Related papers: Calibrated Forecasts: The Minimax Proof

Conformal prediction is a powerful post-hoc framework for uncertainty quantification that provides distribution-free coverage guarantees. However, these guarantees crucially rely on the assumption of exchangeability. This assumption is…

Probability predictions from binary regressions or machine learning methods ought to be calibrated: If an event is predicted to occur with probability $x$, it should materialize with approximately that frequency, which means that the…

To be considered reliable, a model must be calibrated so that its confidence in each decision closely reflects its true outcome. In this blogpost we'll take a look at the most commonly used definition for calibration and then dive into a…

Among the most relevant processes in the Earth system for human habitability are quasi-periodic, ocean-driven multi-year events whose dynamics are currently incompletely characterized by physical models, and hence poorly predictable. This…

When climate forecasts are highly uncertain, the optimal mean squared error strategy is to ignore them. When climate forecasts are highly certain, the optimal mean squared error strategy is to use them as is. In between these two extremes…

This note uses a simple example to show how moment inequality models used in the empirical economics literature lead to general minimax relative efficiency comparisons. The main point is that such models involve inference on a low…

Consider a multi-class labelling problem, where the labels can take values in $[k]$, and a predictor predicts a distribution over the labels. In this work, we study the following foundational question: Are there notions of multi-class…

In safety-critical applications data-driven models must not only be accurate but also provide reliable uncertainty estimates. This property, commonly referred to as calibration, is essential for risk-aware decision-making. In regression a…

We show that the existence of a computationally efficient calibration algorithm, with a low weak calibration rate, would imply the existence of an efficient algorithm for computing approximate Nash equilibria - thus implying the unlikely…

In many applications, accurate class probability estimates are required, but many types of models produce poor quality probability estimates despite achieving acceptable classification accuracy. Even though probability calibration has been…

In this paper, we first provide a simple variational proof of the existence of Nash equilibrium in Hilbert spaces by using optimality conditions in convex minimization and Schauder's fixed-point theorem. Then applications of convex analysis…

We introduce a simple but general online learning framework in which a learner plays against an adversary in a vector-valued game that changes every round. Even though the learner's objective is not convex-concave (and so the minimax…

Forecast reconciliation, an ex-post technique applied to forecasts that must satisfy constraints, has been a prominent topic in the forecasting literature over the past two decades. Recently, several efforts have sought to extend…

The main purpose of this article is to prove that, under certain assumptions in a linear prediction setting, optimal methods based upon model reduction and even an optimal predictor can be provided. The optimality is formulated in terms of…

Hypothesis tests and confidence intervals are ubiquitous in empirical research, yet their connection to subsequent decision-making is often unclear. We develop a theory of certified decisions that pairs recommended decisions with…

We study the problem of making calibrated probabilistic forecasts for a binary sequence generated by an adversarial nature. Following the seminal paper of Foster and Vohra (1998), nature is often modeled as an adaptive adversary who sees…

The distance from calibration, introduced by B{\l}asiok, Gopalan, Hu, and Nakkiran (STOC 2023), has recently emerged as a central measure of miscalibration for probabilistic predictors. We study the fundamental problems of computing and…

For statistical decision problems with finite parameter space, it is well-known that the upper value (minimax value) agrees with the lower value (maximin value). Only under a generalized notion of prior does such an equivalence carry over…

Coherent lower previsions are general probabilistic models allowing incompletely specified probability distributions. However, for complete description of a coherent lower prevision -- even on finite underlying sample spaces -- an infinite…

We provide the theoretical foundation for the recent tests of equal forecast accuracy and encompassing by Pitarakis (2023) and Pitarakis (2025), when the competing forecast specification is that of a factor-augmented regression model. This…