Related papers: Technical report: Two observations on probability …
We study a symmetric random walk (RW) in one spatial dimension in environment, formed by several zones of finite width, where the probability of transition between two neighboring points and corresponding diffusion coefficient are…
For a distribution $p:=\{p_k\}_{k=1}^\infty$ on the positive integers, there are two natural ways to construct a random permutation in $S_n$ or of $\mathbb{N}$ from IID samples from $p$--the $p$-biased construction and the $p$-shifted…
Interesting data often concentrate on low dimensional smooth manifolds inside a high dimensional ambient space. Random projections are a simple, powerful tool for dimensionality reduction of such data. Previous works have studied bounds on…
We show how random subspace methods can be adapted to estimating local projections with many controls. Random subspace methods have their roots in the machine learning literature and are implemented by averaging over regressions estimated…
The computational complexity of some depths that satisfy the projection property, such as the halfspace depth or the projection depth, is known to be high, especially for data of higher dimensionality. In such scenarios, the exact depth is…
We consider the hypothesis testing problem of detecting a shift between the means of two multivariate normal distributions in the high-dimensional setting, allowing for the data dimension p to exceed the sample size n. Specifically, we…
A systematic study of the probability distribution of superimposed random codes is presented through the use of generating functions. Special attention is paid to the cases of either uniformly distributed but not necessarily independent or…
This article deals with random projections applied as a data reduction technique for Bayesian regression analysis. We show sufficient conditions under which the entire $d$-dimensional distribution is approximately preserved under random…
In probability theory, there is a tendency to treat one random variable with a given distribution as being just as good as any other. By and large this is fine because probability is (mostly) concerned with distributional properties of…
This paper considers distributed statistical inference for general symmetric statistics %that encompasses the U-statistics and the M-estimators in the context of massive data where the data can be stored at multiple platforms in different…
A typical computational geometry problem begins: Consider a set P of n points in R^d. However, many applications today work with input that is not precisely known, for example when the data is sensed and has some known error model. What if…
The idea of slicing divergences has been proven to be successful when comparing two probability measures in various machine learning applications including generative modeling, and consists in computing the expected value of a `base…
Motivated by recent work of Au, C{\'e}bron, Dahlqvist, Gabriel, and Male, we study regularity properties of the distribution of a sum of two selfad-joint random variables in a tracial noncommutative probability space which are free over a…
Spherical symmetry arguments are used to produce a general device to convert identities and inequalities for the $p$th absolute moments of real-valued random variables into the corresponding identities and inequalities for the $p$th moments…
A formalism is presented for analytically obtaining the probability density function, (P_{n}(s)), for the random distance (s) between two random points in an (n)-dimensional spherical object of radius (R). Our formalism allows (P_{n}(s)) to…
Let $P$ be a probability distribution on $q$-dimensional space. The so-called Diaconis-Freedman effect means that for a fixed dimension $d << q$, most $d$-dimensional projections of $P$ look like a scale mixture of spherically symmetric…
The conformations of topologically constrained double-folded ring polymers can be described as wrappings of randomly branched primitive trees. We extend previous work on the tree statistics under different (solvent) conditions to explore…
In this paper we describe a theory of a cumulative distribution function on a space with an order from a probability measure defined in this space. This distribution function plays a similar role to that played in the classical case.…
The classic likelihood ratio test for testing the equality of two covariance matrices breakdowns due to the singularity of the sample covariance matrices when the data dimension $p$ is larger than the sample size $n$. In this paper, we…
We formulate and investigate a statistical inverse problem of a random tomographic nature, where a probability density function on $\mathbb{R}^3$ is to be recovered from observation of finitely many of its two-dimensional projections in…