Related papers: Alpha-NML Universal Predictors

The Predictive Normalized Maximum Likelihood (pNML) scheme has been recently suggested for universal learning in the individual setting, where both the training and test samples are individual data. The goal of universal learning is to…

Large language models (LLMs) have recently gained much popularity due to their surprising ability at generating human-like English sentences. LLMs are essentially predictors, estimating the probability of a sequence of words given the past.…

A fundamental principle of learning theory is that there is a trade-off between the complexity of a prediction rule and its ability to generalize. Modern machine learning models do not obey this paradigm: They produce an accurate prediction…

In supervised batch learning, the predictive normalized maximum likelihood (pNML) has been proposed as the min-max regret solution for the distribution-free setting, where no distributional assumptions are made on the data. However, the…

We derive a conditional version of the classical regret-capacity theorem. This result can be used in universal prediction to find lower bounds on the minimal batch regret, which is a recently introduced generalization of the average regret,…

The normalized maximum likelihood (NML) is one of the most important distribution in coding theory and statistics. NML is the unique solution (if exists) to the pointwise minimax regret problem. However, NML is not defined even for simple…

Probabilistic classifiers are central for making informed decisions under uncertainty. Based on the maximum expected utility principle, optimal decision rules can be derived using the posterior class probabilities and misclassification…

Maximum regularized likelihood estimators (MRLEs) are arguably the most established class of estimators in high-dimensional statistics. In this paper, we derive guarantees for MRLEs in Kullback-Leibler divergence, a general measure of…

Many prediction tasks can admit multiple models that can perform almost equally well. This phenomenon can can undermine interpretability and safety when competing models assign conflicting predictions to individuals. In this work, we study…

Recently, much work has been done on extending the scope of online learning and incremental stochastic optimization algorithms. In this paper we contribute to this effort in two ways: First, based on a new regret decomposition and a…

Linear regression is a classical paradigm in statistics. A new look at it is provided via the lens of universal learning. In applying universal learning to linear regression the hypotheses class represents the label $y\in {\cal R}$ as a…

In this paper, we study adaptive online convex optimization, and aim to design a universal algorithm that achieves optimal regret bounds for multiple common types of loss functions. Existing universal methods are limited in the sense that…

Consider the nonparametric logistic regression problem. In the logistic regression, we usually consider the maximum likelihood estimator, and the excess risk is the expectation of the Kullback-Leibler (KL) divergence between the true and…

In linear regression, the least squares (LS) estimator has certain optimality properties if the errors are normally distributed. This assumption is often violated in practice, partly caused by data outliers. Robust estimators can cope with…

We consider model-based reinforcement learning in finite Markov De- cision Processes (MDPs), focussing on so-called optimistic strategies. In MDPs, optimism can be implemented by carrying out extended value it- erations under a constraint…

We consider a three-level meta-analysis of standardized mean differences. The standard method of estimation uses inverse-variance weights and REML/PL estimation of variance components for the random effects. We introduce new moment-based…

This paper revisits Deep Mutual Learning (DML), a simple yet effective computing paradigm. We propose using R\'{e}nyi divergence instead of the KL divergence, which is more flexible and tunable, to improve vanilla DML. This modification is…

The normalized maximized likelihood (NML) provides the minimax regret solution in universal data compression, gambling, and prediction, and it plays an essential role in the minimum description length (MDL) method of statistical modeling…

Machine learning models have exhibited exceptional results in various domains. The most prevalent approach for learning is the empirical risk minimizer (ERM), which adapts the model's weights to reduce the loss on a training set and…

Reinforcement learning from human feedback (RLHF) replaces hard-to-specify rewards with pairwise trajectory preferences, yet regret-oriented theory often assumes that preference labels are generated consistently from a single ground-truth…