Related papers: Normal variation for adaptive feature size
The geometric median, a notion of center for multivariate distributions, has gained recent attention in robust statistics and machine learning. Although conceptually distinct from the mean (i.e., expectation), we demonstrate that both are…
This paper is devoted to the study of a discrepancy-type characteristic -- the fixed volume discrepancy -- of the Fibonacci point set in the unit square. It was observed recently that this new characteristic allows us to obtain optimal rate…
The asymmetric skew divergence smooths one of the distributions by mixing it, to a degree determined by the parameter $\lambda$, with the other distribution. Such divergence is an approximation of the KL divergence that does not require the…
Comparisons on $L^{n\over 2}$-norms of scalar curvatures between Riemannian metrics and standard metrics are obtained. The metrics are restricted to conformal classes or under certain curvature conditions.
A recent paper of Jerison and Figalli proved a relationship between the $H^{1/2}$ norms of smoothed out indicator functions of sets and their perimeter. We continue this line of investigation and extend it in two ways. First, we describe a…
We point out how geometric features affect the scaling properties of non-equilibrium dynamic processes, by a model for surface growth where particles can deposit and evaporate only in dimer form, but dissociate on the surface. Pinning…
We establish both uniform and nonuniform error bounds of the Berry-Esseen type in normal approximation under local dependence. These results are of an order close to the best possible if not best possible. They are more general or sharper…
The surface area of a set which is only observed as a binary pixel image is often estimated by a weighted sum of pixel configurations counts. In this paper we examine these estimators in a design based setting -- we assume that the observed…
Species evolution is essentially a random process of interaction between biological populations and their environments. As a result, some physical parameters in evolution models are subject to statistical fluctuations. In this paper, two…
Finite size fluctuations are a crucial ingredient in kinetic theory of long-range interacting collisionless systems. In this Letter, we introduce a phenomenological theory which predicts an anomalous scaling close to marginal stability for…
We prove a general normal approximation theorem for local graph statistics in the configuration model, together with an explicit bound on the error in the approximation with respect to the Wasserstein metric. Such statistics take the form…
A significant obstacle in the development of robust machine learning models is covariate shift, a form of distribution shift that occurs when the input distributions of the training and test sets differ while the conditional label…
Analysing statistical properties of the normal forms of random braids, we observe that, except for an initial and a final region whose lengths are uniformly bounded (that is, the bound is independent of the length of the braid), the…
The concept of natural pseudo-distance has proven to be a powerful tool for measuring the dissimilarity between topological spaces endowed with continuous real-valued functions. Roughly speaking, the natural pseudo-distance is defined as…
Anomaly Detection is an important problem within computer vision, having variety of real-life applications. Yet, the current set of solutions to this problem entail known, systematic shortcomings. Specifically, contemporary surface Anomaly…
In this paper, we give a simple description of the deformations of a map between two smooth curves with partially prescribed branching, in the cases that both curves are fixed, and that the source is allowed to vary. Both descriptions work…
An asymmetric variant of the contact process where the activity spreads with different and independent random rates to the left and to the right is introduced. A real space renormalization scheme is formulated for model by means of which it…
Phenomena with a constrained sample space appear frequently in practice. This is the case e.g. with strictly positive data and with compositional data, like percentages and the like. If the natural measure of difference is not the absolute…
To quantify the fundamental evolution of time-varying networks, and detect abnormal behavior, one needs a notion of temporal difference that captures significant organizational changes between two successive instants. In this work, we…
One-class anomaly detection aims to detect objects that do not belong to a predefined normal class. In practice training data lack those anomalous samples; hence state-of-the-art methods are trained to discriminate between normal and…