相关论文: Comparison of the generalized centroid with Gaussi…

We suggest efficient and provable methods to compute an approximation for imbalanced point clustering, that is, fitting $k$-centers to a set of points in $\mathbb{R}^d$, for any $d,k\geq 1$. To this end, we utilize \emph{coresets}, which,…

This paper presents Constrained Centroid Clustering (CCC), a method that extends classical centroid-based clustering by enforcing a constraint on the maximum distance between the cluster center and the farthest point in the cluster. Using a…

Let $\{f(t): t\in T\}$ be a smooth Gaussian random field over a parameter space $T$, where $T$ may be a subset of Euclidean space or, more generally, a Riemannian manifold. For any local maximum of $f(t)$ located at $t_0$ in the interior of…

Information about primary transmitter location is crucial in enabling several key capabilities in cognitive radio networks, including improved spatio-temporal sensing, intelligent location-aware routing, as well as aiding spectrum policy…

We study power approximation formulas for peak detection using Gaussian random field theory. The approximation, based on the expected number of local maxima above the threshold $u$, $\mathbb{E}[M_u]$, is proved to work well under three…

We consider random walk on a mildly random environment on finite transitive d- regular graphs of increasing girth. After scaling and centering, the analytic spectrum of the transition matrix converges in distribution to a Gaussian noise. An…

A classification algorithm, called the Linear Centralization Classifier (LCC), is introduced. The algorithm seeks to find a transformation that best maps instances from the feature space to a space where they concentrate towards the center…

In this paper we use the Cramer-Rao lower uncertainty bound to estimate the maximum precision that could be achieved on the joint simultaneous (or 2D) estimation of photometry and astrometry of a point source measured by a linear CCD…

We formally prove the connection between k-means clustering and the predictions of neural networks based on the softmax activation layer. In existing work, this connection has been analyzed empirically, but it has never before been…

Signals with single peak and symmetry property are very common in various fields, such as probability density function of normal distribution. Among the information contained in such signals, peak position is the most important, sometimes…

We derive generic information-theoretic and PAC-Bayesian generalization bounds involving an arbitrary convex comparator function, which measures the discrepancy between the training and population loss. The bounds hold under the assumption…

A recent paper \cite{CaeCaeSchBar06} proposed a provably optimal, polynomial time method for performing near-isometric point pattern matching by means of exact probabilistic inference in a chordal graphical model. Their fundamental result…

$\renewcommand{\Re}{\mathbb{R}}$ We develop a general randomized technique for solving "implic it" linear programming problems, where the collection of constraints are defined implicitly by an underlying ground set of elements. In many…

A simple way of obtaining robust estimates of the "center" (or the "location") and of the "scatter" of a dataset is to use the maximum likelihood estimate with a class of heavy-tailed distributions, regardless of the "true" distribution…

The study of vertex centrality measures is a key aspect of network analysis. Naturally, such centrality measures have been generalized to groups of vertices; for popular measures it was shown that the problem of finding the most central…

This paper formulates a general cross validation framework for signal denoising. The general framework is then applied to nonparametric regression methods such as Trend Filtering and Dyadic CART. The resulting cross validated versions are…

Let $X=C+\mathrm{E}$ with a deterministic matrix $C\in\R^{M\times M}$ and $\mathrm{E}$ some centered Gaussian $M\times M$-matrix whose entries are independent with variance $\sigma^2$. In the present work, the accuracy of reduced-rank…

The sub-optimality of Gauss--Hermite quadrature and the optimality of the trapezoidal rule are proved in the weighted Sobolev spaces of square integrable functions of order $\alpha$, where the optimality is in the sense of worst-case error.…

Several data analysis techniques employ similarity relationships between data points to uncover the intrinsic dimension and geometric structure of the underlying data-generating mechanism. In this paper we work under the model assumption…

In this paper, we analyze some theoretical properties of the problem of minimizing a quadratic function with a cubic regularization term, arising in many methods for unconstrained and constrained optimization that have been proposed in the…