Cross-validation method for bivariate measure with certain mixture

Companion Inequalities for Certain Bivariate Means

Sharp companion inequalities for certain bivariate means are obtained. In particular, companion inequalities for those discovered by Stolarsky and Sándor are established.

Factorizations of Certain Bivariate Polynomials

We determine the factorization of Xf(X) − Y g(Y ) over K[X, Y ] for all squarefree additive polynomials f, g ∈ K[X] and all fields K of odd characteristic. This answers a question of Kaloyan Slavov, who needed these factorizations in connection with an algebraic-geometric analogue of the Kakeya problem.

Gaussian mixture optimization for HMM based on efficient cross-validation

A Gaussian mixture optimization method is explored using cross-validation likelihood as an objective function instead of the conventional training set likelihood. The optimization is based on reducing the number of mixture components by selecting and merging a pair of Gaussians step by step base on the objective function so as to remove redundant components and improve the generality of the mod...

Bivariate Spline Method for

Measure for data partitioning in m × 2 cross-validation

An m × 2 cross-validation based on m half–half partitions is widely used in machine learning. However, the cross-validation performance often relies on the quality of the data partitioning. Poor data partitioning may cause poor inference results, such as a large variance and large Type I and II errors of the corresponding test. To evaluate the quality of the data partitioning, we propose a stat...