arXiv research

Score-fPINN tackles high-dimensional FPL equations using fractional score functions.

MAFLA improves sampling from heavy-tailed distributions using MH-inspired corrections.

Generative Fractional Diffusion Models improve image diversity and quality.

The paper explores how score-driven models can approximate rough volatility.

As data sets grow in size, the ability of learning methods to find structure in them is increasingly hampered by the time needed to search the large spaces of possibilities and generate a score for each that takes all of the observed data into account. For instance, Bayesian networks, the model chosen in this paper, ha…

A method for finding most influential sets reduces a complex problem to a sequence of simpler top-$k$ problems.

Classifies intrinsically linked tournaments by their score sequences.

Paper bridges score estimation to parameter and density estimation in DDPMs.

Develops nonparametric regression for non-smooth functions using fractional Laplacian.

Study examines surfaces with bounded fractional mean curvature, proving control over local parametrization.

Extends fractional $L^p$ uncertainty principles with extremizers and stability results.

We extend neural networks with fractional and mixed activation functions for better function approximation.

Study asymptotics of Poisson kernel and Green's functions for fractional conformal Laplacian.

New framework for ranking distributions using variable fractional parameters.

We formulate the fractional Ricci flow theory for (pseudo) Riemannian geometries enabled with nonholonomic distributions defining fractional integro-differential structures, for non-integer dimensions. There are constructed fractional analogs of Perelman's functionals and derived the corresponding fractional evolution …

Study fractional perimeter asymptotics on Riemannian manifolds as $s$ approaches 0.

In this paper we established the condition for a curve to satisfy stochas- tic fractional HP (Hamilton-Pontryagin) equations. These equations are described using It^o integral. We have also considered the case of stochastic fractional Hamiltonian equa- tions, for a hyperregular Lagrange function. From the stochastic fr…

Proposes a method to measure similarity between anomaly scores from different methods.

Develops fractional de Rham theory for Maxwell equations.

The goal of this paper is to encode equivalently the fractional Lagrange dynamics as a nonholonomic almost Kahler geometry. We use the fractional Caputo derivative generalized for nontrivial nonlinear connections (N-connections) originally introduced in Finsler geometry, with further developments in Lagrange and Hamilt…

In this paper the fractional trading ansatz of money management is reconsidered with special attention to chance and risk parts in the goal function of the related optimization problem. By changing the goal function with due regards to other risk measures like current drawdowns, the optimal fraction solutions reflect t…

Researchers develop neural networks for approximating functions in Banach spaces.

Growth functions of Coxeter groups and the Poincare series of Kleinian and Fuchsian singularities are $2$-tangle $q$-fractions.

A new method calculates fractional moments using the moment-generating function.

We study two problems in high-dimensional robust statistics: \emph{robust mean estimation} and \emph{outlier detection}. In robust mean estimation the goal is to estimate the mean $μ$ of a distribution on $\mathbb{R}^d$ given $n$ independent samples, an $\varepsilon$-fraction of which have been corrupted by a malicious…

Approximates derivative pricing under fractional stochastic volatility.

Filtering data with a pre-trained model improves multimodal contrastive learning performance.

Study proposes a nonlocal approximation of the Willmore functional using fractional Allen-Cahn energies.

Study extends convexity in curved spaces using fractional integrals.

A mass-type invariant for smooth metric measure spaces and its relation with the fractional Yamabe problem

Study optimal partitions on spheres using fractional Q-curvature and variational methods.

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…

Deployment-complete benchmarking assesses if evidence leads to consistent deployment actions.

Regularization improves stability and consistency of sparse autoencoders.

New method uses fractional posteriors for semiparametric inference with improved uncertainty quantification.

It has been recently shown that rough volatility models, where the volatility is driven by a fractional Brownian motion with small Hurst parameter, provide very relevant dynamics in order to reproduce the behavior of both historical and implied volatilities. However, due to the non-Markovian nature of the fractional Br…

Empirical studies show that the volatility may exhibit correlations that decay as a fractional power of the time offset. The paper presents a rigorous analysis for the case when the stationary stochastic volatility model is constructed in terms of a fractional Ornstein Uhlenbeck process to have such correlations. It is…

Explains optimal functional inequalities, focusing on Sobolev and fractional Sobolev.

Here a new notion of fractional length of a smooth curve, which depends on a parameter $σ$, is introduced that is analogous to the fractional perimeter functional of sets that has been studied in recent years. It is shown that in an appropriate limit the fractional length converges to the traditional notion of length u…

In this work we propose a new class of long-memory models with time-varying fractional parameter. In particular, the dynamics of the long-memory coefficient, $d$, is specified through a stochastic recurrence equation driven by the score of the predictive likelihood, as suggested by Creal et al. (2013) and Harvey (2013)…

CJE calibrates cheap LLM judges against an oracle, achieving high accuracy at a fraction of the cost.

This chapter is an attempt to present a mathematical theory of compound fractional Poisson processes. The chapter begins with the characterization of a well-known Lévy process: The compound Poisson process. The semi-Markov extension of the compound Poisson process naturally leads to the compound fractional Poisson proc…

Study large deviations in fractional volatility models with non-Gaussian volatility.

A framework for sensitivity measures using scoring functions.

As Convolutional Neural Networks embed themselves into our everyday lives, the need for them to be interpretable increases. However, there is often a trade-off between methods that are efficient to compute but produce an explanation that is difficult to interpret, and those that are slow to compute but provide a more i…

The purpose of this article is to find a family of curves parametrized by arc length and that depend on an angular function and an intrinsic fraction function, which is defined as the quotient between torsion and curvature. We find for this family of curves explicit formulas of curvature, torsion and geodetic curvature…

We consider a fractional version of the Heston volatility model which is inspired by [16]. Within this model we treat portfolio optimization problems for power utility functions. Using a suitable representation of the fractional part, followed by a reasonable approximation we show that it is possible to cast the proble…

Study rough volatility models using path-dependent PDEs and fractional Brownian motions.