arXiv research

Elliptical processes generalize Gaussian and Student-t models with fat tails and computational efficiency.

We investigate the class of tempered stable distributions and their associated processes. Our analysis of tempered stable distributions includes limit distributions, parameter estimation and the study of their densities. Regarding tempered stable processes, we deal with density transformations and compute their $p$-var…

Bayesian Gaussian Processes layer detects out-of-distribution data in medical imaging.

Elliptical processes extend Gaussian models with heavier tails.

Bayesian layer improves image segmentation and out-of-distribution detection.

This paper investigates the use of distributed processing on the problem of emotion recognition from physiological sensors using a popular machine learning library on distributed mode. Specifically, we run a random forests classifier on the biosignal-data, which have been pre-processed to form exclusive groups in an un…

RML improves generative modeling of complex distributions.

The fractional Poisson process (FPP) is a counting process with independent and identically distributed inter-event times following the Mittag-Leffler distribution. This process is very useful in several fields of applied and theoretical physics including models for anomalous diffusion. Contrary to the well-known Poiss…

Study on gamma-related OU processes with simulation methods.

The Volterra square-root process shows non-uniqueness of limiting distributions and regularity of its law.

NDPs learn to sample from complex function distributions using neural networks and diffusion models.

Monge-Kantorovich distances, otherwise known as Wasserstein distances, have received a growing attention in statistics and machine learning as a powerful discrepancy measure for probability distributions. In this paper, we focus on forecasting a Gaussian process indexed by probability distributions. For this, we provid…

The seemingly disjoint problems of count and mixture modeling are united under the negative binomial (NB) process. A gamma process is employed to model the rate measure of a Poisson process, whose normalization provides a random probability measure for mixture modeling and whose marginalization leads to an NB process f…

Characterizes Lévy-driven Ornstein-Uhlenbeck processes linked to tempered stable distributions.

We investigate the pricing of cliquet options in a geometric Meixner model. The considered option is of monthly sum cap style while the underlying stock price model is driven by a pure-jump Meixner--Lévy process yielding Meixner distributed log-returns. In this setting, we infer semi-analytic expressions for the clique…

Personal income distributions in Japan are analyzed empirically and a simple stochastic model of the income process is proposed. Based on empirical facts, we propose a minimal two-factor model. Our model of personal income consists of an asset accumulation process and a wage process. We show that these simple processes…

We propose a stochastic process driven by the memory effect with novel distributions which include both exponential and leptokurtic heavy-tailed distributions. A class of the distributions is analytically derived from the continuum limit of the discrete binary process with the renormalized auto-correlation. The moment …

Process capability index (PCI) is a commonly used statistic to measure ability of a process to operate within the given specifications or to produce products which meet the required quality specifications. PCI can be univariate or multivariate depending upon the number of process specifications or quality characteristi…

CQNPs enhance predictive performance and distribution modeling using quantile regression.

Distributed Quantum Gaussian Processes improve modeling in multi-agent systems.

Gaussian process priors are commonly used in aerospace design for performing Bayesian optimization. Nonetheless, Gaussian processes suffer two significant drawbacks: outliers are a priori assumed unlikely, and the posterior variance conditioned on observed data depends only on the locations of those data, not the assoc…

Researchers use Gaussian processes to approximate Lagrange multipliers for Maximum-Entropy distributions.

Skew Gaussian Processes improve classification performance by allowing asymmetry.

A new method for deep Wishart processes improves kernel-based models.

This work introduces a new model for complex stochastic processes.

We find the explicit expression for the equilibrium wealth distribution of the Directed Random Market process, recently introduced by Martínez-Martínez and López-Ruiz, which turns out to be a Gamma distribution with shape parameter $\frac{1}{2}$. We also prove the convergence of the discrete-time process describing the…

We present a class of Lévy processes for modelling financial market fluctuations: Bilateral Gamma processes. Our starting point is to explore the properties of bilateral Gamma distributions, and then we turn to their associated Lévy processes. We treat exponential Lévy stock models with an underlying bilateral Gamma pr…

The paper analyzes multivariate Hawkes processes and their induced population processes.

Improved variational approximation for deep Wishart process models.

Paper introduces DQPOPE for estimating return distributions in reinforcement learning.

We analyze the Levy processes produced by means of two interconnected classes of non stable, infinitely divisible distribution: the Variance Gamma and the Student laws. While the Variance Gamma family is closed under convolution, the Student one is not: this makes its time evolution more complicated. We prove that -- a…

A new method for faster prediction in distributed Gaussian processes.

We consider fully connected feed-forward deep neural networks (NNs) where weights and biases are independent and identically distributed as symmetric centered stable distributions. Then, we show that the infinite wide limit of the NN, under suitable scaling on the weights, is a stochastic process whose finite-dimension…

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…

NCS enables efficient and accurate conditional simulation for complex spatial processes.

Conjugate pairs of distributions over infinite dimensional spaces are prominent in statistical learning theory, particularly due to the widespread adoption of Bayesian nonparametric methodologies for a host of models and applications. Much of the existing literature in the learning community focuses on processes posses…

Augmented bridge matching preserves coupling information between distributions.

Consider a reference Markov process with initial distribution $π_{0}$ and transition kernels $\{M_{t}\}_{t\in[1:T]}$, for some $T\in\mathbb{N}$. Assume that you are given distribution $π_{T}$, which is not equal to the marginal distribution of the reference process at time $T$. In this scenario, Schrödinger addressed t…

DistGP models multi-robot mapping with distributed Gaussian process learning.

Deep Gaussian Processes improve likelihood-free inference for complex distributions.

We study how the presence of correlations in physical variables contributes to the form of probability distributions. We investigate a process with correlations in the variance generated by (i) a Gaussian or (ii) a truncated Lévy distribution. For both (i) and (ii), we find that due to the correlations in the variance,…

Modified lognormal distribution with flexible tails for skewed data.

Under the Basel II standards, the Operational Risk (OpRisk) advanced measurement approach is not prescriptive regarding the class of statistical model utilised to undertake capital estimation. It has however become well accepted to utlise a Loss Distributional Approach (LDA) paradigm to model the individual OpRisk loss…

New GLPs split Lévy bridges into non-overlapping subprocesses.

A robust Gaussian process model using Huber likelihood for outlier resistance.

The study analyzes a model for aggregate losses with dependent and overdispersed inter-losses times.

The size distribution of land plots is a result of land allocation processes in the past. In the absence of regulation this is a Markov process leading an equilibrium described by a probabilistic equation used commonly in the insurance and financial mathematics. We support this claim by analyzing the distribution of tw…

Generative models learn latent process to match target distributions.