arXiv research

The paper uses Tukey g-and-h neural networks for non-Gaussian data regression.

This paper discusses different classes of loss models in non-life insurance settings. It then overviews the class Tukey transform loss models that have not yet been widely considered in non-life insurance modelling, but offer opportunities to produce flexible skewness and kurtosis features often required in loss modell…

The paper studies randomized approximations of Tukey's depth for log-concave isotropic data.

Tukey median performance analyzed under TV corruptions.

Study on Tukey depth in machine learning using Hamilton-Jacobi equations.

Over the past half-century, the empirical finance community has produced vast literature on the advantages of the equally weighted S\&P 500 portfolio as well as the often overlooked disadvantages of the market capitalization weighted Standard and Poor's (S\&P 500) portfolio (see \cite{Bloom}, \cite{Uppal}, \cite{Jacobs…

Post hoc test for Sharpe ratio improves pairwise comparisons.

Researchers develop a new spatial process model for non-Gaussian data.

Develops a new framework for robust regression with EGM.

Characterizes weakly linked pairs of complete graphs in 3D space.

Let $G, H$ be two Kleinian groups with homeomorphic quotients $\mathbb H^3/G$ and $\mathbb H^3/H$. We assume that $G$ is of divergence type, and consider the Patterson-Sullivan measures of $G$ and $H$. The measurable rigidity theorem by Sullivan and Tukia says that a measurable and essentially directly measurable equiv…

We extend several techniques and theorems from geometric group theory so that they apply to geometric actions on arbitrary proper metric ARs (absolute retracts). A second way that we generalize earlier results is by eliminating freeness requirements often placed on the group actions. In doing so, we allow for groups wi…

Paper explores robust estimators for kernel exponential families using smoothed total variation distances.

On a smooth manifold M, generalized complex (generalized paracomplex) structures provide a notion of interpolation between complex (paracomplex) and symplectic structures on M. Given a complex manifold (M,j), we define six families of distinguished generalized complex or paracomplex structures on M. Each one of them in…

Paper proposes robust geodesic regression for manifold data.

The paper explores conditions for quasi-isometric subgroups and their filtered ends.

The study identifies unique Delaunay surfaces with constant mean curvature.

Machine learning models predict crash rates on narrow lanes.

Novel power transform unifies various mathematical functions.

We compute the number of (weak) equivalence classes of branched covers from a surface of genus g to the sphere, with 3 branching points, degree 2k, and local degrees over the branching points of the form (2,...,2), (2h+1,1,2,...,2), (d_1,...,d_m), for several values of g and h. We obtain explicit formulae of arithmetic…

We present a new algorithm for the 2D Sliding Window Discrete Fourier Transform (SWDFT). Our algorithm avoids repeating calculations in overlapping windows by storing them in a tree data-structure based on the ideas of the Cooley- Tukey Fast Fourier Transform (FFT). For an $N_0 \times N_1$ array and $n_0 \times n_1$ wi…

The main results of the paper are: \begin{Prop}\label{GenSvarc-Milnor} A group $G$ acting coarsely on a coarse space $(X,\CC)$ induces a coarse equivalence $g\to g\cdot x_0$ from $G$ to $X$ for any $x_0\in X$. \end{Prop} Theorem: \label{GenGromovThm} Two coarse structures $\CC_1$ and $\CC_2$ on the same set $X$ are equ…

Cobordism and signatures of manifolds with similar fundamental groups.

Estimates BV functions from noisy data using Voronoi diagrams.

The paper proves deep learning can be robust with certain loss functions.

Study of group orderability using tensor and exterior squares.

Classifies surfaces with constant Gaussian curvature in Euclidean 3-space.

We continue our computation, using a combinatorial method based on Gronthendieck's dessins d'enfant, of the number of (weak) equivalence classes of surface branched covers matching certain specific branch data. In this note we concentrate on data with the surface of genus g as source surface, the sphere as target surfa…

Classifies zero mean curvature surfaces in Lorentz-Minkowski space.

We construct a solution of the master equation by means of standard tools from homological perturbation theory under just the hypothesis that the ground field be of characteristic zero, thereby avoiding the formality assumption of the relevant Lie algebra. To this end we endow the homology H(g) of any differential grad…

We consider invariant Riemannian metrics on compact homogeneous spaces G/H where an intermediate subgroup K between G and H exists, so that the homogeneous space G/H is the total space of a Riemannian submersion. We study the question as to whether enlarging the fibers of the submersion by a constant scaling factor ret…

We show that Dranishnikov's asymptotic property C is preserved by direct products and the free product of discrete metric spaces. In particular, if $G$ and $H$ are groups with asymptotic property C, then both $G \times H$ and $G * H$ have asymptotic property C. We also prove that a group~$G$ has asymptotic property C i…

Robust feature-weighted jump models for time-dependent clustering

In this paper, we explore various statistical techniques for anomaly detection in conjunction with the popular Long Short-Term Memory (LSTM) deep learning model for transportation networks. We obtain the prediction errors from an LSTM model, and then apply three statistical models based on (i) the Gaussian distribution…

Two groups with same profinite completion have different co-Hopfian properties.

Donoho's JCGS (in press) paper is a spirited call to action for statisticians, who he points out are losing ground in the field of data science by refusing to accept that data science is its own domain. (Or, at least, a domain that is becoming distinctly defined.) He calls on writings by John Tukey, Bill Cleveland, and…

This paper shows how to carry out efficient asymptotic variance reduction when estimating volatility in the presence of stochastic volatility and microstructure noise with the realized kernels (RK) from [Barndorff-Nielsen et al., 2008] and the quasi-maximum likelihood estimator (QMLE) studied in [Xiu, 2010]. To obtain …

Robust estimation under Huber's $ε$-contamination model has become an important topic in statistics and theoretical computer science. Statistically optimal procedures such as Tukey's median and other estimators based on depth functions are impractical because of their computational intractability. In this paper, we est…

The paper classifies surfaces in Euclidean space that minimize the Dirichlet energy.

The interior Kasparov product formula is extended for foliated ρ-classes on Riemannian bundles.

Wave operators and spectral stability for Dirac operators under Ricci flow.

Suppose that S is a surface with boundary and that g and h are diffeomorphisms of S which restrict to the identity on the boundary. Let Y_g, Y_h, and Y_{hg} be the three-manifolds with open book decompositions given by (S,g), (S,h), and (S,hg), respectively. We show that the Ozsvath-Szabo contact invariant is natural u…

The study explores finite quotients of 3-manifold groups and their existence and non-existence.

We consider invariant Riemannian metrics on compact homogeneous spaces $G/H$ where an intermediate subgroup $K$ between $G$ and $H$ exists. In this case, the homogeneous space $G/H$ is the total space of a Riemannian submersion. The metrics constructed by shrinking the fibers in this way can be interpreted as metrics o…

Motivated by the work of Leininger on hyperbolic equivalence of homotopy classes of closed curves on surfaces, we investigate a similar phenomenon for free groups. Namely, we study the situation when two elements $g,h$ in a free group $F$ have the property that for every free isometric action of $F$ on an $\mathbb{R}$-…

A new depth measure based on optimal control theory captures multi-modal data.

Following the seminal idea of Tukey, data depth is a function that measures how close an arbitrary point of the space is located to an implicitly defined center of a data cloud. Having undergone theoretical and computational developments, it is now employed in numerous applications with classification being the most po…

We prove a completely new integral criterion for the existence and completeness of the wave operators $W_{\pm}(-Δ_h,-Δ_g, I_{g,h})$ corresponding to the (unique self-adjoint realizations of) the Laplace-Beltrami operators $-Δ_j$, $j=1,2$, that are induced by two quasi-isometric complete Riemannian metrics $g$ and $h$ o…