Péter Kövesárki

Peter Kövesarki

This article applies the principle of Occam's Razor to non-parametric model building of statistical data, by finding a model with the minimal number of bits, leading to an exceptionally effective regularization method for probability density estimators. The idea comes from the fact that likelihood maximization also minimizes the number of bits required to encode a dataset. However, traditional methods overlook that the optimization of model parameters may also inadvertently play the part in encoding data points. The article shows how to extend the bit counting to the model parameters as well, providing the first true measure of complexity for parametric models. Minimizing the total bit requirement of a model of a dataset favors smaller derivatives, smoother probability density function estimates and most importantly, a phase space with fewer relevant parameters. In fact, it is able prune parameters and detect features with small probability at the same time. It is also shown, how it can be applied to any smooth, non-parametric probability density estimator.

Peter Kovesarki, Ian C. Brock

This article describes a multivariate polynomial regression method where the uncertainty of the input parameters are approximated with Gaussian distributions, derived from the central limit theorem for large weighted sums, directly from the training sample. The estimated uncertainties can be propagated into the optimal fit function, as an alternative to the statistical bootstrap method. This uncertainty can be propagated further into a loss function like quantity, with which it is possible to calculate the expected loss function, and allows to select the optimal polynomial degree with statistical significance. Combined with simple phase space splitting methods, it is possible to model most features of the training data even with low degree polynomials or constants.

Péter Kövesárki

This paper describes a novel method to approximate the polynomial coefficients of regression functions, with particular interest on multi-dimensional classification. The derivation is simple, and offers a fast, robust classification technique that is resistant to over-fitting.