We present and study the Contribution-Selection algorithm (CSA), a novel algorithm for feature selection. The algorithm is based on the Multiperturbation Shapley Analysis, a framework which relies on game theory to estimate usefulness. The algorithm iteratively estimates the usefulness of features and selects them accordingly, using either forward selection or backward elimination. Empirical co...

We present and examine a novel Contribution-Selection algorithm (CSA) for feature selection based on the Multi-perturbation Shapley Analysis. The algorithm combines both the filter and wrapper approaches in a multi-phasic manner to estimate features’ usefulness and select them accordingly, either using forward selection or backward elimination. Empirical comparison of several feature selection ...

Dimension Reduction for Model-Based Clustering via Mixtures of Multivariate t-Distributions Katherine Morris Advisor University of Guelph, 2012 Prof. Paul D. McNicholas We introduce a dimension reduction method for model-based clustering obtained from a finite mixture of t-distributions. This approach is based on existing work on reducing dimensionality in the case of finite Gaussian mixtures. ...

Let X = (Xi,j)m×n,m ≥ n, be a complex Gaussian random matrix with mean zero and variance 1 n , let S = XX be a sample covariance matrix. In this paper we are mainly interested in the limiting behavior of eigenvalues when m n → γ ≥ 1 as n → ∞. Under certain conditions on k, we prove the central limit theorem holds true for the k-th largest eigenvalues λ(k) as k tends to infinity as n → ∞. The pr...

The notion of typical sequences plays a key role in the theory of information. Central to the idea of typicality is that a sequence x1, x2, . . . , xn that is PX -typical should, loosely speaking, have an empirical distribution that is in some sense close to the distribution PX . The two most common notions of typicality are that of strong (letter) typicality and weak (entropy) typicality. Whil...

An explicit formula is derived for the Fourier transform of a Gaussian measure on the Heisenberg group at the Schrödinger representation. Using this explicit formula, necessary and sufficient conditions are given for the convolution of two Gaussian measures to be a Gaussian measure.

We study a class of linear first and second order partial differential equations driven by weak geometric p-rough paths, and prove the existence of a unique solution for these equations. This solution depends continuously on the driving rough path. This allows a robust approach to stochastic partial differential equations. In particular, we may replace Brownian motion by more general Gaussian a...

In this paper we investigate Gaussian composition. Furthermore, we study the correspondence theorem of ideal classes and classes of binary quadratic forms. We also show a generalization of this correspondence and composition to higher dimensions recently discovered by Manual Bhargava. Along with this generalization, Gaussian composition is one of at least 14 such correspondences. Although, more...