We introduce the Randomized Dependence Coefficient (RDC), a measure of nonlinear dependence between random variables of arbitrary dimension based on the Hirschfeld-Gebelein-Rényi Maximum Correlation Coefficient. RDC is defined in terms of correlation of random non-linear copula projections; it is invariant with respect to marginal distribution transformations, has low computational cost and is ...

In previous lectures we saw examples in which active learning gives an exponential improvement in the number of labels required for learning. In this lecture we describe the Disagreement Coefficient —a measure of the complexity of an active learning problem proposed by Steve Hanneke in 2007. We will derive an algorithm for the realizable case and analyze it using the disagreement coefficient. I...

For a prime p and nonnegative integers n, k, consider the set A (p) n,k = {x ∈ [0, 1, ..., n] : p|| ( n x ) }. Let the expansion of n + 1 in base p be n + 1 = α0p ν + α1p ν−1 + · · · + αν , where 0 ≤ αi ≤ p − 1, i = 0, . . . , ν. Then n is called a binomial coefficient predictor in base p(p-BCP), if |A (p) n,k| = αkp , k = 0, 1, . . . , ν. We give a full description of the p-BCP’s in every base p.

It has been a long history of using interactions in regression analysis to investigate alterations in covariate-effects on response variables. In this article, we aim to address two kinds of new challenges arising from the inclusion of such high-order effects in the regression model for complex data. The first kind concerns a situation where interaction effects of individual covariates are weak...

in this work, 137cs activity concentration of soil in five depths and in six meteorology stations in terms of bq/kg has been measured. for each thirty soil's samples, parameters such as kind of soil, density and hydraulic coefficient of transmission were determined. correlation coefficient between 137cs activity concentration and raining average, hydraulic coefficient of transmission and s...