A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
New models for short rates show longer periods at higher rates.
Fold maps associated to geodesic random walks on curved spaces.
Graph diffusion processes approximate manifold heat semigroups using graph transition matrices.
Proposes a method for approximating transition densities of SDEs driven by gamma processes.
Study refracted skew Brownian motion, find densities and asymptotics.
We consider a Markov process , which is the solution of a stochastic differential equation driven by a Lévy process and an independent Wiener process . Under some regularity conditions, including non-degeneracy of the diffusive and jump components of the process as well as smoothness of the Lévy density of $Z…
FourNet approximates financial transition densities using Fourier transforms.
An unsupervised learning algorithm to cluster hyperspectral image (HSI) data is proposed that exploits spatially-regularized random walks. Markov diffusions are defined on the space of HSI spectra with transitions constrained to near spatial neighbors. The explicit incorporation of spatial regularity into the diffusion…
Calibrating a Lévy process usually requires characterizing its jump distribution. Traditionally this problem can be solved with nonparametric estimation using the empirical characteristic functions (ECF), assuming certain regularity, and results to date are mostly in 1D. For multivariate Lévy processes and less smooth …
We introduce closed-form transition density expansions for multivariate affine jump-diffusion processes. The expansions rely on a general approximation theory which we develop in weighted Hilbert spaces for random variables which possess all polynomial moments. We establish parametric conditions which guarantee existen…
Study on signal recovery from low-rank matrix with sparse noise.
We prove a Weyl Law for the phase transition spectrum based on the techniques of Liokumovich-Marques-Neves. As an application we give phase transition adaptations of the proofs of the density and equidistribution of minimal hypersufaces for generic metrics by Irie-Marques-Neves and Marques-Neves-Song, respectively. We …
We analyse a linear regression problem with nonconvex regularization called smoothly clipped absolute deviation (SCAD) under an overcomplete Gaussian basis for Gaussian random data. We propose an approximate message passing (AMP) algorithm considering nonconvex regularization, namely SCAD-AMP, and analytically show tha…
New findings confirm parallels to De Giorgi's conjecture for phase transitions in higher dimensions.
This paper develops a novel analytically tractable Neumann series of Bessel functions representation for pricing (and hedging) European-style double barrier knock-out options, which can be applied to the whole class of one-dimensional time-homogeneous diffusions even for the cases where the corresponding transition den…
Regularized mixtures improve inflation and interest rate forecasts, especially correcting overconfidence.
New method resolves density ratio estimation saturation issues.
In this paper we introduce efficient Monte Carlo estimators for the valuation of high-dimensional derivatives and their sensitivities (''Greeks''). These estimators are based on an analytical, usually approximative representation of the underlying density. We study approximative densities obtained by the WKB method. Th…
New method learns diffusion transition density for Bayesian inference.
We consider a defaultable asset whose risk-neutral pricing dynamics are described by an exponential Levy-type martingale subject to default. This class of models allows for local volatility, local default intensity, and a locally dependent Levy measure. Generalizing and extending the novel adjoint expansion technique o…
This paper derives the non-analytic solution to the Fokker-Planck equation of fractional Brownian motion using the method of Laplace transform. Sequentially, by considering the fundamental solution of the non-analytic solution, this paper obtains the transition probability density function of the random variable that i…
Method estimates noise transition matrix from noisy labels without relying on unreliable class-posterior estimation.
A new method learns robust policies from offline data with latent structures.
This work improves convergence guarantees for unadjusted HMC in KL and Rényi divergences.
This paper shows semi-equivelar toroidal maps are vertex-transitive covers.
We show that a surface group contained in a reductive real algebraic group can be deformed to become Zariski dense, unless its Zariski closure acts transitively on a Hermitian symmetric space of tube type. This is a kind of converse to a rigidity result of Burger, Iozzi and Wienhard.
The paper introduces new estimators for multivariate functions using Fourier methods.
We discuss the geometric foundation behind the use of stochastic processes in the frame bundle of a smooth manifold to build stochastic models with applications in statistical analysis of non-linear data. The transition densities for the projection to the manifold of Brownian motions developed in the frame bundle lead …
SMRL uses score matching for efficient RL with exponential family models.
The goal of reinforcement learning (RL) is to let an agent learn an optimal control policy in an unknown environment so that future expected rewards are maximized. The model-free RL approach directly learns the policy based on data samples. Although using many samples tends to improve the accuracy of policy learning, c…
New filters for non-linear systems achieve closed-form solutions.
Detect changes in noisy dynamical systems using empirical approximations and finite-sample bounds.
This work reveals how label noise can cause a final ascent in neural network performance curves.
We find various exact solutions for a new stochastic volatility (SV) model: the transition probability density, European-style option values, and (when it exists) the martingale defect. This may represent the first example of an SV model combining exact solutions, GBM-type volatility noise, and a stationary volatility …
Study phase transitions in noisy transformer dynamics on spheres.
New study shows low-degree polynomial algorithms struggle at clause densities close to Fix's.
Paper proposes a new approach to optimal transport for vector and matrix densities.
Improves GCNNs with node transition probabilities and DropNode regularization.
Anosov flows found on many hyperbolic 3-manifolds.
The paper analyzes the score field of diffusion models using Burgers dynamics.
Study non-transitive pseudo-Anosov flows using group actions.
The calculation of minimum energy paths for transitions such as atomic and/or spin re-arrangements is an important task in many contexts and can often be used to determine the mechanism and rate of transitions. An important challenge is to reduce the computational effort in such calculations, especially when ab initio …
Proposes a thermodynamic work minimization framework for guiding generative models.
Representations based on random walks can exploit discrete data distributions for clustering and classification. We extend such representations from discrete to continuous distributions. Transition probabilities are now calculated using a diffusion equation with a diffusion coefficient that inversely depends on the dat…
Recurrent neural networks are a widely used class of neural architectures. They have, however, two shortcomings. First, it is difficult to understand what exactly they learn. Second, they tend to work poorly on sequences requiring long-term memorization, despite having this capacity in principle. We aim to address both…
Stable solutions to a specific equation are one-dimensional.
We study optimal estimation for sparse principal component analysis when the number of non-zero elements is small but on the same order as the dimension of the data. We employ approximate message passing (AMP) algorithm and its state evolution to analyze what is the information theoretically minimal mean-squared error …
This work explores efficient reinforcement learning with density features in low-rank MDPs.