure to evaluate future rewards. We also find a saddle point for an…
We analyze safety problems of complex systems using the methods of mathematical statistics for testing the output variables of a code simulating the operation of the system under consideration when the input variables are uncertain. We have…
Technology has had an unquestionable impact on the way people watch sports. Along with this technological evolution has come a higher standard to ensure a good viewing experience for the casual sports fan. It can be argued that the…
For zero-sum two-player continuous-time games with integral payoff and incomplete information on one side, one shows that the optimal strategy of the informed player can be computed through an auxiliary optimization problem over some…
This position paper argues for two claims regarding AI testing and evaluation. First, to remain informative about deployment behaviour, evaluations need account for the possibility that AI systems understand their circumstances and reason…
Mean field games are studied in the framework of controlled martingale problems, and general existence theorems are proven in which the equilibrium control is Markovian. The framework is flexible enough to include degenerate volatility,…
Algorithmic analysis of Markov decision processes (MDP) and stochastic games (SG) in practice relies on value-iteration (VI) algorithms. Since the basic version of VI does not provide guarantees on the precision of the result, variants of…
Semi-implicit variational inference (SIVI) greatly enriches the expressiveness of variational families by considering implicit variational distributions defined in a hierarchical manner. However, due to the intractable densities of…
A nonnegative martingale with initial value equal to one measures evidence against a probabilistic hypothesis. The inverse of its value at some stopping time can be interpreted as a Bayes factor. If we exaggerate the evidence by considering…
Continuous-time assessments of game outcomes in sports have become increasingly common in the last decade. In American football, only discrete-time estimates of play value were possible, since the most advanced public football datasets were…
Reproducibility is imperative for any scientific discovery. More often than not, modern scientific findings rely on statistical analysis of high-dimensional data. At a minimum, reproducibility manifests itself in stability of statistical…