Related papers: Exact Stiefel Optimization for Probabilistic PLS: …
Reliable uncertainty estimation is critical for deploying neural networks (NNs) in real-world applications. While existing calibration techniques often rely on post-hoc adjustments or coarse-grained binning methods, they remain limited in…
We develop efficient algorithms for optimizing piecewise smooth (PWS) functions where the underlying partition of the domain into smooth pieces is \emph{unknown}. For PWS functions satisfying a quadratic growth (QG) condition, we propose a…
Overparameterization in deep learning is powerful: Very large models fit the training data perfectly and yet often generalize well. This realization brought back the study of linear models for regression, including ordinary least squares…
Ensuring that predicted probabilities align with observed frequencies is critical in high-stakes domains such as clinical decision support, autonomous driving and financial risk assessment. Existing calibration methods typically apply a…
Linear fixed point equations in Hilbert spaces arise in a variety of settings, including reinforcement learning, and computational methods for solving differential and integral equations. We study methods that use a collection of random…
Partial label learning (PLL) is a typical weakly supervised learning problem in which each instance is associated with a candidate label set, and among which only one is true. However, the assumption that the ground-truth label is always…
We consider a finite volume scheme with two-point flux approximation (TPFA) to approximate a Laplace problem when the solution exhibits no more regularity than belonging to $H^1_0(\Omega)$. We establish in this case some error bounds for…
Large sectors of the recent optimization literature focused in the last decade on the development of optimal stochastic first order schemes for constrained convex models under progressively relaxed assumptions. Stochastic proximal point is…
We study the problem of deriving compressibility measures for Piecewise Linear Approximations (PLAs), i.e., error-bounded approximations of a set of two-dimensional increasing data points using a sequence of segments. Such approximations…
This paper addresses the observability analysis and the optimal design of observation parameters in the presence of noisy measurements and parametric uncertainties. The main underlying frameworks are the nonlinear constrained moving horizon…
Machine learning can significantly improve performance for decision-making under uncertainty across a wide range of domains. However, ensuring robustness guarantees requires well-calibrated uncertainty estimates, which can be difficult to…
We consider the use of Gaussian Processes (GPs) or Neural Networks (NNs) to numerically approximate the solutions to nonlinear partial differential equations (PDEs) with rough forcing or source terms, which commonly arise as pathwise…
Piecewise Linear-Quadratic (PLQ) penalties are widely used to develop models in statistical inference, signal processing, and machine learning. Common examples of PLQ penalties include least squares, Huber, Vapnik, 1-norm, and their…
Low rank tensor completion is a highly ill-posed inverse problem, particularly when the data model is not accurate, and some sort of regularization is required in order to solve it. In this article we focus on the calibration of the data…
The autocovariance least squares (ALS) method is a computationally efficient approach for estimating noise covariances in Kalman filters without requiring specific noise models. However, conventional ALS and its variants rely on the classic…
This study presents a generalised least squares based method for fitting polygons and ellipses to data points. The method is based on a trigonometric fitness function that approximates a unit shape accurately, making it applicable to…
This paper presents a linear least squares method for fiber-longitudinal power profile estimation (PPE), which estimates an optical signal power distribution throughout a fiber-optic link at a coherent receiver. The method finds the global…
As computational machines become larger and more complex, the probability of hardware failure rises. ``Silent errors'', or bit flips, may not be immediately apparent but can cause detrimental effects to algorithm behavior. In this work, we…
Linear Least Squares is a very well known technique for parameter estimation, which is used even when sub-optimal, because of its very low computational requirements and the fact that exact knowledge of the noise statistics is not required.…
We introduce a probabilistic approach to the LMS filter. By means of an efficient approximation, this approach provides an adaptable step-size LMS algorithm together with a measure of uncertainty about the estimation. In addition, the…