Similarity measures are essential to solve many pattern recognition problems such as classification, clustering, and retrieval problems. Various similarity measures are categorized in both syntactic and semantic relationships. In this paper we present a novel similarity, Unilateral Jaccard Similarity Coefficient (uJaccard), which doesn’t only take into consideration the space among two points b...

This paper studies a general class of nonlinear varying coefficient time series models with possible nonstationarity in both the regressors and the varying coefficient components. The model accommodates a cointegrating structure and allows for endogeneity with contemporaneous correlation among the regressors, the varying coefficient drivers, and the residuals. This framework allows for a mixtur...

We are interested in learning causal relationships between pairs of random variables, purely from observational data. To effectively address this task, the state-of-the-art relies on strong assumptions on the mechanisms mapping causes to effects, such as invertibility or the existence of additive noise, which only hold in limited situations. On the contrary, this short paper proposes to learn h...

Elements in a sample date are demonstrated based on their characteristics and in turn the characteristics are represented by variables. Identifying the relationship between these variables is crucial for prediction, hypothesis testing, and decision making. The relation between two variables is often quantified using a correlation factor. Once correlation is known it can be used to make predicti...

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...