arXiv research

An analytic solution for asset allocation with Laplace distribution.

A mixture of shifted asymmetric Laplace distributions is introduced and used for clustering and classification. A variant of the EM algorithm is developed for parameter estimation by exploiting the relationship with the general inverse Gaussian distribution. This approach is mathematically elegant and relatively comput…

This paper investigates the statistical properties of within-country GDP and industrial production (IP) growth rate distributions. Many empirical contributions have recently pointed out that cross-section growth rates of firms, industries and countries all follow Laplace distributions. In this work, we test whether als…

Researchers calculate the Laplace transform of a geometric Brownian motion integral.

Bayesian meta-reinforcement learning improves over point estimates with Laplace approximation.

Corrected and improved simulation methods for Dirichlet-Laplace prior.

Improved bounds for estimating discrete distributions in KL divergence.

QLA improves Bayesian uncertainty estimation for DNNs without increasing computational cost.

Paper proposes GAS-ALD model for financial risk prediction.

We obtain an asymptotic formula for the eigenvalue distribution function of the Laplace-Beltrami operator on the two-dimensional torus in the adiabatic limit given by a Kronecker foliation. Related problems in number theory are discussed.

This research proves that quadratic regularized optimal transport can approximate the Laplace-Beltrami operator on smooth manifolds.

New techniques save bits in image compression with upsampling.

Modeling stock returns and volatility using a bivariate gamma generalized Laplace law.

Develops a new method to compute risk-sharing allocations using Laplace transforms.

The paper calculates moments and conditional risks for skewed elliptical distributions.

The paper uses the variance-gamma model to price options and explain excess kurtosis.

Modeling stock returns is not a new task for mathematicians, investors, and portfolio managers, but it remains a difficult objective due to the ebb and flow of stock markets. One common solution is to approximate the distribution of stock returns with a normal distribution. However, normal distributions place infinites…

A family of parsimonious shifted asymmetric Laplace mixture models is introduced. We extend the mixture of factor analyzers model to the shifted asymmetric Laplace distribution. Imposing constraints on the constitute parts of the resulting decomposed component scale matrices leads to a family of parsimonious models. An…

Enhances predictive performance in Bayesian deep learning via generalized Laplace approximation.

Researchers derive an explicit Laplace transform for integrated Volterra Wishart process.

Fast approximate inference for non-Gaussian data.

Improves Laplace approximation for Bayesian inference on Riemannian manifolds.

Bayesian neural networks approximate Gaussian, this method adapts to non-Gaussian posteriors.

For a fundamental solution of Laplace's equation on the $R$-radius $d$-dimensional hypersphere, we compute the azimuthal Fourier coefficients in closed form in two and three dimensions. We also compute the Gegenbauer polynomial expansion for a fundamental solution of Laplace's equation in hyperspherical geometry in geo…

We introduce a model of proportional growth to explain the distribution $P(g)$ of business firm growth rates. The model predicts that $P(g)$ is Laplace in the central part and depicts an asymptotic power-law behavior in the tails with an exponent $ζ=3$. Because of data limitations, previous studies in this field have b…

We propose a generalized double Pareto prior for Bayesian shrinkage estimation and inferences in linear models. The prior can be obtained via a scale mixture of Laplace or normal distributions, forming a bridge between the Laplace and Normal-Jeffreys' priors. While it has a spike at zero like the Laplace density, it al…

Paper develops privacy-preserving mechanisms for machine learning using wavelet transforms.

This study examines the practical equivalence of Laplace and neural tangent kernels.

In this paper we propose a novel framework for the construction of sparsity-inducing priors. In particular, we define such priors as a mixture of exponential power distributions with a generalized inverse Gaussian density (EP-GIG). EP-GIG is a variant of generalized hyperbolic distributions, and the special cases inclu…

Efficiently transforms samples from various statistical models.

Bayesian tensor train kernel machine uses Laplace approximation for scalable GP regression.

Exact 1-Wasserstein distance between location-scale distributions derived, with privacy effects studied.

New method calculates geometric Brownian motion with affine drift and its integral.

This paper stidies the first passage times to constant boundaries for mixed-exponential jump diffusion processes. Explicit solutions of the Laplace transforms of the distribution of the first passage times, the joint distribution of the first passage times and undershoot (overshoot) are obtained. As applications, we pr…

New VAE model improves data fitting without sacrificing computational efficiency.

Proposes sampling from reverse diffusion posteriors for contextual bandits.

A novel Laplace-approximated Bayesian Tensor Network Kernel Machine (LA-TNKM) provides principled uncertainty estimates.

Logistic Gaussian process (LGP) priors provide a flexible alternative for modelling unknown densities. The smoothness properties of the density estimates can be controlled through the prior covariance structure of the LGP, but the challenge is the analytically intractable inference. In this paper, we present approximat…

On a compact Kähler manifold there is a canonical action of a Lie-superalgebra on the space of differential forms. It is generated by the differentials, the Lefschetz operator and the adjoints of these operators. We determine the asymptotic distribution of irreducible representations of this Lie-superalgebra on the eig…

Efficiently approximates uncertainty in classification models using Dirichlet distributions.

The future predictive performance of a Bayesian model can be estimated using Bayesian cross-validation. In this article, we consider Gaussian latent variable models where the integration over the latent values is approximated using the Laplace method or expectation propagation (EP). We study the properties of several B…

L2R learns to denoise images without needing noise distribution knowledge.

A new method combines ANN and Laplace for fast Bayesian inference in ODE models.

New iterative methods improve Vecchia-Laplace approximations for large data sets.

The paper presents an evolutionary economic model for the price evolution of stocks. Treating a stock market as a self-organized system governed by a fast purchase process and slow variations of demand and supply the model suggests that the short term price distribution has the form a logistic (Laplace) distribution. T…

We analyze a simple asset transfer model in which the transfer amount is a fixed fraction $f$ of the giver's wealth. The model is analyzed in a new way by Laplace transforming the master equation, solving it analytically and numerically for the steady-state distribution, and exploring the solutions for various values o…

Proposes an alternative probabilistic interpretation of Huber loss.

It is proved that if a Paley-Wiener family of eigenfunctions of the Laplace operator in $\mathbb R^3$ vanishes on a real analytically ruled two-dimensional surface $S \subset \mathbb R^3$ then $S$ is a union of cones, each of which is contained in a translate of the zero set of a nonzero harmonic homogeneous polynomial…