Related papers: The stochastic approximation method for the estima…
Random feature approximation is arguably one of the most widely used techniques for kernel methods in large-scale learning algorithms. In this work, we analyze the generalization properties of random feature methods, extending previous…
Predictive recursion (PR) is a fast stochastic algorithm for nonparametric estimation of mixing distributions in mixture models. It is known that the PR estimates of both the mixing and mixture densities are consistent under fairly mild…
A structure-preserving kernel ridge regression method is presented that allows the recovery of nonlinear Hamiltonian functions out of datasets made of noisy observations of Hamiltonian vector fields. The method proposes a closed-form…
Despite the numerous applications that may be expeditiously modelled by counting processes, stochastic filtering strategies involving Poisson-type observations still remain somewhat poorly developed. In this work, we propose a Monte Carlo…
Density estimation is a fundamental task in statistics and machine learning applications. Kernel density estimation is a powerful tool for non-parametric density estimation in low dimensions; however, its performance is poor in higher…
Estimating the ratio of two probability densities from finitely many observations of the densities is a central problem in machine learning and statistics with applications in two-sample testing, divergence estimation, generative modeling,…
We obtain non asymptotic concentration bounds for two kinds of stochastic approximations. We first consider the deviations between the expectation of a given function of the Euler scheme of some diffusion process at a fixed deterministic…
In this paper, we consider a partial deconvolution kernel estimator for nonparametric regression when some covariates are measured with error while others are observed without error. We focus on a general and realistic setting in which the…
We view sequential design as a model selection problem to determine which new observation is expected to be the most informative, given the existing set of observations. For estimating a probability distribution on a bounded interval, we…
In this paper, we propose to construct confidence bands by bootstrapping the debiased kernel density estimator (for density estimation) and the debiased local polynomial regression estimator (for regression analysis). The idea of using a…
In this paper, we propose a variable selection method for general nonparametric kernel-based estimation. The proposed method consists of two-stage estimation: (1) construct a consistent estimator of the target function, (2) approximate the…
In frequentist inference, minimizing the Hellinger distance between a kernel density estimate and a parametric family produces estimators that are both robust to outliers and statistically efficienty when the parametric model is correct.…
Stochastic versions of proximal methods have gained much attention in statistics and machine learning. These algorithms tend to admit simple, scalable forms, and enjoy numerical stability via implicit updates. In this work, we propose and…
In the gravitational-wave analysis of pulsar-timing-array datasets, parameter estimation is usually performed using Markov Chain Monte Carlo methods to explore posterior probability densities. We introduce an alternative procedure that…
We present a simple and robust strategy for the selection of sampling points in Uncertainty Quantification. The goal is to achieve the fastest possible convergence in the cumulative distribution function of a stochastic output of interest.…
Despite the significance of probabilistic time-series forecasting models, their evaluation metrics often involve intractable integrations. The most widely used metric, the continuous ranked probability score (CRPS), is a strictly proper…
Approximate Bayesian inference on the basis of summary statistics is well-suited to complex problems for which the likelihood is either mathematically or computationally intractable. However the methods that use rejection suffer from the…
This paper develops a nonparametric density estimator with parametric overtones. Suppose $f(x,\theta)$ is some family of densities, indexed by a vector of parameters $\theta$. We define a local kernel smoothed likelihood function which for…
A fundamental drawback of kernel-based statistical models is their limited scalability to large data sets, which requires resorting to approximations. In this work, we focus on the popular Gaussian kernel and on techniques to linearize…
We study the problem of estimating linear response statistics under external perturbations using time series of unperturbed dynamics. Based on the fluctuation-dissipation theory, this problem is reformulated as an unsupervised learning task…