A new sparse kernel probability density function (pdf) estimator based on zero-norm constraint is constructed using the classical Parzen window (PW) estimate as the target function. The so-called zero-norm of the parameters is used in order to achieve enhanced model sparsity, and it is suggested to minimize an approximate function of the zero-norm. It is shown that under certain condition, the ...

The maximum entropy method is a theoretically sound approach to construct an analytical form for the probability density function (pdf) given a sample of random events. In practice, numerical methods employed to determine the appropriate Lagrange multipliers associated with a set of moments are generally unstable in the presence of noise due to limited sampling. A robust method is presented tha...

Supervised relational learning over labeled graphs, e.g. via recursive neural nets, received considerable attention from the connectionist community. Surprisingly, with the exception of recursive self organizing maps, unsupervised paradigms have been far less investigated. In particular, no algorithms for density estimation over graphs are found in the literature. This paper introduces first a ...

The statistical properties of the multivariate GammaGamma (ΓΓ) distribution with arbitrary correlation have remained unknown. In this paper, we provide analytical expressions for the joint probability density function (PDF), cumulative distribution function (CDF) and moment generation function of the multivariate ΓΓ distribution with arbitrary correlation. Furthermore, we present novel approxim...

We present a nonlinear stochastic differential equation (SDE) which mimics the probability density function (PDF) of the return and the power spectrum of the absolute return in financial markets. Absolute return as a measure of market volatility is considered in the proposed model as a long-range memory stochastic variable. The SDE is obtained from the analogy with earlier proposed model of tra...

The distribution of backscattered intensities as described by the probability density function (PDF) of tissue-scattered light contains information that may be useful for tissue assessment and diagnosis, including characterization of its pathology. In this Letter, we examine the PDF description of the light scattering statistics in a well characterized tissue-like particulate medium using optic...

This paper discusses a novel method called ‘ICA with OS’ (‘Independent Component Analysis with Order Statistics’) to solve the vital problem of Blind Source Separation. The key of the procedure is a new alternative Gaussianity measure estimated by Order Statistics of the cdf (cumulative density function) instead of the common pdf (probability density function) moments. The maximization of this ...

[1] Spatial and temporal heterogeneity of ambient natural environments play a significant role in large scale transport phenomena. Uncertainty about spatio‐temporal fluctuations in system parameters (e.g., flow velocity) make deterministic predictions of macroscopic system states (e.g., solute concentration) elusive. Distributions of system states generally exhibit highly non‐Gaussian behavior,...

Deterministic population balance models including aggregation phenomena with more than two internal coordinates and without reduction to e.g. moments are to the best of the authors knowledge not published in literature so far. The problem of such models is the high computational demand and long simulation times which can easily reach the duration of weeks. Here the authors present a 3-dimension...