arXiv research

Method uses DNNs to approximate functions with specific asymptotic behavior.

We derive caplet volatilities for quadratic models, providing an asymptotic approximation.

We develop an efficient method to calibrate CDS spreads using asymptotic approximations.

We use geometric measure theory to introduce the notion of asymptotic cones associated with a singular subspace of a Riemannian manifold. This extends the classical notion of asymptotic directions usually defined on smooth submanifolds. We get a simple expression of these cones for polyhedra in E^3, as well as converge…

Stochastic approximation proves asymptotic normality for non-smooth problems.

Study on stochastic approximation with Polyak-Ruppert averaging for linear systems.

This paper establishes the asymptotic consistency of the {\it loss-calibrated variational Bayes} (LCVB) method. LCVB was proposed in~\cite{LaSiGh2011} as a method for approximately computing Bayesian posteriors in a `loss aware' manner. This methodology is also highly relevant in general data-driven decision-making con…

The paper develops time-uniform inference methods for stochastic approximation parameters.

Approximates bond option volatilities using affine short-rate models.

Paper approximates risk measures using SGD with Langevin dynamics.

We give a short proof of a strong version of the short time asymptotic expansion of heat kernels associated to Laplace type operators acting on sections of vector bundles over compact Riemannian manifolds, including exponential decay of the difference of the approximate heat kernel and the true heat kernel. We use this…

We present and implement two algorithms for analytic asymptotic evaluation of the marginal likelihood of data given a Bayesian network with hidden nodes. As shown by previous work, this evaluation is particularly hard for latent Bayesian network models, namely networks that include hidden variables, where asymptotic ap…

Stochastic algo learns from evolving data, achieving optimal performance.

In an abstract Wiener space setting, we constract a rigorous mathematical model of the one-loop approximation of the perturbative Chern-Simons integral, and derive its explicit asymptotic expansion for stochastic Wilson lines.

New algorithms improve likelihood of finding global optima in Bayesian inference.

Paper derives convergence rates and confidence intervals for LSA with Markovian noise.

Improved control approach for correlated bandits with better performance.

Asymptotic results for weighted floating bodies are established and used to obtain new proofs for the existence of floating areas on the sphere and in hyperbolic space and to establish the existence of floating areas in Hilbert geometries. Results on weighted best and random approximation and the new approach to floati…

The paper develops AMP theory for sparse and robust regression with polynomial iterations.

We conduct cluster analysis on a class of locally asymptotically self-similar stochastic processes, which includes multifractional Brownian motion as a representative. When the true number of clusters is supposed to be known, a new covariance-based dissimilarity measure is introduced, from which we obtain the approxima…

Optimal strategies are found for a repeated betting game using diffusion approximation.

The BBF, SABR, and rough SABR formulas provide nearly arbitrage-free implied vol approximations.

Randomized neural networks improve function approximation on manifolds.

Stochastic EM with biased MCMC improves inference stability.

Study on statistical inference for nonlinear stochastic approximation with Markovian data.

Asymptotic error distribution for approximation of a stochastic integral with respect to continuous semimartingale by Riemann sum with general stochastic partition is studied. Effective discretization schemes of which asymptotic conditional mean-squared error attains a lower bound are constructed. Two applications are …

Estimates Markov chain variance efficiently without storing samples.

In this paper, we consider an obstruction to asymptotic Chow-semistability of a polarized Kaehler algebraic manifold. Even when a linear algebraic group of positive dimension acts nontrivially and holomorphically on a polarized Kaehler algebraic manifold with constant scalar curvature, the vanishing of the obstruction …

This paper derives a new semi closed-form approximation formula for pricing an up-and-out barrier option under a certain type of stochastic volatility model including SABR model by applying a rigorous asymptotic expansion method developed by Kato, Takahashi and Yamada (2012). We also demonstrate the validity of our app…

Authors prove an asymptotic expansion for spectral zeta functions on discrete tori.

The paper proposes methods to estimate MCMC quality with couplings, bounding Wasserstein distance.

Paper analyzes LPSA algorithm for constrained optimization, revealing phase transitions and bias-variance trade-offs.

This work analyzes nonexpansive stochastic approximations with Markovian noise, proving convergence in reinforcement learning.

We study positive solutions of the Yamabe equation with isolated singularity and prove the existence of solutions with prescribed asymptotic expansions near singular points and an arbitrarily high order of approximation.

Unified framework for FDR control in knockoffs, validating Gaussian knockoffs.

This study presents new analytic approximations of the stochastic-alpha-beta-rho (SABR) model. Unlike existing studies that focus on the equivalent Black-Scholes (BS) volatility, we instead derive the equivalent constant-elasticity-of-variance (CEV) volatility. Our approach effectively reduces the approximation error i…

Paper improves confidence set construction for SGD using multiplier bootstrap.

Asynchronous stochastic approximations (SAs) are an important class of model-free algorithms, tools and techniques that are popular in multi-agent and distributed control scenarios. To counter Bellman's curse of dimensionality, such algorithms are coupled with function approximations. Although the learning/ control pro…

Double Q-learning has the same mean-squared error as Q-learning under certain conditions.

Paper develops Gaussian approximations and bootstrap for federated LSA with trade-off bounds.

New quasi-Newton method guarantees global superlinear convergence.

To any smooth compact manifold $M$ endowed with a contact structure $H$ and partially integrable almost CR structure $J$, we prove the existence and uniqueness, modulo high-order error terms and diffeomorphism action, of an approximately Einstein ACH (asymptotically complex hyperbolic) metric $g$ on $M\times (-1,0)$. W…

Paper examines risk measure expansions under FGM dependence, improving accuracy at extreme levels.

Stochastic approximation (SA) is a key method used in statistical learning. Recently, its non-asymptotic convergence analysis has been considered in many papers. However, most of the prior analyses are made under restrictive assumptions such as unbiased gradient estimates and convex objective function, which significan…

Randomization tests rely on simple data transformations and possess an appealing robustness property. In addition to being finite-sample valid if the data distribution is invariant under the transformation, these tests can be asymptotically valid under a suitable studentization of the test statistic, even if the invari…

Develops a new risk measure for Markov chains' asymptotic behavior.

New methods improve temporal difference learning for policy evaluation in Markov decision processes.

Study optimal and instance-dependent guarantees for solving linear equations with Markovian data.