arXiv research

Estimates time-varying network connections using multi-stage smoothing.

Estimates smooth functions and their derivatives from noisy data.

Smoothed SGD improves quantile estimation without crossing curves.

In high dimensional sparse regression, pivotal estimators are estimators for which the optimal regularization parameter is independent of the noise level. The canonical pivotal estimator is the square-root Lasso, formulated along with its derivatives as a "non-smooth + non-smooth" optimization problem. Modern technique…

A boosting method improves nonparametric density estimation without smoothing assumptions.

We generalize stochastic smoothing for gradient estimation of non-differentiable functions.

Improved OOD detection using label smoothing and k-NN density estimates.

Non-parametric estimation of a multivariate density estimation is tackled via a method which combines traditional local smoothing with a form of global smoothing but without imposing a rigid structure. Simulation work delivers encouraging indications on the effectiveness of the method. An application to density-based c…

Post-estimation smoothing improves prediction accuracy with structural indices.

New matching estimators correct bias in multivariate settings without smoothing parameters.

The paper proves estimates for solutions to nonlinear equations on manifolds with boundary.

The paper provides gradient estimates for nonlinear heat-type equations on smooth metric measure spaces.

Label smoothing improves model robustness against misspecification.

We establish local elliptic and parabolic gradient estimates for positive smooth solutions to a nonlinear parabolic equation on a smooth metric measure space. As applications, we determine various conditions on the equation's coefficients and the growth of solutions that guarantee the nonexistence of nontrivial positiv…

Sparse Polyak improves high-dimensional statistical estimation.

The paper proves gradient estimates for nonlinear parabolic equations on smooth metric measure spaces.

The paper provides new gradient estimates for solutions to a nonlinear elliptic equation on smooth metric measure spaces.

The paper establishes bounds on the smoothness parameter in Gaussian process interpolation.

Paper optimizes statistical estimation for randomized smoothing to reduce adversarial robustness certification time.

Smoothing splines provide a powerful and flexible means for nonparametric estimation and inference. With a cubic time complexity, fitting smoothing spline models to large data is computationally prohibitive. In this paper, we use the theoretical optimal eigenspace to derive a low rank approximation of the smoothing spl…

In this paper, we propose a method for estimating the Sobolev type embedding constant on a domain with minimally smooth boundary. We estimate the embedding constant by constructing an extension operator and computing its operator norm. We also present some examples of estimating the embedding constant for certain domai…

Study on when smooth Ricci flow remains smooth at the start.

Improved MLMC method for robust and efficient probability and density estimation.

Improved estimators for causal inference using cross-fitting and undersmoothing.

We propose a novel method to determine the dissimilarity between subjects for functional data clustering. Spline smoothing or interpolation is common to deal with data of such type. Instead of estimating the best-representing curve for each subject as fixed during clustering, we measure the dissimilarity between subjec…

The estimation of probabilities of network edges from the observed adjacency matrix has important applications to predicting missing links and network denoising. It has usually been addressed by estimating the graphon, a function that determines the matrix of edge probabilities, but this is ill-defined without strong a…

Paper proposes new density estimators for high-dimensional data.

A new clustering method uses nonparametric smoothing to estimate cluster membership functions.

Kernel smoothing on unknown manifolds with bounds and asymptotic normality.

Spatial smoothing improves BNNs' accuracy, uncertainty, and robustness without increasing computational cost.

Smoothed analysis of complexity bounds and condition numbers has been done, so far, on a case by case basis. In this paper we consider a reasonably large class of condition numbers for problems over the complex numbers and we obtain smoothed analysis estimates for elements in this class depending only on geometric inva…

We establish fundamental results for a parabolic flow of Riemannian metrics introduced by Bahuaud-Helliwell in arXiv:1010:4287v1 which is based on the Fefferman-Graham ambient obstruction tensor. First, we obtain local $L^2$ smoothing estimates for the curvature tensor and use them to prove pointwise smoothing estimate…

Many problems on signal processing reduce to nonparametric function estimation. We propose a new methodology, piecewise convex fitting (PCF), and give a two-stage adaptive estimate. In the first stage, the number and location of the change points is estimated using strong smoothing. In the second stage, a constrained s…

Paper studies minimax optimal regression using Laplacian smoothing over graphs.

Proves smoothness and estimates for special Lagrangian solutions with semi-convexity.

Optimizes spectral density estimation for stationary and nonstationary processes.

The paper optimizes estimating transport maps between distributions.

Optimal nonparametric regression estimator adapts to unknown smoothness.

Develops a novel ML smoothing method for incomplete data in state-space models.

Smooth solutions found for modified mean curvature flow in Riemannian manifolds.

The paper proposes a decoupled approach to efficiently estimate CoVaR, a measure of systemic financial risk.

We define a diffeomorphism invariant of smooth 4-manifolds which we can estimate for many smoothings of R^4 and other smooth 4-manifolds. Using this invariant we can show that uncountably many smoothings of R^4 support no Stein structure. (Gompf has constructed uncountably many smoothings of R^4 which do support Stein …

New method for adaptive estimation and inference in econometric models without knowing smoothness.

In the previous paper, we considered a link diagram invariant of Hass and Nowik type using regular smoothing and unknotting number, to estimate the number of Reidemeister moves needed for unlinking. In this paper, we introduce a new link diagram invariant using irregular smoothing, and give an example of a knot diagram…

Estimates smooth graph signals from partial measurements.

Proves existence of smooth convex solutions to capillary curvature equations.

In this paper, we consider the following general evolution equation $u_t=Δ_fu+au\log^αu+bu$ on smooth metric measure spaces $(M^n, g, e^{-f}dv)$. We give a local gradient estimate of Souplet-Zhang type for positive smooth solution of this equation provided that the Bakry-Émery curvature bounded from below. When $f$…

A non-Bayesian, regression-based or generalized least squares (GLS)-based approach is formally proposed to estimate a class of time-varying AR parameter models. This approach has partly been used by Ito et al. (2014, 2016a,b), and is proven to be efficient because, unlike conventional methods, it does not require Kalma…