arXiv research

The paper introduces a new method to find meaningful data subsets in multivariate probability density functions.

New supervised and unsupervised NFLTs for elliptical distributions.

Important information concerning a multivariate data set, such as clusters and modal regions, is contained in the derivatives of the probability density function. Despite this importance, nonparametric estimation of higher order derivatives of the density functions have received only relatively scant attention. Kernel …

Principal Components Analysis is a widely used technique for dimension reduction and characterization of variability in multivariate populations. Our interest lies in studying when and why the rotation to principal components can be used effectively within a response-predictor set relationship in the context of mode hu…

Two methods use simulation to improve anomaly detection in particle physics.

Exchanges implement intentional trade delays to limit the harmful impact of low-latency trading. Do such "speed bumps" curb investment in fast trading technology? Data is scarce since trading technologies are proprietary. We build an experimental trading platform where participants face speed bumps and can invest in fa…

We leverage recent breakthroughs in neural density estimation to propose a new unsupervised anomaly detection technique (ANODE). By estimating the probability density of the data in a signal region and in sidebands, and interpolating the latter into the signal region, a likelihood ratio of data vs. background can be co…

We consider the multi-bump solutions of the following fractional Nirenberg problem \begin{equation}\label{01} (-Δ)^s u=K(x)u^{\frac{n+2s}{n-2s}}, \;\;\;\;u>0\;\;\text{ in }\mathbb{R}^n, \end{equation} where $s\in (0,1)$ and $n>2+2s$. If $K$ is a periodic function in some $k$ variables with $1\leq k<\frac{n-2s}2$, we pr…

We show here that the Nielsen core of the bumping set of the domain of discontinuity of a Kleinian group $Γ$ is the boundary of the characteristic submanifold of the associated 3-manifold with boundary. Some examples of interesting characteristic submanifolds are given. We also give a construction of the characteristic…

Autoencoders misidentify anomalies due to data topology.

Dimensionality reduction is one of the key issues in the design of effective machine learning methods for automatic induction. In this work, we introduce recursive maxima hunting (RMH) for variable selection in classification problems with functional data. In this context, variable selection techniques are especially a…

Inspired by the unsupervised learning or self-organization in the machine learning context, here we attempt to draw `learning curve' for the collective behavior of job-seeking `zero-intelligence' labors in successive job-hunting processes. Our labor market is supposed to be opened especially for university graduates in…

VAE improves anomaly detection for jet tagging at the LHC.

We prove the following new characterization of $C^p$ (Lipschitz) smoothness in Banach spaces. An infinite-dimensional Banach space $X$ has a $C^p$ smooth (Lipschitz) bump function if and only if it has another $C^p$ smooth (Lipschitz) bump function $f$ such that $f'(x)\neq 0$ for every point $x$ in the interior of the …

The level curves of an analytic function germ almost always have bumps at unexpected points near the singularity. This profound discovery of N. A'Campo is fully explored in this paper for $f(z,w)\in \C\{z,w\}$, using the Newton-Puiseux infinitesimals and the notion of gradient canyon. Equally unexpected is the Dirac ph…

Finite-precision learning of $anh$ networks is limited by the Monte Carlo rate.

PHBench predicts Series A funding from Product Hunt launch signals with 7.8% accuracy.

Splat Regression Models use mixtures of bump functions to approximate complex data.

The study classifies geometrically finite polynomials on the boundary of Blaschke products.

Study shows market makers can cooperate without communication.

Machine-learned anomaly detection in new-physics searches needs calibration and look-elsewhere correction

Bayesian predictive inference analyzes a dataset to make predictions about new observations. When a model does not match the data, predictive accuracy suffers. We develop population empirical Bayes (POP-EB), a hierarchical framework that explicitly models the empirical population distribution as part of Bayesian analys…

We give a new and complete proof of Hamilton's injectivity radius estimate for sequences with bounded and almost nonnegative curvature operators, unbounded diameters, and bump-like origins. Such sequences arise in particular from dilations about a singularity of the Ricci flow on a 3-manifold.

Mixed-SCORE+ improves community detection in weak signal networks.

In this paper, we study the topology of the boundaries of quasi-Fuchsian spaces. We first show for a given convergent sequence of quasi-Fuchsian groups, how we can know the end invariant of the limit group from the information on the behaviour of conformal structures at infinity of the groups. This result gives rise to…

The concept of subdifferentiability is studied in the context of $C^1$ Finsler manifolds (modeled on a Banach space with a Lipschitz $C^1$ bump function). A class of Hamilton-Jacobi equations defined on $C^1$ Finsler manifolds is studied and several results related to the existence and uniqueness of viscosity solutions…

To coordinate actions with an interaction partner requires a constant exchange of sensorimotor signals. Humans acquire these skills in infancy and early childhood mostly by imitation learning and active engagement with a skilled partner. They require the ability to predict and adapt to one's partner during an interacti…

We have carried out simulations of a financial model of the firm to analyse the validity of the concept of Trade on Equity in dynamics. The results exhibit the ability of the borrowing policy connected to a cautious dividend distribution to inject chaos into the profit motion. The 3D system built with the van der Pol's…

In this paper we construct a parametrix for the forward fundamental solution of the wave and Klein-Gordon equations on asymptotically de Sitter spaces without caustics. We use this parametrix to obtain asymptotic expansions for solutions of the inhomogeneous equation and to obtain a uniform L^p estimate for a family of…

In this note we give sufficient conditions to ensure that the weak Finsler structure of a complete $C^k$ Finsler manifold $M$ is determined by the normed algebra $C_b^k(M)$ of all real-valued, bounded and $C^k$ smooth functions with bounded derivative defined on $M$. As a consequence, we obtain: (i) the Finsler structu…

Let $N$ be a hyperbolic 3-manifold and $B$ a component of the interior of $AH(π_1(N))$, the space of marked hyperbolic 3-manifolds homotopy equivalent to $N$. We will give topological conditions on $N$ sufficient to give $ρ\in \bar{B}$ such that for every small neighborhood $V$ of $ρ$, $V \cap B$ is disconnected. This …

Recently, self-normalizing neural networks (SNNs) have been proposed with the intention to avoid batch or weight normalization. The key step in SNNs is to properly scale the exponential linear unit (referred to as SELU) to inherently incorporate normalization based on central limit theory. SELU is a monotonically incre…

In this paper we give a necessary and sufficient condition in which a sequence of Kleinian punctured torus groups converges. This result tells us that every exotically convergent sequence of Kleinian punctured torus groups is obtained by the method due to Anderson and Canary. Thus we obtain a complete description of th…

New study shows acceleration in hyperbolic spaces is impossible for strongly geodesically convex functions.

Novel power transform unifies various mathematical functions.

Given a Finsler space, we introduce a system of partial differential equations, called the Landsberg equation. Based on a careful analysis of the Landsberg equation and the observation that the solution space is invariant under the linear isometries of the tangent Minkowski spaces, we prove that an $(α_1, α_2)$-metric …

This text is intended to become in the long run Chapter 3 of our long saga dedicated to Riemann, Ahlfors and Rohlin. Yet, as its contents evolved as mostly independent (due to our inaptitude to interconnect both trends as strongly as we wished), it seemed preferable to publish it separately. More factually, our account…

We present a method for finding high density, low-dimensional structures in noisy point clouds. These structures are sets with zero Lebesgue measure with respect to the $D$-dimensional ambient space and belong to a $d<D$ dimensional space. We call them "singular features." Hunting for singular features corresponds to f…

We introduce the functional mean-shift algorithm, an iterative algorithm for estimating the local modes of a surrogate density from functional data. We show that the algorithm can be used for cluster analysis of functional data. We propose a test based on the bootstrap for the significance of the estimated local modes …

Spectral embedding uses eigenfunctions of the discrete Laplacian on a weighted graph to obtain coordinates for an embedding of an abstract data set into Euclidean space. We propose a new pre-processing step of first using the eigenfunctions to simulate a low-frequency wave moving over the data and using both position a…

Hedging methods to mitigate the exposure of variable annuity products to market risks require the calculation of market risk sensitivities (or "Greeks"). The complex, path-dependent nature of these products means these sensitivities typically must be estimated by Monte Carlo simulation. Standard market practice is to m…

This is supplementary material for the main Geodesics article by the authors. In Appendix A, we present some general results on the construction of Gaussian random fields. In Appendix B, we restate our Shape Theorem, specialized to the setting of this article. In Appendix C, we state some straightforward consequences o…

In the modal approach to clustering, clusters are defined as the local maxima of the underlying probability density function, where the latter can be estimated either non-parametrically or using finite mixture models. Thus, clusters are closely related to certain regions around the density modes, and every cluster corr…

New measures detect HFT activity, revealing its impact on stock prices.

A machine learning model may exhibit discrimination when used to make decisions involving people. One potential cause for such outcomes is that the model uses a statistical proxy for a protected demographic attribute. In this paper we formulate a definition of proxy use for the setting of linear regression and present …

The failure of landing a job for college students could cause serious social consequences such as drunkenness and suicide. In addition to academic performance, unconscious biases can become one key obstacle for hunting jobs for graduating students. Thus, it is necessary to understand these unconscious biases so that we…

Study on optimal ReLU networks with weight decay for interpolation.

Study invariant minimizers in convex functions under amenable groups.