Related papers: Stationary Point Constrained Inference via Diffeom…
The inability to guarantee robustness is one of the major obstacles to the application of deep learning models in security-demanding domains. We identify that the most commonly used cross-entropy (CE) loss does not guarantee robust boundary…
The segmentation of data into stationary stretches also known as multiple change point problem is important for many applications in time series analysis as well as signal processing. Based on strong invariance principles, we analyse data…
We consider a non-proportional hazards model where the regression coefficient is not constant but piecewise constant. Following Andersen and Gill (1982), we know that a knowledge of the changepoint leads to a relatively straightforward…
In this work, we consider a multivariate regression model with one-sided errors. We assume for the regression function to lie in a general H\"{o}lder class and estimate it via a nonparametric local polynomial approach that consists of…
In the context of nonparametric regression models with one-sided errors, we consider parametric transformations of the response variable in order to obtain independence between the errors and the covariates. We focus in this paper on…
We prove lower bounds on the complexity of finding $\epsilon$-stationary points (points $x$ such that $\|\nabla f(x)\| \le \epsilon$) of smooth, high-dimensional, and potentially non-convex functions $f$. We consider oracle-based complexity…
This paper presents a comprehensive analysis of a broad range of variations of the stochastic proximal point method (SPPM). Proximal point methods have attracted considerable interest owing to their numerical stability and robustness…
Traditional statistical estimation, or statistical inference in general, is static, in the sense that the estimate of the quantity of interest does not change the future evolution of the quantity. In some sequential estimation problems…
Over the last years, the transportation community has witnessed a tremendous amount of research contributions on new deep learning approaches for spatio-temporal forecasting. These contributions tend to emphasize the modeling of spatial…
Inference for mechanistic models is challenging because of nonlinear interactions between model parameters and a lack of identifiability. Here we focus on a specific class of mechanistic models, which we term stable differential equations.…
Image registration is a widespread problem which applies models about image transformation or image similarity to align discrete images of the same scene. Nevertheless, the theoretical limits on its accuracy are not understood even in the…
We study parameter estimation and asymptotic inference for sparse nonlinear regression. More specifically, we assume the data are given by $y = f( x^\top \beta^* ) + \epsilon$, where $f$ is nonlinear. To recover $\beta^*$, we propose an…
We study the problem of change point localisation and inference for sequentially collected fragmented functional data, where each curve is observed only over discrete grids randomly sampled over a short fragment. The sequence of underlying…
We consider the inference problem for parameters in stochastic differential equation models from discrete time observations (e.g. experimental or simulation data). Specifically, we study the case where one does not have access to…
We derive an exact and efficient Bayesian regression algorithm for piecewise constant functions of unknown segment number, boundary location, and levels. It works for any noise and segment level prior, e.g. Cauchy which can handle outliers.…
Graph representations offer powerful and intuitive ways to describe data in a multitude of application domains. Here, we consider stochastic processes generating graphs and propose a methodology for detecting changes in stationarity of such…
Stationary stochastic processes (SPs) are a key component of many probabilistic models, such as those for off-the-grid spatio-temporal data. They enable the statistical symmetry of underlying physical phenomena to be leveraged, thereby…
Dynamic factor models are often estimated by point-estimation methods, disregarding parameter uncertainty. We propose a method accounting for parameter uncertainty by means of posterior approximation, using variational inference. Our…
This paper proposes a new test for a change point in the mean of high-dimensional data based on the spatial sign and self-normalization. The test is easy to implement with no tuning parameters, robust to heavy-tailedness and theoretically…
It is well-known that given a bounded, smooth nonconvex function, standard gradient-based methods can find $\epsilon$-stationary points (where the gradient norm is less than $\epsilon$) in $\mathcal{O}(1/\epsilon^2)$ iterations. However,…