arXiv research

Lagrangian contact supersymmetries (depending on derivatives of arbitrary order) are treated in very general setting. The cohomology of the variational bicomplex on an arbitrary graded manifold and the iterated cohomology of a generic nilpotent contact supersymmetry are computed. In particular, the first variational fo…

Study tail risk aggregation under dependence uncertainty.

e-LOND algorithm controls FDR in online testing with arbitrary dependencies.

Paper tackles matrix estimation under arbitrary noise, achieving minimax optimality.

We introduce the notion of "special superpolynomials" by putting q=1 in the formulas for reduced superpolynomials. In this way we obtain a generalization of special HOMFLY polynomials depending on one extra parameter t. Special HOMFLY are known to depend on representation R in especially simple way: as |R|-th power of …

We prove a new lower bound for the dilatation of an arbitrary pseudo-Anosov map on a surface of genus g with n punctures. Our bound improves the former super-exponential dependence on the genus by a polynomial dependence.

We study the problem of learning graphical models with latent variables. We give the first algorithm for learning locally consistent (ferromagnetic or antiferromagnetic) Restricted Boltzmann Machines (or RBMs) with {\em arbitrary} external fields. Our algorithm has optimal dependence on dimension in the sample complexi…

We introduce the Randomized Dependence Coefficient (RDC), a measure of non-linear dependence between random variables of arbitrary dimension based on the Hirschfeld-Gebelein-Rényi Maximum Correlation Coefficient. RDC is defined in terms of correlation of random non-linear copula projections; it is invariant with respec…

Posterior Matching enables VAEs to model arbitrary conditional densities.

Paper improves signal proportion estimation by accounting for variable dependence.

Sequence feature embedding is a challenging task due to the unstructuredness of sequence, i.e., arbitrary strings of arbitrary length. Existing methods are efficient in extracting short-term dependencies but typically suffer from computation issues for the long-term. Sequence Graph Transform (SGT), a feature embedding …

We consider the problem of asynchronous online testing, aimed at providing control of the false discovery rate (FDR) during a continual stream of data collection and testing, where each test may be a sequential test that can start and stop at arbitrary times. This setting increasingly characterizes real-world applicati…

Monotone aggregation of dependent random vectors has an absolutely continuous distribution under certain conditions.

We introduce a class of dependence structures, that we call the Multiple Risk Factor (MRF) dependence structures. On the one hand, the new constructions extend the popular CreditRisk+ approach, and as such they formally describe default risk portfolios exposed to an arbitrary number of fatal risk factors with condition…

The study models insurance dependence using Bernstein copulas.

Study on coskewness under varying dependence uncertainty.

The quadric ansatz solves dKP equations in arbitrary dimensions, leading to Einstein-Weyl structures.

We present a unified derivation of covariant time derivatives, which transform as tensors under a time-dependent coordinate change. Such derivatives are essential for formulating physical laws in a frame-independent manner. Three specific derivatives are described: convective, corotational, and directional. The covaria…

We classify invariant Lagrangians of the form $L(g_{ij},g_{ij,k},g_{ij,kl},D_I,D_{I,j})$ depending at most quadratically on the variables $g_{ij,k},g_{ij,kl}$ and $D_I,D_{I,j}$, where $g$ is a Lorentz metric and $D$ is a tensor field of arbitrary rank on a smooth manifold. As a corollary, we prove a conjecture of Bray'…

Non-Euclidean, or incompatible elasticity is an elastic theory for pre-stressed materials, which is based on a modeling of the elastic body as a Riemannian manifold. In this paper we derive a dimensionally-reduced model of the so-called membrane limit of a thin incompatible body. By generalizing classical dimension red…

Optimizes insurance pricing to minimize ruin probability under various claim dependencies.

The Fu-Yau equation is an equation introduced by J. Fu and S.T. Yau as a generalization to arbitrary dimensions of an ansatz for the Strominger system. As in the Strominger system, it depends on a slope parameter $α'$. The equation was solved in dimension $2$ by Fu and Yau in two successive papers for $α'>0$, and for $…

The study examines MCMC methods for arbitrary objectives and finds likelihood sharpness impacts performance and regularization.

We compute Vassiliev invariants up to order six for arbitrary pretzel knots, which depend on $g+1$ parameters $n_1,\ldots,n_{g+1}$. These invariants are symmetric polynomials in $n_1,\ldots,n_{g+1}$ whose degree coincide with their order. We also discuss their topological and integer-valued properties.

This paper proposes a technique for the unsupervised detection and tracking of arbitrary objects in videos. It is intended to reduce the need for detection and localization methods tailored to specific object types and serve as a general framework applicable to videos with varied objects, backgrounds, and image qualiti…

In this work we prove the fact that, for a short time, it is possible to construct a smooth parametrized family of isometric embeddings of an arbitrary smooth parametrized family of Riemannian metrics on a smooth closed manifold into an Euclidean space. In order to prove this statement we work out stability estimates w…

We introduce a copula mixture model to perform dependency-seeking clustering when co-occurring samples from different data sources are available. The model takes advantage of the great flexibility offered by the copulas framework to extend mixtures of Canonical Correlation Analysis to multivariate data with arbitrary c…

A new tree-based estimator, FastPD, efficiently estimates PD functions for machine learning models.

A clustering method for multivariate populations with similar dependence structures.

We exhibit large classes of local actions for the vacuum Einstein equations. In presence of fermions, or more generally of matter which couple to the connection, these actions lead to inequivalent equations revealing an arbitrary number of parameters. Even in the pure gravitational sector, any corresponding quantum the…

We examine the dependence of the deformation obtained by bending quasi-Fuchsian structures on the bending lamination. We show that when we consider bending quasi-Fuchsian structures on a closed surface, the conditions obtained by Epstein and Marden to relate weak convergence of arbitrary laminations to the convergence …

Understanding the dependencies among features of a dataset is at the core of most unsupervised learning tasks. However, a majority of generative modeling approaches are focused solely on the joint distribution $p(x)$ and utilize models where it is intractable to obtain the conditional distribution of some arbitrary sub…

Randomly initialized neural networks can linearly separate arbitrary sets.

The estimation of dependencies between multiple variables is a central problem in the analysis of financial time series. A common approach is to express these dependencies in terms of a copula function. Typically the copula function is assumed to be constant but this may be inaccurate when there are covariates that cou…

We introduce the nonparametric metadata dependent relational (NMDR) model, a Bayesian nonparametric stochastic block model for network data. The NMDR allows the entities associated with each node to have mixed membership in an unbounded collection of latent communities. Learned regression models allow these memberships…

Proves positive mass theorem for spin initial data sets with arbitrary ends and dominant energy shields.

PED-ANOVA efficiently calculates HP importance in arbitrary subspaces.

We prove Noether's direct and inverse second theorems for Lagrangian systems on fiber bundles in the case of gauge symmetries depending on derivatives of dynamic variables of an arbitrary order. The appropriate notions of reducible gauge symmetries and Noether's identities are formulated, and their equivalence by means…

We prove that the variance swap rate (fair strike) equals the price of a co-terminal European-style contract when the underlying is an exponential Markov process, time-changed by an arbitrary continuous stochastic clock, which has arbitrary correlation with the driving Markov process, provided that the payoff function …

Paper presents robust confidence sequences for means with known moment bounds and arbitrary corruption.

We consider a contextual version of multi-armed bandit problem with global knapsack constraints. In each round, the outcome of pulling an arm is a scalar reward and a resource consumption vector, both dependent on the context, and the global knapsack constraints require the total consumption for each resource to be bel…

Study on tilings of the plane with two types of tiles of varying areas.

For $n\geq 1$, we exhibit a lower bound for the volume of a unit vector field on $\mathbb{S}^{2n+1}\backslash\{\pm p\}$ depending on the absolute values of its Poincaré indices around $\pm p$. We determine which vector fields achieve this volume, and discuss the idea of having multiple isolated singularities of arbitra…

New random forest variants achieve optimal performance in high dimensions.

New quantum algorithm simplifies complex financial derivatives pricing.

New measures quantify dependence between variables without distribution estimation.

A quantization over a manifold can be seen as a way to construct a differential operator with prescribed principal symbol. The quantization map is moreover required to be a linear bijection. It is known that there is in general no natural quantization procedure. However, considering manifolds endowed with additional st…

Study generalizes Möbius energy to non-smooth sets in arbitrary dimensions.