Related papers: Error Bounds for Piecewise Smooth and Switching Re…
Distributional regression aims at estimating the conditional distribution of a targetvariable given explanatory co-variates. It is a crucial tool for forecasting whena precise uncertainty quantification is required. A popular methodology…
Online model predictive control (MPC) for piecewise affine (PWA) systems requires the online solution to an optimization problem that implicitly optimizes over the switching sequence of PWA regions, for which the computational burden can be…
When concept shifts and sample scarcity are present in the target domain of interest, nonparametric regression learners often struggle to generalize effectively. The technique of transfer learning remedies these issues by leveraging data or…
Performative prediction, as introduced by Perdomo et al, is a framework for studying social prediction in which the data distribution itself changes in response to the deployment of a model. Existing work in this field usually hinges on…
The spatial linear mixed model (SLMM) consists of fixed and spatial random effects that may be linearly dependent. Partially motivated as a means to address potential issues with confounding, the Restricted spatial regression (RSR) model…
Over the last decade, a series of applied mathematics papers have explored a type of inverse problem--called by a variety of names including "inverse sensitivity", "pushforward based inference", "consistent Bayesian inference", or…
When using stochastic gradient descent to solve large-scale machine learning problems, a common practice of data processing is to shuffle the training data, partition the data across multiple machines if needed, and then perform several…
Given a robust model trained to be resilient to one or multiple types of distribution shifts (e.g., natural image corruptions), how is that "robustness" encoded in the model weights, and how easily can it be disentangled and/or "zero-shot"…
Supremum norm loss is intuitively more meaningful to quantify function estimation error in statistics. In the context of multivariate nonparametric regression with unknown error, we propose a Bayesian procedure based on spike-and-slab prior…
This paper describes the RRMSE (Relative Root Mean Square Error) based weights to weight the occurrences of predictive values before averaging for the ensemble voting regression. The core idea behind ensemble regression is to combine…
To detect changes in the mean of a time series, one may use previsible detection procedures based on nonparametric kernel prediction smoothers which cover various classic detection statistics as special cases. Bandwidth selection,…
We study the foundations of variational inference, which frames posterior inference as an optimisation problem, for probabilistic programming. The dominant approach for optimisation in practice is stochastic gradient descent. In particular,…
A key problem in deep learning and computational neuroscience is relating the geometrical properties of neural representations to task performance. Here, we consider this problem for continuous decoding tasks where neural variability may…
Optimization in the presence of sharp (non-Lipschitz), unpredictable (w.r.t. time and amount) changes is a challenging and largely unexplored problem of great significance. We consider the class of piecewise Lipschitz functions, which is…
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…
Realistic physical phenomena exhibit random fluctuations across many scales in the input and output processes. Models of these phenomena require stochastic PDEs. For three-dimensional coupled (vector-valued) stochastic PDEs (SPDEs), for…
Identifying breakpoints in piecewise regression is critical in enhancing the reliability and interpretability of data fitting. In this paper, we propose novel algorithms based on the greedy algorithm to accurately and efficiently identify…
This work proposes a Bayesian rule based on the mixture of a point mass function at zero and the logistic distribution to perform wavelet shrinkage in nonparametric regression models with stationary errors (with short or long-memory…
This study examines the optimal selections of bandwidth and semi-metric for a functional partial linear model. Our proposed method begins by estimating the unknown error density using a kernel density estimator of residuals, where the…
Almost sure bounds are established on the uniform error of smoothing spline estimators in nonparametric regression with random designs. Some results of Einmahl and Mason (2005) are used to derive uniform error bounds for the approximation…