Related papers: Diffusion index forecasts under weaker loadings: P…

Principal component analysis (PCA) is one of the most popular dimension reduction techniques in statistics and is especially powerful when a multivariate distribution is concentrated near a lower-dimensional subspace. Multivariate extreme…

Accurate production forecasts are essential to continue facilitating the integration of renewable energy sources into the power grid. This paper illustrates how to obtain probabilistic day-ahead forecasts of wind power generation via…

Principal component analysis (PCA) aims at estimating the direction of maximal variability of a high-dimensional dataset. A natural question is: does this task become easier, and estimation more accurate, when we exploit additional…

We present a novel class of projected methods, to perform statistical analysis on a data set of probability distributions on the real line, with the 2-Wasserstein metric. We focus in particular on Principal Component Analysis (PCA) and…

Machine learning methods have been shown to be effective for weather forecasting, based on the speed and accuracy compared to traditional numerical models. While early efforts primarily concentrated on deterministic predictions, the field…

Principal Component Analysis (PCA) is a very successful dimensionality reduction technique, widely used in predictive modeling. A key factor in its widespread use in this domain is the fact that the projection of a dataset onto its first…

We propose Diffusion-Informed Model Predictive Control (D-I MPC), a generic framework for uncertainty-aware prediction and decision-making in partially observable stochastic systems by integrating diffusion-based time series forecasting…

Conformal prediction is a method of producing prediction sets that can be applied on top of a wide range of prediction algorithms. The method has a guaranteed coverage probability under the standard IID assumption regardless of whether the…

We use a decision-theoretic framework to study the problem of forecasting discrete outcomes when the forecaster is unable to discriminate among a set of plausible forecast distributions because of partial identification or concerns about…

Probabilistic Time Series Forecasting (PTSF) plays a critical role in domains requiring accurate and uncertainty-aware predictions for decision-making. However, existing methods offer suboptimal distribution modeling and suffer from a…

We propose LOCO, an algorithm for large-scale ridge regression which distributes the features across workers on a cluster. Important dependencies between variables are preserved using structured random projections which are cheap to compute…

Diffusion models have become popular for policy learning in robotics due to their ability to capture high-dimensional and multimodal distributions. However, diffusion policies are stochastic and typically trained offline, limiting their…

This study aims to improve the spatial representation of uncertainties when regressing surface wind speeds from large-scale atmospheric predictors for sub-seasonal forecasting. Sub-seasonal forecasting often relies on large-scale…

While shrinkage is essential in high-dimensional settings, its use for low-dimensional regression-based prediction has been debated. It reduces variance, often leading to improved prediction accuracy. However, it also inevitably introduces…

The estimation of the diffusion matrix $\Sigma$ of a high-dimensional, possibly time-changed L\'evy process is studied, based on discrete observations of the process with a fixed distance. A low-rank condition is imposed on $\Sigma$.…

Short term load forecasting has an essential medium for the reliable, economical and efficient operation of the power system. Most of the existing forecasting approaches utilize fixed statistical models with large historical data for…

Recently, diffusion models have gained popularity due to their impressive generative abilities. These models learn the implicit distribution given by the training dataset, and sample new data by transforming random noise through the reverse…

In our previous work, a reduced order model (ROM) for a stochastic system was made, where noisy data was projected onto principal component analysis (PCA)-derived basis vectors to obtain an accurate reconstruction of the noise-free data.…

We study the estimation of a high dimensional approximate factor model in the presence of both cross sectional dependence and heteroskedasticity. The classical method of principal components analysis (PCA) does not efficiently estimate the…

Conformal prediction provides rigorous distribution-free finite-sample guarantees for marginal coverage under the assumption of exchangeability, but may exhibit systematic undercoverage or overcoverage for specific subpopulations. Assessing…