Recent language models generate false but plausible-sounding text with surprising
frequency. Such “hallucinations” are an obstacle to the usability of language-based AI …

Decision-making in the face of uncertainty is a significant challenge in machine learning,
and the multi-armed bandit model is a commonly used framework to address it. This …

Concentration inequalities have been the subject of exciting developments during the last
two decades, and have been intensively studied and used as a powerful tool in various …

We explore uncertainty quantification in large language models (LLMs), with the goal to
identify when uncertainty in responses given a query is large. We simultaneously consider …

We obtain the optimal proxy variance for the sub-Gaussianity of Beta distribution, thus
proving upper bounds recently conjectured by Elder (2016). We provide different proof …

We show that a recently proposed 1-nearest-neighbor-based multiclass learning algorithm
is universally strongly Bayes consistent in all metric spaces where such Bayes consistency …

The upper confidence reinforcement learning (UCRL2) algorithm introduced in\citep
{jaksch2010near} is a popular method to perform regret minimization in unknown discrete …

An infinite urn scheme is defined by a probability mass function (p_j)_j\geq1 over positive
integers. A random allocation consists of a sample of N independent drawings according to …

We study concentration inequalities for the Kullback–Leibler (KL) divergence between the
empirical distribution and the true distribution. Applying a recursion technique, we improve …

In Bayesian nonparametric models, Gaussian processes provide a popular prior choice for
regression function estimation. Existing literature on the theoretical investigation of the …