arXiv research

This study links blockchain design to cryptos' distributional characteristics.

The paper simulates Lévy processes and their extremum and hitting time.

We connect shift-invariant characteristic kernels to infinitely divisible distributions on $\mathbb{R}^{d}$. Characteristic kernels play an important role in machine learning applications with their kernel means to distinguish any two probability measures. The contribution of this paper is two-fold. First, we show, usi…

We determine the expected curvature polynomial of random real projective varieties given as the zero set of independent random polynomials with Gaussian distribution, whose distribution is invariant under the action of the orthogonal group. In particular, the expected Euler characteristic of such random real projective…

Paper presents characteristic function of Tsallis q-Gaussian and its applications.

CCs learn high-dimensional distributions from heterogeneous data.

For large-scale industrial processes under closed-loop control, process dynamics directly resulting from control action are typical characteristics and may show different behaviors between real faults and normal changes of operating conditions. However, conventional distributed monitoring approaches do not consider the…

ECS evaluates synthetic CXR images' distributional fidelity.

In mathematical finance and other applications of stochastic processes, it is frequently the case that the characteristic function may be known but explicit forms for density functions are not available. The simulation of any distribution is greatly facilitated by a knowledge of the quantile function, by which uniforml…

Study investigates induced geometry on surfaces in 3D contact manifolds.

Extends residue theory to flags of holomorphic distributions.

Paper proposes GAS-ALD model for financial risk prediction.

Introduces partial Jacobi manifolds in convenient spaces.

We study a Laplacian operator related to the characteristic cohomology of a smooth manifold endowed with a distribution. We prove that this Laplacian does not behave very well: it is not hypoelliptic in general and does not respect the bigrading on forms in a complex setting. We also discuss the consequences of these n…

Time-subordinated Brownian motion models improve financial market stochastic distribution.

A new method for fair classification using characteristic function distance.

The study explains stock return distributions using reaction functions.

Review and generalize Haefliger's differentiable cohomology for diffeomorphisms and flat Cartan groupoids.

The effectiveness of biosignal generation and data augmentation with biosignal generative models based on generative adversarial networks (GANs), which are a type of deep learning technique, was demonstrated in our previous paper. GAN-based generative models only learn the projection between a random distribution as in…

A statistical test of independence may be constructed using the Hilbert-Schmidt Independence Criterion (HSIC) as a test statistic. The HSIC is defined as the distance between the embedding of the joint distribution, and the embedding of the product of the marginals, in a Reproducing Kernel Hilbert Space (RKHS). It has …

Germs of Goursat distributions can be classified according to a geometric coding called an RVT code. Jean (1996) and Mormul (2004) have shown that this coding carries precisely the same data as the small growth vector. Montgomery and Zhitomirskii (2010) have shown that such germs correspond to finite jets of Legendrian…

The multivariate version of the Mixed Tempered Stable is proposed. It is a generalization of the Normal Variance Mean Mixtures. Characteristics of this new distribution and its capacity in fitting tails and capturing dependence structure between components are investigated. We discuss a random number generating procedu…

Survey on Nambu-Poisson structures in infinite dimensions.

Unified method for calculating financial option prices from characteristic functions.

Demand functions for goods are generally cyclical in nature with characteristics such as trend or stochasticity. Most existing demand forecasting techniques in literature are designed to manage and forecast this type of demand functions. However, if the demand function is lumpy in nature, then the general demand foreca…

Implicit Generative Models (IGMs) such as GANs have emerged as effective data-driven models for generating samples, particularly images. In this paper, we formulate the problem of learning an IGM as minimizing the expected distance between characteristic functions. Specifically, we minimize the distance between charact…

Optimal portfolio selection problems are determined by the (unknown) parameters of the data generating process. If an investor wants to realise the position suggested by the optimal portfolios, he/she needs to estimate the unknown parameters and to account for the parameter uncertainty in the decision process. Most oft…

It is well known that a foliation F of a smooth manifold M gives rise to a rich cohomological theory, its characteristic (i.e., leafwise) cohomology. Characteristic cohomologies of F may be interpreted, to some extent, as functions on the space P of integral manifolds (of any dimension) of the characteristic distributi…

New method compresses non-Gaussian distributions exponentially.

ReVol normalizes stock price features to mitigate distribution shifts, improving prediction accuracy.

In 1910 E. Cartan constructed a canonical frame and found the most symmetric case for maximally nonholonomic rank 2 distributions in $\mathbb R^5$. We solve the analogous problem for germs of generic rank 2 distributions in ${\mathbb R}^n$ for n>5. We use a completely different approach based on the symplectification o…

The paper gives the complete characterization of all graded nilpotent Lie algebras with infinite-dimensional Tanaka prolongation as extensions of graded nilpotent Lie algebras of lower dimension by means of a commutative ideal. We introduce a notion of weak characteristics of a vector distribution and prove that if a b…

A definition for elliptical tempered stable distribution, based on the characteristic function, have been explained which involve a unique spectral measure. This definition provides a framework for creating a connection between infinite divisible distribution, and particularly elliptical tempered stable distribution, w…

Study examines implied volatility behavior in Bachelier model.

Proposes a new method to describe graph vertex features using characteristic functions.

A new GAN model uses characteristic functions to improve image generation.

We derive a general multivariate theory for realised characteristics of `model-free discretisation-invariant swaps', so-called because the standard no-arbitrage assumption of martingale forward prices is sufficient to derive fair-value swap rates for such characteristics which have no jump or discretisation errors. Thi…

Classifies non-integrable distributions with simple infinite-dimensional Lie superalgebras of symmetries.

A new model for stock price fluctuations is proposed, based upon an analogy with the motion of tracers in Gaussian random fields, as used in turbulent dispersion models and in studies of transport in dynamically disordered media. Analytical and numerical results for this model in a special limiting case of a single-sca…

This paper analyzes consumer choices over lunchtime restaurants using data from a sample of several thousand anonymous mobile phone users in the San Francisco Bay Area. The data is used to identify users' approximate typical morning location, as well as their choices of lunchtime restaurants. We build a model where res…

This paper introduces DCE for better counterfactual explanations using optimal transport.

This note optimizes distributions using kernel mean embeddings with a new parameterization.

Strictly proper kernel scores are well-known tool in probabilistic forecasting, while characteristic kernels have been extensively investigated in the machine learning literature. We first show that both notions coincide, so that insights from one part of the literature can be used in the other. We then show that the m…

Kernel mean embeddings have recently attracted the attention of the machine learning community. They map measures $μ$ from some set $M$ to functions in a reproducing kernel Hilbert space (RKHS) with kernel $k$. The RKHS distance of two mapped measures is a semi-metric $d_k$ over $M$. We study three questions. (I) For a…

In foreign exchange markets monotonic rate changes can be observed in time scale of order of an hour on the days that governmental interventions took place. We estimate the starting time of an intervention using this characteristic behavior of the exchange rates. We find that big amount of interventions can shift the a…

Efficient algorithm learns mixture models of heavy-tailed distributions.

Improved eigenvalue distribution method for financial data.

Estimates personalized policies robust to shifts in target populations.