Related papers: Technical report: Two observations on probability …
Fourier analysis and representation of circular distributions in terms of their Fourier coefficients, is quite commonly discussed and used for model-free inference such as testing uniformity and symmetry etc. in dealing with 2-dimensional…
We develop a new variational scheme to approximate the position dependent spatial probability distribution of a zero dimensional manifold in a random medium. This celebrated 'toy-model' is associated via a mapping with directed polymers in…
Suppose X is a frequency vector that follows a central multiple hyper-geometric distribution, such as arises in random sampling of an m-category attribute from a finite population without replacement. We show that the probability that X…
We study the shrinking Pearson random walk in two dimensions and greater, in which the direction of the Nth is random and its length equals lambda^{N-1}, with lambda<1. As lambda increases past a critical value lambda_c, the endpoint…
Random projection is widely used as a method of dimension reduction. In recent years, its combination with standard techniques of regression and classification has been explored. Here we examine its use with principal component analysis…
We study the distribution regression problem assuming the distribution of distributions has a doubling measure larger than one. First, we explore the geometry of any distributions that has doubling measure larger than one and build a small…
The design of a metric between probability distributions is a longstanding problem motivated by numerous applications in Machine Learning. Focusing on continuous probability distributions on the Euclidean space $\mathbb{R}^d$, we introduce…
We present DUAL-LOCO, a communication-efficient algorithm for distributed statistical estimation. DUAL-LOCO assumes that the data is distributed according to the features rather than the samples. It requires only a single round of…
The aim of the present article is to introduce a concept which allows to generalise the notion of Poissonian pair correlation, a second-order equidistribution property, to higher dimensions. Roughly speaking, in the one-dimensional setting,…
Fitting linear regression models can be computationally very expensive in large-scale data analysis tasks if the sample size and the number of variables are very large. Random projections are extensively used as a dimension reduction tool…
As a typical dimensionality reduction technique, random projection can be simply implemented with linear projection, while maintaining the pairwise distances of high-dimensional data with high probability. Considering this technique is…
Probabilistic submeasures generalizing the classical (numerical) submeasures are introduced and discussed in connection with some classes of aggregation functions. A special attention is paid to triangular norm-based probabilistic…
Manifold hypothesis states that data points in high-dimensional space actually lie in close vicinity of a manifold of much lower dimension. In many cases this hypothesis was empirically verified and used to enhance unsupervised and…
We study random graphs with latent geometric structure, where the probability of each edge depends on the underlying random positions corresponding to the two endpoints. We focus on the setting where this conditional probability is a…
We introduce a new framework for dimension reduction in the context of high-dimensional regression. Our proposal is to aggregate an ensemble of random projections, which have been carefully chosen based on the empirical regression…
The probability distribution for the free energy of directed polymers in random media (DPRM) with uncorrelated noise in $d=1+1$ dimensions satisfies the Tracy-Widom distribution. We inquire if and how this universal distribution is modified…
The ratio $P(S_n=x)/P(Z_n=x)$ is investigated for three cases: (a) when $S_n$ is a sum of 1-dependent non-negative integer-valued random variables (rvs), satisfying some moment conditions, and $Z_n$ is Poisson rv; (b) when $S_n$ is a…
This article brings in two new discrete distributions: multidimensional Binomial distribution and multidimensional Poisson distribution. Those distributions were created in eventology as more correct generalizations of Binomial and Poisson…
We consider statistical analysis of double couple (DC) earthquake focal mechanism orientation. The symmetry of DC changes with its geometrical properties, and the number of 3-D rotations one DC source can be transformed into another depends…
Random matrix theory (RMT) is based on two assumptions: (1) matrix-element independence, and (2) base invariance. Most of the proposed generalizations keep the first assumption and violate the second. Recently, several authors presented…