arXiv research

New algorithm for risk-sensitive reinforcement learning with natural policy gradients.

Tensor decomposition methods are popular tools for learning latent variables given only lower-order moments of the data. However, the standard assumption is that we have sufficient data to estimate these moments to high accuracy. In this work, we consider the case in which certain dimensions of the data are not always …

The paper derives formulas for moments of a Student t distribution and applies them to quantify $L_p$-quantiles.

A new game-theoretic approach balances downside risk with expected reward.

This paper examines how data affects risk measures in uncertain distributions.

Stiefel-Whitney classes of moment-angle manifolds are trivial.

We show that the moment explosion time in the rough Heston model [El Euch, Rosenbaum 2016, arxiv:1609.02108] is finite if and only if it is finite for the classical Heston model. Upper and lower bounds for the explosion time are established, as well as an algorithm to compute the explosion time (under some restrictions…

The paper derives risk measures for metalog distributions.

The paper analyzes extreme risk measures with limited distributional information.

The third moment variation of a financial asset return process is defined by the quadratic covariation between the return and square return processes. The skew and fat tail risk of an underlying asset can be hedged using a third moment variation swap under which a predetermined fixed leg and the floating leg of the rea…

We show how to compute lower bounds for the supremum Bayes error if the class-conditional distributions must satisfy moment constraints, where the supremum is with respect to the unknown class-conditional distributions. Our approach makes use of Curto and Fialkow's solutions for the truncated moment problem. The lower …

A novel estimator for linear coefficients in semiparametric models without assuming model structure.

New SQ lower bounds for NGCA without requiring chi-squared condition.

In this paper, we investigate the popular deep learning optimization routine, Adam, from the perspective of statistical moments. While Adam is an adaptive lower-order moment based (of the stochastic gradient) method, we propose an extension namely, HAdam, which uses higher order moments of the stochastic gradient. Our …

Given a multisymplectic manifold $(M,ω)$ and a Lie algebra $\frak{g}$ acting on it by infinitesimal symmetries, Fregier-Rogers-Zambon define a homotopy (co-)moment as an $L_{\infty}$-algebra-homomorphism from $\frak{g}$ to the observable algebra $L(M,ω)$ associated to $(M,ω)$, in analogy with and generalizing the notio…

Python package ajdmom simplifies moment formula derivation for jump diffusions.

New method for causal inference with observed covariates improves learning rates.

MuML models predict molecular dipole moments using atomic partial charges and dipoles.

Paper proposes an efficient algorithm to handle high-order portfolio moments.

Estimates high-dimensional posterior densities by marginal distributions and neural networks.

The paper sets limits on the accuracy of macroeconomic forecasts based on statistical moments and trade volumes.

We propose a method of moments (MoM) algorithm for training large-scale implicit generative models. Moment estimation in this setting encounters two problems: it is often difficult to define the millions of moments needed to learn the model parameters, and it is hard to determine which properties are useful when specif…

Study finds the minimum number of finite Gaussian mixtures for best approximation.

We examine whether hedging effectiveness is affected by asymmetry in the return distribution by applying tail specific metrics to compare the hedging effectiveness of short and long hedgers using crude oil futures contracts. The metrics used include Lower Partial Moments (LPM), Value at Risk (VaR) and Conditional Value…

Learning rate needs to decrease with higher data moments for effective ICA in high dimensions.

The paper proves that Gaussian field critical points have finite moments.

Optimal SQ bounds for learning binary product distributions and Ising models.

Many interesting real world domains involve reinforcement learning (RL) in partially observable environments. Efficient learning in such domains is important, but existing sample complexity bounds for partially observable RL are at least exponential in the episode length. We give, to our knowledge, the first partially …

Paper develops methods for inference on time series data using neural networks and sieves.

The paper examines higher moments in insurance, focusing on coskewness and its impact on actuarial quantities.

This paper provides estimation and inference methods for an identified set's boundary (i.e., support function) where the selection among a very large number of covariates is based on modern regularized tools. I characterize the boundary using a semiparametric moment equation. Combining Neyman-orthogonality and sample s…

New method learns near-optimal policies with polynomial samples in A and H.

Sum-of-Squares lower bound shows NGCA requires more samples than known algorithms.

We show that the conformal structure for the Riemannian analogues of Kerr black-hole metrics can be given an ambitoric structure. We then discuss the properties of the moment maps. In particular, we observe that the moment map image is not locally convex near the singularity corresponding to the ring singularity in the…

Generalizes moment-angle manifolds to arbitrary nice manifolds with corners.

Study compares Kähler quotients of torus actions under varying moment maps.

Paper tackles stochastic control with mean and higher-order moments, finding Nash equilibria.

New approach to goal-based investing using hedging and reinforcement learning.

New estimator tackles multi-task linear regression with outliers, avoiding eigenvalue lower bounds.

Paper proposes robust risk measures for non-negative risks with partial information.

We prove explicit upper and lower bounds for the $L^1$-moment spectra for the Brownian motion exit time from extrinsic metric balls of submanifolds $P^m$ in ambient Riemannian spaces $N^{n}$. We assume that $P$ and $N$ both have controlled radial curvatures (mean curvature and sectional curvature, respectively) as view…

A new method extracts features and reconstructs moments in dynamical systems using information geometry.

Instead of controlling "symmetric" risks measured by central moments of investment return or terminal wealth, more and more portfolio models have shifted their focus to manage "asymmetric" downside risks that the investment return is below certain threshold. Among the existing downside risk measures, the lower-partial …

New algorithms avoid a dominant lower-order term in heavy-tailed loss settings.

Paper derives analytical formulas for NLD-CEV moments with regime switching.

Paper tackles moment estimation under covariate shift with a two-stage algorithm.

A new filter reduces density fitting to a linear solve, improving performance on nonlinear systems.

We consider a large, homogeneous portfolio of life or disability annuity policies. The policies are assumed to be independent conditional on an external stochastic process representing the economic-demographic environment. Using a conditional law of large numbers, we establish the connection between claims reserving an…