arXiv research

A new DL framework preserves geometric structures for causal predictions.

We propose a differentiable nonparametric algorithm, the Delaunay triangulation learner (DTL), to solve the functional approximation problem on the basis of a $p$-dimensional feature space. By conducting the Delaunay triangulation algorithm on the data points, the DTL partitions the feature space into a series of $p$-d…

We study the finite horizon Merton portfolio optimization problem in a general local-stochastic volatility setting. Using model coefficient expansion techniques, we derive approximations for the both the value function and the optimal investment strategy. We also analyze the `implied Sharpe ratio' and derive a series a…

GeoStat simplifies time series classification with fast, intuitive features.

We explore the connection between two problems that have arisen independently in the signal processing and related fields: the estimation of the geometric mean of a set of symmetric positive definite (SPD) matrices and their approximate joint diagonalization (AJD). Today there is a considerable interest in estimating t…

New method improves DAG learning by using large coefficients for higher-order terms.

Graph Neural Networks improve financial time series forecasting accuracy.

This is a survey of our research on geometric structures of projective embeddings and includes some topics of our talks in several symposia during 1990-99. We clarify our main problem, which is to construct a kind of geometric composition series of projective embeddings. The concept of "geometric composition series" is…

New explanation of reservoir computing using random projections.

The study of record statistics of correlated series is gaining momentum. In this work, we study the records statistics of the time series of select stock market data and the geometric random walk, primarily through simulations. We show that the distribution of the age of records is a power law with the exponent $α$ lyi…

New algebraic approach for approximating Hamiltonian dynamics.

New findings on how convolutional architectures approximate time series data.

DM approximates submanifolds with error bounds.

Geometric pruning rules improve change point detection in multiple time series.

QABBA improves time series storage efficiency while preserving shape information.

Using classical Taylor series techniques, we develop a unified approach to pricing and implied volatility for European-style options in a general local-stochastic volatility setting. Our price approximations require only a normal CDF and our implied volatility approximations are fully explicit (ie, they require no spec…

Extends diffusion models to non-Euclidean spaces with geometric priors.

This article revisits an analysis on inaccuracies of time series averaging under dynamic time warping conducted by \cite{Niennattrakul2007}. The authors presented a correctness-criterion and introduced drift-outs of averages from clusters. They claimed that averages are inaccurate if they are incorrect or drift-outs. F…

Geometric Gaussian approximations capture any distribution.

Generative Adversarial Graph Neural Network (Sig-Graph GAN) models financial time series data.

The paper reviews Hankel low-rank methods for time series analysis and forecasting.

The paper proposes using path signatures for better inference in time series data.

For geometrically finite hyperbolic manifolds $Γ\backslash H^{n+1}$, we prove the meromorphic extension of the resolvent of Laplacian, Poincaré series, Einsenstein series and scattering operator to the whole complex plane. We also deduce the asymptotics of lattice points of $Γ$ in large balls of $H^{n+1}$ in terms of t…

NCDEs improve predictions for irregular time series data.

We propose an approximation algorithm for efficient correlation search in time series data. In our method, we use Fourier transform and neural network to embed time series into a low-dimensional Euclidean space. The given space is learned such that time series correlation can be effectively approximated from Euclidean …

Geometric analysis of nonlinear dynamics applied to financial time series.

We develop a geometric scattering theory for a geometrically finite group acting on (a vector bundle over) a symmetric space of negative curvature. In particular, we obtain the meromorphic continuation of Eisenstein series and scattering matrices and their functional equations.

We propose a new perspective on representation learning in reinforcement learning based on geometric properties of the space of value functions. We leverage this perspective to provide formal evidence regarding the usefulness of value functions as auxiliary tasks. Our formulation considers adapting the representation t…

ASTRA improves TDA by more accurately approximating iHVP.

Motion Code models time series dynamics with sparse approximations.

New scalable GP approximation using Fourier series decomposition.

New sampling method for Heston model reduces complexity.

New method for estimating high-dimensional binary time series coefficients.

Neural likelihood approximates integer time series data efficiently.

New geometric proof of convex function differentiability and approximation.

Kernel quadrature improves CRPS estimation for probabilistic time-series forecasting.

A perturbative approach is used to derive approximations of arbitrary order to estimate high percentiles of sums of positive independent random variables that exhibit heavy tails. Closed-form expressions for the successive approximations are obtained both when the number of terms in the sum is deterministic and when it…

Bayesian analysis of financial time series using R-INLA.

This is the first in a series of four papers (with research announcement posted on this arXiv) that together develop a decomposition theory for subgroups of Out(F_n). In this paper we develop further the theory of geometric EG strata of relative train track maps originally introduced in the work of Bestvina, Feighn, an…

Efficient method classifies locally stationary time series based on second-order characteristics.

JANA trains networks to approximate Bayesian models efficiently.

We prove and test an efficient series representation for the European Black-Scholes call, which generalizes and refines previously known approximations, and works in every market configuration.

Lie-Butcher (LB) series are formal power series expressed in terms of trees and forests. On the geometric side LB-series generalizes classical B-series from Euclidean spaces to Lie groups and homogeneous manifolds. On the algebraic side, B-series are based on pre-Lie algebras and the Butcher-Connes-Kreimer Hopf algebra…

GANs can approximate SDEs for large time steps.

Our aim is to prove that two formal power series of importance to quantum topology are Gevrey. These series are the Kashaev invariant of a knot (reformulated by Huynh and the second author) and the Gromov norm of the LMO of an integral homology 3-sphere. It follows that the power series associated to a simple Lie algeb…

Based on representation theory of Clifford algebra, Ferus, Karcher and Münzner constructed a series of isoparametric foliations. In this paper, we will survey recent studies on isoparametric hypersurfaces of OT-FKM type and investigate related geometric constructions with mean curvature flow.

Study geodesic properties of time series data using Wasserstein metric.

In this paper, a new algorithm based on differential geometry viewpoint to solve the 3D rotating Navier-Stokes equations with complex Boundary is proposed, which is called Bi-parallel algorithm. For xample, it can be applied to passage flow between two blades in impeller and circulation flow through aircrafts with comp…