arXiv research

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

UN-AVOIDS visualizes and detects anomalies without needing labeled data.

Paper converts quantiles to cumulative distribution functions to simplify risk measures.

We study the rank distribution, the cumulative probability, and the probability density of returns of stock prices of listed firms traded in four stock markets. We find that the rank distribution and the cumulative probability of stock prices traded in are consistent approximately with the Zipf's law or a power law. It…

Proposes a method to partition univariate data into unimodal subsets.

New method corrects bias in datasets using cumulative distribution functions.

We leverage neural networks as universal approximators of monotonic functions to build a parameterization of conditional cumulative distribution functions (CDFs). By the application of automatic differentiation with respect to response variables and then to parameters of this CDF representation, we are able to build bl…

New model for density estimation using tensor trains.

Study refracted skew Brownian motion, find densities and asymptotics.

This paper investigates the rank distribution, cumulative probability, and probability density of price returns for the stocks traded in the KSE and the KOSDAQ market. This research demonstrates that the rank distribution is consistent approximately with the Zipf's law with exponent $α= -1.00$ (KSE) and -1.31 (KOSDAQ),…

Paper models and forecasts intra-day electricity price spreads.

This paper formulates dynamic density functions, based upon skewed-t and similar representations, to model and forecast electricity price spreads between different hours of the day. This supports an optimal day ahead storage and discharge schedule, and thereby facilitates a bidding strategy for a merchant arbitrage fac…

We investigate the distribution function and the cumulative probability for Korean household incomes, i.e., the current, labor, and property incomes. For our case, the distribution functions are consistent with a power law. It is also showed that the probability density of income growth rates almost has the form of a e…

Exponential dispersion model is a useful framework in machine learning and statistics. Primarily, thanks to the additive structure of the model, it can be achieved without difficulty to estimate parameters including mean. However, tight conditions on cumulant function, such as analyticity, strict convexity, and steepne…

This work tackles multivariate CDFs and copulas using tensor factorization.

Spectral analysis of neighborhood graphs is one of the most widely used techniques for exploratory data analysis, with applications ranging from machine learning to social sciences. In such applications, it is typical to first encode relationships between the data samples using an appropriate similarity function. Popul…

We investigate the position of the Buchen-Kelly density in a family of entropy maximising densities which all match European call option prices for a given maturity observed in the market. Using the Legendre transform which links the entropy function and the cumulant generating function, we show that it is both the uni…

A new model uses neural networks to efficiently learn multivariate temporal point processes.

Develops deep learning for fast, accurate option pricing models.

We consider discrete graphical models Markov with respect to a graph $G$ and propose two distributed marginal methods to estimate the maximum likelihood estimate of the canonical parameter of the model. Both methods are based on a relaxation of the marginal likelihood obtained by considering the density of the variable…

When selecting locations for a set of facilities, standard clustering algorithms may place unfair burden on some individuals and neighborhoods. We formulate a fairness concept that takes local population densities into account. In particular, given $k$ facilities to locate and a population of size $n$, we define the "n…

Study spectral density of neural networks using resolvent method.

A flexible nonparametric online changepoint detection algorithm for high-frequency data.

The problem of inhomogeneous cluster densities has been a long-standing issue for distance-based and density-based algorithms in clustering and anomaly detection. These algorithms implicitly assume that all clusters have approximately the same density. As a result, they often exhibit a bias towards dense clusters in th…

Estimates financial market impacts of COVID-19 using time-varying kernel density.

A new method for density estimation using nearest neighbor Dirichlet mixtures.

New scoring rules for multivariate distributions and level sets.

This work studies the chord length distribution, in the case where both ends lie on a $N$-dimensional hypersphere ($N \geq 2$). Actually, after connecting this distribution to the recently estimated surface of a hyperspherical cap \cite{SLi11}, closed-form expressions of both the probability density function and the cu…

Private estimation of many quantiles using differential privacy.

SNG-DBSCAN clusters data faster with subsampled similarity queries.

Graph representation learning, aiming to learn low-dimensional representations which capture the geometric dependencies between nodes in the original graph, has gained increasing popularity in a variety of graph analysis tasks, including node classification and link prediction. Existing representation learning methods …

We propose a novel approach for density estimation with exponential families for the case when the true density may not fall within the chosen family. Our approach augments the sufficient statistics with features designed to accumulate probability mass in the neighborhood of the observed points, resulting in a non-para…

GT is a new method for denoising and enhancing datasets using Gaussian density estimates.

Structure learning in random fields has attracted considerable attention due to its difficulty and importance in areas such as remote sensing, computational biology, natural language processing, protein networks, and social network analysis. We consider the problem of estimating the probabilistic graph structure associ…

Paper uses a new copula to model risk aggregation and capital allocation.

The CSA-ES is an Evolution Strategy with Cumulative Step size Adaptation, where the step size is adapted measuring the length of a so-called cumulative path. The cumulative path is a combination of the previous steps realized by the algorithm, where the importance of each step decreases with time. This article studies …

Improved regret bounds for adversarial linear contextual bandits.

Plots show miscalibration directly as slopes of secant lines.

A new UU-test decides unimodality of datasets.

Introduces CuFun model for more accurate TPPs using CDF.

In this work, we study the problem of reconstructing shapes from simple nonasymptotic densities measured only along shape boundaries. The particular density we study is also known as the integral area invariant and corresponds to the area of a disk centered on the boundary that is also inside the shape. It is easy to s…

A new GAN loss function based on cumulant generating functions improves stability and robustness.

New approach to Generalized Beta family using SDEs.

Algorithm infers sampling distribution from i.i.d. samples without supervision.

In this work we present an analytical model, based on the path-integral formalism of Statistical Mechanics, for pricing options using first-passage time problems involving both fixed and deterministically moving absorbing barriers under possible non-gaussian distributions of the underlying object. We adapt to our probl…

Unified framework for various probability distribution distances.

We investigate relaxation and correlations in a class of mean-reverting models for stochastic variances. We derive closed-form expressions for the correlation functions and leverage for a general form of the stochastic term. We also discuss correlation functions and leverage for three specific models -- multiplicative,…

The study compares parametric and nonparametric models for estimating mean-variance mixtures and finds that nonparametric models perform better.