arXiv research

Introduces Exponentially Weighted Signature for better path representation.

Signature volatility models are analyzed for existence, arbitrage, completeness, and hedging-error decomposition.

This paper develops a path-first theory using signatures and jump lifts for self-exiting processes.

Volterra signature provides a clear, interpretable feature for history-dependent systems.

Signatures simplify analysis of evolving data streams.

Global approximation for piecewise linear paths via signatures.

Functional input neural networks approximate continuous functions on weighted spaces.

We compute the average Tristram---Levine signature of any graph link with positive weights in a three sphere, generalizing the results of Kirby and Melvin. The main tools are the Neumann's algorithm for computing the equivariant signatures of graph links and the Reciprocity Law for Dedekind sums.

A new neural network model reduces features in high-dimensional sequential data.

Reconstructing signature features from randomized vector fields in differential equations.

Signature portfolios approximate optimal wealth in non-Markovian markets.

We give manifolds in both the Riemannian and in the higher signature settings whose Riemann curvature operators commute, i.e. which satisfy R(a,b)R(c,d)=R(c,d)R(a,b) for all tangent vectors. These manifolds have global geometric phenomena which are quite different for higher signature manifolds than they are for Rieman…

Researchers develop Malliavin calculus for signatures, simplifying option Greeks computation.

Extends online learning to metric spaces using exponential weights.

Universal approximation for stochastic processes using Brownian motion.

We introduce a covariance matrix estimator that both takes into account the heteroskedasticity of financial returns (by using an exponentially weighted moving average) and reduces the effective dimensionality of the estimation (and hence measurement noise) via techniques borrowed from random matrix theory. We calculate…

Study on TQFT signatures converging to modular form.

Generative model prices basket options efficiently.

A new method for exponentially weighted moving models using approximations.

Scalable machine learning with path signatures for time series and graphs.

It is well known that the classification of the Weyl tensor in Lorentzian manifolds of dimension four, the so called Petrov classification, was a great tool to the development of general relativity. Using the bivector approach it is shown in this article a classification for the Weyl tensor in all four-dimensional mani…

Researchers extend asymptotic analysis to Bergman projections with Gevrey weights.

A new VWAP execution method using transformer and signature features.

The study analyzes how neural reward models learn features for policy optimization in a Gaussian single-index model.

Paper explores exact recovery of communities in weighted graphs using Gaussian and exponential distributions.

A new accelerated method with simpler momentum update rules.

The paper extends a prediction method to curved spaces.

Paper analyzes sparse aggregation in GLMs with Kullback-Leibler risk bounds.

Decentralized algorithm reduces regret and converges to Nash equilibrium in online congestion games.

We improve deep threshold networks' memorization capacity exponentially.

Abstract result on correlations of pairs in exponentially growing discrete subsets.

New algorithm optimizes online network resource allocation with long-term constraints.

Paper characterizes DLN distribution, its properties, and estimation methods.

Nonuniform tubular neighborhoods of curves in Euclidean n-space are studied by using weighted distance functions and generalizing the normal exponential map. Different notions of injectivity radii are introduced to investigate singular but injective exponential maps. A generalization of the thickness formula is obtaine…

We propose an explicit recursive method to approximate a power-law with a finite sum of weighted exponentials. Applications to moving averages with long memory are discussed in relationship with stochastic volatility models.

Improved averaging method for noisy observations converges strongly.

New aggregation strategy handles unbounded losses with regret bounds.

Annealed Entropic Allocation improves ranking and selection by mitigating hard switching and improving finite-budget discrimination.

Study addresses RTB model performance drops due to distribution shifts.

Guyon-Lekeufack model accurately predicts market volatility.

A checkerboard graph of a special diagram of an oriented link is made a directed, edge-weighted graph in a natural way so that a principal minor of its Laplacian matrix is a Seifert matrix of the link. Doubling and weighting the edges of the graph produces a second Laplacian matrix such that a principal minor is an Ale…

Let $φ\in C^\infty(\Complex^n)$ be a given real valued function. We assume that $\pr\ddbarφ$ is non-degenerate of constant signature $(n_-,n_+)$ on $\Complex^n$. When $q=n_-$, it is well-known that the Bergman kernel for $(0,q)$ forms with respect to the $k$-th weight $e^{-2kφ}$, $k>0$, admits a full asymptotic expansi…

Develops a new fuzzy model using QPs and ewl2 regularization to improve local region behavior.

AEW estimator achieves optimal risk in expectation for large enough temperatures.

This work improves polynomial approximations for functions with asymmetric behavior.

Researchers prove constant solutions for a specific Finslerian equation.

Efficiently optimizes boolean functions using multilinear polynomials and exponential weight updates.

Paper introduces kernel deformed exponential families for sparse continuous attention.