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We develop a novel Empirical Bayes methodology for prediction under check loss in high-dimensional Gaussian models. The check loss is a piecewise linear loss function having differential weights for measuring the amount of underestimation…

Causal machine-learning is about predicting the net-effect (true-lift) of treatments. Given the data of a treatment group and a control group, it is similar to a standard supervised-learning problem. Unfortunately, there is no similarly…

In many real-world prediction tasks, class labels contain information about the relative order between labels that are not captured by commonly used loss functions such as multicategory cross-entropy. Recently, the preference for unimodal…

It is becoming increasingly common in regression to train neural networks that model the entire distribution even if only the mean is required for prediction. This additional modeling often comes with performance gain and the reasons behind…

Model-based geostatistical design involves the selection of locations to collect data to minimise an expected loss function over a set of all possible locations. The loss function is specified to reflect the aim of data collection, which,…

Neural network emulators have become an invaluable tool for a wide variety of climate and weather prediction tasks. While showing incredibly promising results, these networks do not have an inherent ability to produce equitable predictions.…

Diffusion models have emerged as powerful generative models, inspiring extensive research into their underlying mechanisms. One of the key questions in this area is the loss functions these models shall train with. Multiple formulations…

In many areas of engineering and sciences, decision rules and control strategies are usually designed based on nominal values of relevant system parameters. To ensure that a control strategy or decision rule will work properly when the…

Many forecasts consist not of point predictions but concern the evolution of quantities. For example, a central bank might predict the interest rates during the next quarter, an epidemiologist might predict trajectories of infection rates,…

We derive a family of loss functions to train models in the presence of sampling bias. Examples are when the prevalence of a pathology differs from its sampling rate in the training dataset, or when a machine learning practioner rebalances…

In this article we develop a general theory of exact parametric penalty functions for constrained optimization problems. The main advantage of the method of parametric penalty functions is the fact that a parametric penalty function can be…

Asymmetric statistical errors arise for experimental results obtained by Maximum Likelihood estimation, in cases where the number of results is finite and the log likelihood function is not a symmetric parabola. This note discusses how…

We study a multi-agent decision problem in population games, where agents select from multiple available strategies and continually revise their selections based on the payoffs associated with these strategies. Unlike conventional…

This paper presents a comprehensive review of loss functions and performance metrics in deep learning, highlighting key developments and practical insights across diverse application areas. We begin by outlining fundamental considerations…

Recent work introduced loss functions which measure the error of a prediction based on multiple simultaneous observations or outcomes. In this paper, we explore the theoretical and practical questions that arise when using such…

The earth system is exceedingly complex and often chaotic in nature, making prediction incredibly challenging: we cannot expect to make perfect predictions all of the time. Instead, we look for specific states of the system that lead to…

In a sequential regression setting, a decision-maker may be primarily concerned with whether the future observation will increase or decrease compared to the current one, rather than the actual value of the future observation. In this…

Robustness, domain adaptation, photometric/occlusion invariance, sensor drift, and alignment style are treated as separate literatures with separate method families. Under label-preserving deployment shift they share one geometric object:…

We introduce a sharpness functional for probabilistic models that quantifies sharpness as an intrinsic property of the probability distribution. The measure is derived based on a rank-based concentration principle that tracks upward…

Computing the similarity between two probability distributions is a recurring theme across control. We introduce a unified family of distances between the probability distributions of two random variables that is based on the discrepancy…