Modeling probability density through ultraspherical polynomial transformations

ABSTRACT

We present a method for fitting parametric probability density models using an integrated square error criterion on a continuum of weighted Lebesgue spaces formed by ultraspherical polynomials. This approach is inherently suitable for creating mixture model representations of complex distributions and allows fully autonomous cluster analysis of high-dimensional datasets. The method is also suitable for extremely large sets, allowing post facto model selection and analysis even in the absence of the original data. Furthermore, the fitting procedure only requires the parametric model to be pointwise evaluable, making it trivial to fit user-defined models through a generic algorithm.

KEYWORDS:

• Cluster analysis
• Density estimation
• Multivariate analysis
• Orthogonal polynomials

MATHEMATICS SUBJECT CLASSIFICATION:

• 42C10
• 62G07
• 62H30

Funding

Work of LH supported by grant no. 24301034 from the Academy of Finland.