Related papers: Convergence rates for smooth k-means change-point …
Practical implementations of Gaussian smoothing algorithms have received a great deal of attention in the last 60 years. However, almost all work focuses on estimating complete time series (''fixed-interval smoothing'', $\mathcal{O}(K)$…
We propose a new stochastic gradient method for optimizing the sum of a finite set of smooth functions, where the sum is strongly convex. While standard stochastic gradient methods converge at sublinear rates for this problem, the proposed…
We consider the problem of robust mean and location estimation w.r.t. any pseudo-norm of the form $x\in\mathbb{R}^d\to ||x||_S = \sup_{v\in S}<v,x>$ where $S$ is any symmetric subset of $\mathbb{R}^d$. We show that the deviation-optimal…
Given 2D point correspondences between an image pair, inferring the camera motion is a fundamental issue in the computer vision community. The existing works generally set out from the epipolar constraint and estimate the essential matrix,…
This paper develops change-point methods for the spectrum of a locally stationary time series. We focus on series with a bounded spectral density that change smoothly under the null hypothesis but exhibits change-points or becomes less…
In modern contexts, some types of data are observed in high-resolution, essentially continuously in time. Such data units are best described as taking values in a space of functions. Subject units carrying the observations may have…
We analyze online and mini-batch k-means variants. Both scale up the widely used Lloyd 's algorithm via stochastic approximation, and have become popular for large-scale clustering and unsupervised feature learning. We show, for the first…
In this article, we present the mathematical analysis of the convergence of the linearized Crank-Nicolson Galerkin method for a nonlinear Schrodinger problem related to a domain with a moving boundary. The convergence analysis of the…
We consider the problem of estimating a smooth functional of an unknown signal with discontinuity from Gaussian observations. The signal is a known function that depends on an unknown parameter. This problem is closely related to the famous…
This paper considers the problems of detecting a change point and estimating the location in the correlation matrices of a sequence of high-dimensional vectors, where the dimension is large enough to be comparable to the sample size or even…
Probabilistic smoothing is a standard tool for global optimization, but existing methods rely on Gaussian kernels and specific transforms, often resulting in strong hyperparameter sensitivity and limited robustness. We propose a general…
Change-points are a routine feature of 'big data' observed in the form of high-dimensional data streams. In many such data streams, the component series possess group structures and it is natural to assume that changes only occur in a small…
We introduce a robust and fully adaptive method for pointwise estimation in heteroscedastic regression. We allow for noise and design distributions that are unknown and fulfill very weak assumptions only. In particular, we do not impose…
We give an improved theoretical analysis of score-based generative modeling. Under a score estimate with small $L^2$ error (averaged across timesteps), we provide efficient convergence guarantees for any data distribution with second-order…
We present novel retrospective change point detection approach based on optimal transport and geometric discrepancy. The method does not require any parametric assumptions about distributions separated by change points. It can be used both…
We address the problem of detection and estimation of one or two change-points in the mean of a series of random variables. We use the formalism of set estimation in regression: To each point of a design is attached a binary label that…
It is common to model a deterministic response function, such as the output of a computer experiment, as a Gaussian process with a Mat\'ern covariance kernel. The smoothness parameter of a Mat\'ern kernel determines many important…
This paper addresses the problem of localizing change points in high-dimensional linear regression models with piecewise constant regression coefficients. We develop a dynamic programming approach to estimate the locations of the change…
We establish minimax optimal rates of convergence for estimation in a high dimensional additive model assuming that it is approximately sparse. Our results reveal an interesting phase transition behavior universal to this class of high…
We assume a nonparametric regression model where the signal is given by the sum of a piecewise constant function and a smooth function. To detect the change-points and estimate the regression functions, we propose PCpluS, a combination of…