We propose randomized techniques for speeding up Kernel Principal Component Analysis on three levels: sampling and quantization of the Gram matrix in training, randomized rounding in evaluating the kernel expansions, and random projections in evaluating the kernel itself. In all three cases, we give sharp bounds on the accuracy of the obtained approximations. Rather intriguingly, all three tech...

We present an algorithm to overcome the local maxima problem in estimating the parameters of mixture models. It combines existing approaches from both EM and a robust fitting algorithm, RANSAC, to give a data-driven stochastic learning scheme. Minimal subsets of data points, sufficient to constrain the parameters of the model, are drawn from proposal densities to discover new regions of high li...

Given a computable probability measure P over natural numbers or infinite binary sequences, there is no method that can produce an arbitrarily large sample such that all its members are typical of P . This paper also contains upper bounds on the minimal encoding length of a predicate (over the set of natural numbers) consistent with another predicate over a finite domain.

• In the quality control of a production process (of goods or services), from a statistical point of view, the focus is either on the process itself with application of Statistical Process Control or on its frontiers, with application of Acceptance Sampling (AS) and Experimental Design. AS is used to inspect either the process output (final product) or the process input (raw material). The purp...

The sampling method has been paid much attention in the field of complex network in general and statistical physics in particular. This paper presents two new sampling methods based on the perspective that a small part of vertices with high node degree can possess the most structure information of a network. The two proposed sampling methods are efficient in sampling the nodes with high degree....