arXiv research

This work improves SGMs' convergence guarantees for semiconvex distributions with discontinuous gradients.

Properties of two classes of generally convex sets in the n-dimentional real Euclidean space, called m-semiconvex and weakly m-semiconvex, 1<=m<n, are investigated in the present work. In particular, it is established that an open set with smooth boundary in the plan which is weakly 1-semiconvex but not 1-semiconvex co…

Estimates for polynomial operators using determinant majorization and subharmonics.

Equipped with the L^2-distortion distance, the space "X" of all metric measure spaces (X,d,m) is proven to have nonnegative curvature in the sense of Alexandrov. Geodesics and tangent spaces are characterized in detail. Moreover, classes of semiconvex functionals and their gradient flows on "X" are presented.

The paper proves constant rank theorems for special Lagrangian equations.

We consider an optimal stochastic impulse control problem over an infinite time horizon motivated by a model of irreversible investment choices with fixed adjustment costs. By employing techniques of viscosity solutions and relying on semiconvexity arguments, we prove that the value function is a classical solution to …

Solutions near infinity to special Lagrangian equations are asymptotic to quadratic polynomials with logarithmic terms.

We prove that ideal sub-Riemannian manifolds (i.e., admitting no non-trivial abnormal minimizers) support interpolation inequalities for optimal transport. A key role is played by sub-Riemannian Jacobi fields and distortion coefficients, whose properties are remarkably different with respect to the Riemannian case. As …

Geodesics found in spacetime satisfy curvature conditions.

Given a real-valued function $c$ defined on the cartesian product of a generic Carnot group $\G$ and the first layer $V_1$ of its Lie algebra, we introduce a notion of $c$ horizontal convex ($c$ H-convex) function on $\G$ as the supremum of a suitable family of affine functions; this family is defined pointwisely, and …

Paper analyzes convergence of proximal algorithm in metric spaces without geodesic convexity.

The paper explores solutions to the distributional Bellman equation in reinforcement learning.

Proposes vMF distribution for skewed elliptical distributions.

Study calculates tail risk for various mixture distributions.

We realise the first and second Grushin distributions as symmetry reductions of the 3-dimensional Heisenberg distribution and 4-dimensional Engel distribution respectively. Similarly, we realise the Martinet distribution as an alternative symmetry reduction of the Engel distribution. These reductions allow us to derive…

Recent work has shown that deep generative models assign higher likelihood to out-of-distribution inputs than to training data. We show that a factor underlying this phenomenon is a mismatch between the nature of the prior distribution and that of the data distribution, a problem found in widely used deep generative mo…

Method uses optimal transport to complete distributional matrices.

Income and wealth distribution affect stability of a society to a large extent and high inequality affects it negatively. Moreover, in the case of developed countries, recently has been proven that inequality is closely related to all negative phenomena affecting society. So far, Econophysics papers tried to analyse in…

Study clusters distributions with known or unknown clusters using distribution testing.

Gradually Truncated Log-normal distribution - Size distribution of firms Abstract Many natural and economical phenomena are described through power law or log- normal distributions. In these cases, probability decreases very slowly with step size compared to normal distribution. Thus it is essential to cut-off these di…

A new distribution family extends the $\alpha$-stable distribution with a degree of freedom parameter.

Paper develops a new method to improve model calibration under distribution shifts.

New class of heavy-tailed distributions shows weighted averages dominate individual variables.

Researchers derived formulas for joint moments of elliptical distributions.

Paper proposes a new method for designing materials using deep learning.

One-shot algorithm for feature-distributed kernel PCA reduces communication costs.

Paper finds how many neurons are needed to approximate histogram distributions.

Paper analyzes origami slope gaps and their distribution, finding a unique pattern.

A new distributed clustering framework using distributional kernel.

Paper introduces a new distributional successor measure for reinforcement learning.

The paper extends distributions by singular curves, revealing structural equivalences.

Random matrix ensembles yield uniform distributions on manifolds.

New distributions allow greedy arm selection in sparse bandit problems.

Study error bounds in evaluating distributional computational graphs.

Study on continuous sequence classification with distribution uncertainty.

The paper shows strong correlation between in-distribution and out-of-distribution performance in various machine learning models.

Study explores geometric structure and prior for beta-logistic distribution.

We propose to interpret distribution model risk as sensitivity of expected loss to changes in the risk factor distribution, and to measure the distribution model risk of a portfolio by the maximum expected loss over a set of plausible distributions defined in terms of some divergence from an estimated distribution. The…

Method learns statistics of return distributions via neural networks and maximum mean discrepancy.

Deep networks can approximate high-dimensional distributions from low-dimensional ones.

The paper defines MTCov for skewed elliptical distributions.

Paper proposes MMC to avoid high-density bias in clustering.

Universal tester-learner for halfspaces over structured distributions.

The paper uses FRFT to fit GTS distribution to asset returns.

Proves Sard conjecture for specific distributions, controlling divergence of vector fields.

The study improves model performance prediction on unseen distributions.

New method relaxes TV distance for two-sample testing without distributional assumptions.

New theory of distributions on spaces with singular submanifolds.