Related papers: Detecting changes in slope with an $L_0$ penalty

Birg{\'e} and Massart proposed in 2001 the slope heuristics as a way to choose optimally from data an unknown multiplicative constant in front of a penalty. It is built upon the notion of minimal penalty, and it has been generalized since…

In practical applications, machine learning algorithms are often needed to learn classifiers that optimize domain specific performance measures. Previously, the research has focused on learning the needed classifier in isolation, yet…

Identifying changes in the generative process of sequential data, known as changepoint detection, has become an increasingly important topic for a wide variety of fields. A recently developed approach, which we call EXact Online Bayesian…

We propose a Multi-step Screening Procedure (MSP) for the recovery of sparse linear models in high-dimensional data. This method is based on a repeated small penalty strategy that quickly converges to an estimate within a few iterations.…

Changepoint detection is the problem of finding abrupt or gradual changes in time series data when the distribution of the time series changes significantly. There are many sophisticated statistical algorithms for solving changepoint…

We consider the 0-1 Penalized Knapsack Problem (PKP). Each item has a profit, a weight and a penalty and the goal is to maximize the sum of the profits minus the greatest penalty value of the items included in a solution. We propose an…

Data selection has emerged as a core issue for large-scale visual-language model pretaining (e.g., CLIP), particularly with noisy web-curated datasets. Three main data selection approaches are: (1) leveraging external non-CLIP models to aid…

A new statistical procedure, based on a modified spline basis, is proposed to identify the linear components in the panel data model with fixed effects. Under some mild assumptions, the proposed procedure is shown to consistently estimate…

We consider the quickest change detection problem where both the parameters of pre- and post- change distributions are unknown, which prevents the use of classical simple hypothesis testing. Without additional assumptions, optimal solutions…

We construct an efficient numerical scheme for solving obstacle problems in divergence form. The numerical method is based on a reformulation of the obstacle in terms of an L1-like penalty on the variational problem. The reformulation is an…

The problem of univariate mean change point detection and localization based on a sequence of $n$ independent observations with piecewise constant means has been intensively studied for more than half century, and serves as a blueprint for…

We propose a new class of sequential change point tests, both for changes in the mean parameter and in the overall distribution function. The methodology builds on a two-window inspection scheme (TWIN), which aggregates data into symmetric…

In this work we are interested in the construction of numerical methods for high dimensional constrained nonlinear optimization problems by particle-based gradient-free techniques. A consensus-based optimization (CBO) approach combined with…

We consider the nonlinear optimization problem with least $\ell_1$-norm measure of constraint violations and introduce the concepts of the D-stationary point, the DL-stationary point and the DZ-stationary point with the help of exact…

Predicting the long-term behavior of chaotic systems remains a formidable challenge due to their extreme sensitivity to initial conditions and the inherent limitations of traditional data-driven modeling approaches. This paper introduces a…

Equations governing the nonlinear dynamics of complex systems are usually unknown and indirect methods are used to reconstruct their manifolds. In turn, they depend on embedding parameters requiring other methods and long temporal sequences…

Conformal prediction (CP) is an important tool for distribution-free predictive uncertainty quantification. Yet, a major challenge is to balance computational efficiency and prediction accuracy, particularly for multiple predictions. We…

In high-dimensional time series, the component processes are often assembled into a matrix to display their interrelationship. We focus on detecting mean shifts with unknown change point locations in these matrix time series. Series that…

In many change point problems it is reasonable to assume that compared to a benchmark at a given time point $t_0$ the properties of the observed stochastic process change gradually over time for $t >t_0$. Often, these gradual changes are…

Sorted L-One Penalized Estimation is a relatively new convex optimization procedure which allows for adaptive selection of regressors under sparse high dimensional designs. Here we extend the idea of SLOPE to deal with the situation when…