Related papers: A Kernel Score Perspective on Forecast Disagreemen…
Causal inference analyses often use existing observational data, which in many cases has some clustering of individuals. In this paper we discuss propensity score weighting methods in a multilevel setting where within clusters individuals…
Most supervised machine learning tasks are subject to irreducible prediction errors. Probabilistic predictive models address this limitation by providing probability distributions that represent a belief over plausible targets, rather than…
We introduce a novel kernel-based framework for learning differential equations and their solution maps that is efficient in data requirements, in terms of solution examples and amount of measurements from each example, and computational…
In real word applications, data generating process for training a machine learning model often differs from what the model encounters in the test stage. Understanding how and whether machine learning models generalize under such…
Generative models, like large language models, are becoming increasingly relevant in our daily lives, yet a theoretical framework to assess their generalization behavior and uncertainty does not exist. Particularly, the problem of…
The use of tiered warnings and multicategorical forecasts are ubiquitous in meteorological operations. Here, a flexible family of scoring functions is presented for evaluating the performance of ordered multicategorical forecasts. Each…
Forecasts of various processes have always been a sophisticated problem for statistics and data science. Over the past decades the solution procedures were updated by deep learning and kernel methods. According to many specialists, these…
We provide a comprehensive examination of the predictive performance of panel forecasting methods based on individual, pooling, fixed effects, and empirical Bayes estimation, and propose optimal weights for forecast combination schemes. We…
Real-world data streams can change unpredictably due to distribution shifts, feedback loops and adversarial actors, which challenges the validity of forecasts. We present a forecasting framework ensuring valid uncertainty estimates…
In this paper, we propose a kernel principal component analysis model for multi-variate time series forecasting, where the training and prediction schemes are derived from the multi-view formulation of Restricted Kernel Machines. The…
This paper deals with the speed of convergence of the learning curve in a Gaussian process regression framework. The learning curve describes the average generalization error of the Gaussian process used for the regression. More…
Consistency, in a narrow sense, denotes the alignment between the forecast-optimization strategy and the verification directive. The current recommended deterministic solar forecast verification practice is to report the skill score based…
We prove the statistical consistency of kernel Partial Least Squares Regression applied to a bounded regression learning problem on a reproducing kernel Hilbert space. Partial Least Squares stands out of well-known classical approaches as…
We consider the problem of kernel classification. While worst-case bounds on the decay rate of the prediction error with the number of samples are known for some classifiers, they often fail to accurately describe the learning curves of…
We introduce a unified framework for random forest prediction error estimation based on a novel estimator of the conditional prediction error distribution function. Our framework enables simple plug-in estimation of key prediction…
Several researchers have experimentally shown that substantial improvements can be obtained in difficult pattern recognition problems by combining or integrating the outputs of multiple classifiers. This chapter provides an analytical…
The classical paradigm of scoring rules is to discriminate between two different forecasts by comparing them with observations. The probability distribution of the observed record is assumed to be perfect as a verification benchmark. In…
Distributed learning facilitates the scaling-up of data processing by distributing the computational burden over several nodes. Despite the vast interest in distributed learning, generalization performance of such approaches is not well…
This paper focuses on generalization performance analysis for distributed algorithms in the framework of learning theory. Taking distributed kernel ridge regression (DKRR) for example, we succeed in deriving its optimal learning rates in…
The importance of accurately quantifying forecast uncertainty has motivated much recent research on probabilistic forecasting. In particular, a variety of deep learning approaches has been proposed, with forecast distributions obtained as…