Related papers: Smoothness-Penalized Deconvolution (SPeD) of a Den…
Kernel density estimation is a well known method involving a smoothing parameter (the bandwidth) that needs to be tuned by the user. Although this method has been widely used the bandwidth selection remains a challenging issue in terms of…
We prove optimal convergence results of a stochastic particle method for computing the classical solution of a multivariate McKean-Vlasov equation, when the measure variable is in the drift, following the classical approach of [BT97,…
Speden is a computer program that reconstructs the electron density of single particles from their x-ray diffraction patterns, using a single-particle adaptation of the Holographic Method in crystallography. (Szoke, A., Szoke, H., and…
Because diffusion models have shown impressive performances in a number of tasks, such as image synthesis, there is a trend in recent works to prove (with certain assumptions) that these models have strong approximation capabilities. In…
Two maximum likelihood-based algorithms for unfolding or deconvolution are considered: the Richardson-Lucy method and the Data Unfolding method with Mean Integrated Square Error (MISE) optimization [10]. Unfolding is viewed as a procedure…
Smoothing splines have been used pervasively in nonparametric regressions. However, the computational burden of smoothing splines is significant when the sample size $n$ is large. When the number of predictors $d\geq2$, the computational…
In this paper, we study randomized methods for feedback design of uncertain systems. The first contribution is to derive the sample complexity of various constrained control problems. In particular, we show the key role played by the…
This paper describes a recursive estimation procedure for multivariate binary densities (probability distributions of vectors of Bernoulli random variables) using orthogonal expansions. For $d$ covariates, there are $2^d$ basis coefficients…
Smoothing classifiers and probability density functions with Gaussian kernels appear unrelated, but in this work, they are unified for the problem of robust classification. The key building block is approximating the $\textit{energy…
Dilated convolutions, also known as atrous convolutions, have been widely explored in deep convolutional neural networks (DCNNs) for various dense prediction tasks. However, dilated convolutions suffer from the gridding artifacts, which…
Deconvolution microscopy has been extensively used to improve the resolution of the widefield fluorescent microscopy. Conventional approaches, which usually require the point spread function (PSF) measurement or blind estimation, are…
This paper studies density estimation under pointwise loss in the setting of contamination model. The goal is to estimate $f(x_0)$ at some $x_0\in\mathbb{R}$ with i.i.d. observations, $$ X_1,\dots,X_n\sim (1-\epsilon)f+\epsilon g, $$ where…
A new data-based smoothing parameter for circular kernel density (and its derivatives) estimation is proposed. Following the plug-in ideas, unknown quantities on an optimal smoothing parameter are replaced by suitable estimates. This paper…
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…
We study the non-parametric estimation of an unknown stationary density fV of an unobserved strictly stationary volatility process $(\bm V_t)_{t\geq 0}$ on $\IRp^2 := (0,\infty)^2$ based on discrete-time observations in a stochastic…
In recent years, kernel density estimation has been exploited by computer scientists to model machine learning problems. The kernel density estimation based approaches are of interest due to the low time complexity of either O(n) or…
Unlinked regression, in which covariates and responses are observed separately without known correspondence, has recently gained increasing attention. Deconvolution, on the other hand, is a fundamental and challenging problem in…
In this paper we investigate the application of optimisation techniques in the deconvolution of mineral fractionation data obtained from a mathematical model for the operation of a fluidised bed with a set of inclined parallel channels…
Smooth Estimation of probability density and distribution functions from its sample is an attractive and an important problem that has applications in several fields such as, business, medicine, and environment. This article introduces a…
Semisupervised methods inevitably invoke some assumption that links the marginal distribution of the features to the regression function of the label. Most commonly, the cluster or manifold assumptions are used which imply that the…