相关论文: Local regression on path spaces with signature met…

Nonstationary high-dimensional time series are increasingly encountered in biomedical research as measurement technologies advance. Owing to the homeostatic nature of physiological systems, such datasets are often located on, or can be well…

Motion planning can be cast as a trajectory optimisation problem where a cost is minimised as a function of the trajectory being generated. In complex environments with several obstacles and complicated geometry, this optimisation problem…

We provide the first regression framework that simultaneously accommodates responses taking values in a general metric space and predictors lying on a general torus. We propose intrinsic local constant and local linear estimators that…

Distribution regression refers to the supervised learning problem where labels are only available for groups of inputs instead of individual inputs. In this paper, we develop a rigorous mathematical framework for distribution regression…

We propose a new method for input variable selection in nonlinear regression. The method is embedded into a kernel regression machine that can model general nonlinear functions, not being a priori limited to additive models. This is the…

This paper deals with a nonparametric Nadaraya-Watson (NW) estimator of the transition density function computed from independent continuous observations of a diffusion process. A risk bound is established on this estimator. The paper also…

Recent advances in deep learning have achieved impressive gains in classification accuracy on a variety of types of data, including images and text. Despite these gains, however, concerns have been raised about the calibration, robustness,…

Nonparametric regression is a standard statistical tool with increased importance in the Big Data era. Boundary points pose additional difficulties but local polynomial regression can be used to alleviate them. Local linear regression, for…

Generative models are often conditioned on a small set of examples via cross-attention. Under the Gaussian optimal-transport path, we show that the exact velocity field induced by a finite support set is a Nadaraya--Watson kernel smoother…

In this paper a new smooth backfitting estimate is proposed for additive regression models. The estimate has the simple structure of Nadaraya--Watson smooth backfitting but at the same time achieves the oracle property of local linear…

In this paper, we prove large deviations principle for the Nadaraya-Watson estimator and for the semi-recursive kernel estimator of the regression in the multidimensional case. Under suitable conditions, we show that the rate function is a…

We frame novelty detection on path space as a hypothesis testing problem with signature-based test statistics. Using transportation-cost inequalities of Gasteratos and Jacquier (2023), we obtain tail bounds for false positive rates that…

The signature is a representation of a path as an infinite sequence of its iterated integrals. Under certain assumptions, the signature characterizes the path, up to translation and reparameterization. Therefore, a crucial question of…

We propose a new method for construction of the absolute permeability map consistent with the interpreted results of well logging and well test measurements in oil reservoirs. Nadaraya-Watson kernel regression is used to approximate…

We present algorithms for nonparametric regression in settings where the data are obtained sequentially. While traditional estimators select bandwidths that depend upon the sample size, for sequential data the effective sample size is…

We propose a novel class of time-varying nonparanormal graphical models, which allows us to model high dimensional heavy-tailed systems and the evolution of their latent network structures. Under this model, we develop statistical tests for…

Regression evaluation has been performed for decades. Some metrics have been identified to be robust against shifting and scaling of the data but considering the different distributions of data is much more difficult to address (imbalance…

We address the problem of learning an unknown smooth function and its derivatives from noisy pointwise evaluations under the supremum norm. While classical nonparametric regression provides a strong theoretical foundation, traditional…

We extend our work for compression of currents and varifolds to a compression algorithm for the embedded normal cycles representation of shape, restricted to the constant normal kernel case, using the Nystrom approximation in Reproducing…

Rough path theory is focused on capturing and making precise the interactions between highly oscillatory and non-linear systems. It draws on the analysis of LC Young and the geometric algebra of KT Chen. The concepts and the uniform…