Related papers: Nonparametric ridge estimation
We consider a problem of manifold estimation from noisy observations. Many manifold learning procedures locally approximate a manifold by a weighted average over a small neighborhood. However, in the presence of large noise, the assigned…
Averaging provides an alternative to bandwidth selection for density kernel estimation. We propose a procedure to combine linearly several kernel estimators of a density obtained from different, possibly data-driven, bandwidths. The method…
Features in predictive models are not exchangeable, yet common supervised models treat them as such. Here we study ridge regression when the analyst can partition the features into $K$ groups based on external side-information. For example,…
Kernel ridge regression is an important nonparametric method for estimating smooth functions. We introduce a new set of conditions, under which the actual rates of convergence of the kernel ridge regression estimator under both the L_2 norm…
We present a robust refinement method for estimating oriented normals from unstructured point clouds. In contrast to previous approaches that either suffer from high computational complexity or fail to achieve desirable accuracy, our novel…
We establish precise structural and risk equivalences between subsampling and ridge regularization for ensemble ridge estimators. Specifically, we prove that linear and quadratic functionals of subsample ridge estimators, when fitted with…
We consider learning two layer neural networks using stochastic gradient descent. The mean-field description of this learning dynamics approximates the evolution of the network weights by an evolution in the space of probability…
We propose and study a set of algorithms for discovering community structure in networks -- natural divisions of network nodes into densely connected subgroups. Our algorithms all share two definitive features: first, they involve iterative…
Random Feature (RF) models are used as efficient parametric approximations of kernel methods. We investigate, by means of random matrix theory, the connection between Gaussian RF models and Kernel Ridge Regression (KRR). For a Gaussian RF…
An algorithm to improve performance parameter for unsupervised decision forest clustering and density estimation is presented. Specifically, a dual assignment parameter is introduced as a density estimator by combining Random Forest and…
We study a ridge estimator for the high-dimensional two-way fixed effect regression model with a sparse bipartite network. We develop concentration inequalities showing that when the ridge parameters increase as the log of the network size,…
Random forests is a common non-parametric regression technique which performs well for mixed-type unordered data and irrelevant features, while being robust to monotonic variable transformations. Standard random forests, however, do not…
Mean shift clustering finds the modes of the data probability density by identifying the zero points of the density gradient. Since it does not require to fix the number of clusters in advance, the mean shift has been a popular clustering…
We investigate density estimation from a $n$-sample in the Euclidean space $\mathbb R^D$, when the data is supported by an unknown submanifold $M$ of possibly unknown dimension $d < D$ under a reach condition. We study nonparametric kernel…
Modal regression estimates the local modes of the distribution of $Y$ given $X=x$, instead of the mean, as in the usual regression sense, and can hence reveal important structure missed by usual regression methods. We study a simple…
We derive and analyze a generic, recursive algorithm for estimating all splits in a finite cluster tree as well as the corresponding clusters. We further investigate statistical properties of this generic clustering algorithm when it…
This work presents an accurate and robust method for estimating normals from point clouds. In contrast to predecessor approaches that minimize the deviations between the annotated and the predicted normals directly, leading to direction…
Density Estimation Trees (DETs) are decision trees trained on a multivariate dataset to estimate its probability density function. While not competitive with kernel techniques in terms of accuracy, they are incredibly fast, embarrassingly…
Data analysis in high-dimensional spaces aims at obtaining a synthetic description of a data set, revealing its main structure and its salient features. We here introduce an approach providing this description in the form of a topography of…
We consider the problem of positioning a cloud of points in the Euclidean space $\mathbb{R}^d$, using noisy measurements of a subset of pairwise distances. This task has applications in various areas, such as sensor network localization and…