arXiv research

A new graphical model for discrete data without parametric restrictions.

Investigates VaR behavior for sums of one-sided random variables, showing impossibilities and conditions for super-additivity.

The paper explores risk-minimization for exponential additive models, providing mathematical expressions and numerical examples.

Simple conditions for comonotonic additive risk measures from acceptance sets.

Improved Bayesian optimization for conditional parameter spaces.

We present a novel approach for nonparametric regression using wavelet basis functions. Our proposal, $\texttt{waveMesh}$, can be applied to non-equispaced data with sample size not necessarily a power of 2. We develop an efficient proximal gradient descent algorithm for computing the estimator and establish adaptive m…

The paper identifies generators of linear SDEs with noise types.

Constraint-based structure learning algorithms infer the causal structure of multivariate systems from observational data by determining an equivalent class of causal structures compatible with the conditional independencies in the data. Methods based on additive-noise (AN) models have been proposed to further discrimi…

New method identifies causal relationships in presence of hidden variables.

Bayesian model estimates treatment effects near cutoffs in regression discontinuity designs.

Given a rational homology sphere M, whose splice diagram satisfy the semigroup condition, Neumann and Wahl were able to define a complete intersection surface singularity called splice diagram singularity from the splice diagram of M. They were also able to show that under an additional hypothesis on M called the congr…

We discuss the conditions for additional supersymmetry and twisted supersymmetry in N = (2, 2) supersymmetric non-linear sigma models described by one left and one right semi-chiral superfield and carrying a pair of non-commuting complex structures. Focus is on linear non-manifest transformations of these fields that h…

A RL-based method adds conditional controls to pre-trained diffusion models.

Thompson Sampling with bilateral uncertainty improves performance in Bayesian Optimization.

Novel covariance function improves Bayesian optimization efficiency.

Study on compact manifolds for exact G$_{2}$-Structures without additional constraints.

Identifying causal direction in location-scale noise models with hidden variables

We present a unified framework for estimation and analysis of generalized additive models in high dimensions. The framework defines a large class of penalized regression estimators, encompassing many existing methods. An efficient computational algorithm for this class is presented that easily scales to thousands of ob…

We propose a method for inferring the existence of a latent common cause ('confounder') of two observed random variables. The method assumes that the two effects of the confounder are (possibly nonlinear) functions of the confounder plus independent, additive noise. We discuss under which conditions the model is identi…

Probit Monotone BART estimates binary outcomes using monotonic functions.

In two recent papers necessary and sufficient conditions for a given system of second-order ordinary differential equations to be of Lagrangian form with additional dissipative forces were derived. We point out that these conditions are not independent and prove a stronger result accordingly.

We describe work on solutions of certain non-divergence type and therefore non-variational elliptic and parabolic systems on manifolds. These systems include Hermitian and affine harmonics which should become useful tools for studying Hermitian and affine manifolds, resp. A key point is that in addition to the standard…

We analyze a family of methods for statistical causal inference from sample under the so-called Additive Noise Model. While most work on the subject has concentrated on establishing the soundness of the Additive Noise Model, the statistical consistency of the resulting inference methods has received little attention. W…

We consider a 3-dimensional Riemannian manifold with additional structure q. We find a condition that the affine structure q is parallel with respect to the Riamannian connection.We prove the sectional curvatures of three 2-sections formed linearly independent vectors are equal among them.

Study pinched self-dual Weyl curvature in compact 4-manifolds.

v2: An additional assumption was added in Theorem 4.8. In order to show that a connected abelian group is admissible on the site of locally compact spaces we must in addition assume that it is locally topologically divisible. This condition is used in the proof of Lemma 4.62.

Let $S$ be any closed hyperbolic surface and let $λ$ be a maximal geodesic lamination on $S$. The amount of bending of an abstract pleated surface (homeomorphic to $S$) with the pleating locus $λ$ is completely determined by an $(\mathbb{R}/2π\mathbb{Z})$-valued finitely additive transverse cocycle $β$ to the geodesic …

Much recent work has concerned sparse approximations to speed up the Gaussian process regression from the unfavorable O(n3) scaling in computational time to O(nm2). Thus far, work has concentrated on models with one covariance function. However, in many practical situations additive models with multiple covariance func…

We investigate the formation of singularities for surfaces evolving by volume preserving mean curvature flow. For axially symmetric flows - surfaces of revolution - in $\mathbb{R}^3$ with Neumann boundary conditions, we prove that the first developing singularity is of Type I. The result is obtained without any additio…

Cosmological singularity theorems such as that of Hawking and Penrose assume local curvature conditions as well as global ones like the existence of a compact (achronal) slice. Here, we prove a new singularity theorem for chronological spacetimes that satisfy what we call a `past null focusing' condition. Such a condit…

New algorithm broadens BART models applicability.

Study Penrose inequality for metrics with singular sets.

We give the rectangle condition for strong irreducibility of Heegaard splittings of $3$-manifolds with non-empty boundary. We apply this to a generalized Heegaard splitting of a $2$-fold covering of $S^3$ branched along a link. The condition implies that any thin meridional level surface in the link complement is incom…

Study selective classification with halfspaces, achieving error bounds under Gaussian distributions.

Equilibrium pricing has been proven to underlie the rational Insured expectancy of premia additivity for composition of policies fully covering independent risks.

It is proven here that if the connected sum of two tunnel number one knots in the 3-sphere is a tunnel number two knot, then at least one of the summand knots has a genus two Heegaard splitting with a meridian as a primitive element. Hence this is a necessary and sufficient condition for tunnel number one knots to have…

Affine jump-diffusions constitute a large class of continuous-time stochastic models that are particularly popular in finance and economics due to their analytical tractability. Methods for parameter estimation for such processes require ergodicity in order establish consistency and asymptotic normality of the associat…

Paper classifies structures on 5D manifolds with specific rank and conditions.

In this paper, we study a new type of BSDE, where the distribution of the Y-component of the solution is required to satisfy an additional constraint, written in terms of the expectation of a loss function. This constraint is imposed at any deterministic time t and is typically weaker than the classical pointwise one a…

Characterizes spherical Finsler metrics satisfying a specific condition.

Two new estimators improve VAE training for hierarchical and prior parameters.

We study a portfolio selection problem in a continuous-time Itô-Markov additive market with prices of financial assets described by Markov additive processes which combine Lévy processes and regime switching models. Thus the model takes into account two sources of risk: the jump diffusion risk and the regime switching …

Despite recent advances, the remaining bottlenecks in deep generative models are necessity of extensive training and difficulties with generalization from small number of training examples. We develop a new generative model called Generative Matching Network which is inspired by the recently proposed matching networks …

The study examines different types of equilibria for stopping problems in one-dimensional diffusion processes.

A well-known property of the signature of closed oriented 4n-dimensional manifolds is Novikov additivity, which states that if a manifold is split into two manifolds with boundary along an oriented smooth hypersurface, then the signature of the original manifold equals the sum of the signatures of the resulting manifol…

New algorithm reduces bandit problem's regret bound to logarithmic in dimension.

Paper introduces a nonparametric functional graphical model for random functions.

Variable screening is a fast dimension reduction technique for assisting high dimensional feature selection. As a preselection method, it selects a moderate size subset of candidate variables for further refining via feature selection to produce the final model. The performance of variable screening depends on both com…