Random Fourier features is one of the most popular techniques for scaling up kernel methods, such as kernel ridge regression. However, despite impressive empirical results, the statistical properties of random Fourier features are still not well understood. In this paper we take steps toward filling this gap. Specifically, we approach random Fourier features from a spectral matrix approximation...

In this paper we define the modified q-Stancu-Beta operators and study the weighted statistical approximation by these operators with the help of the Korovkin type approximation theorem. We also establish the rates of statistical convergence by means of the modulus of continuity and the Lipschitz type maximal function. Our results show that rates of convergence of our operators are at least as ...

Variational approximations facilitate approximate inference for the parameters in complex statistical models and provide fast, deterministic alternatives to Monte Carlo methods. However, much of the contemporary literature on variational approximations is in Computer Science rather than Statistics, and uses terminology, notation, and examples from the former field. In this article we explain va...

We investigate the setting in which Monte Carlo methods are used and draw a parallel to the formal setting of statistical inference. In particular, we nd that Monte Carlo approximation gives rise to a bias-variance dilemma. We show that it is possible to construct a biased approximation scheme with a lower approximation error than a related unbiased algorithm.

We consider the space of analytic functions in polydisc with the topology of compact convergence, and prove some theorems on the approximation and statistical approximation of functions in this space by the sequences of linear operators.

In this work we introduce and investigate the ideas of statistical Riemann integrability, summability, Lebesgue integrability summability via deferred weighted mean. We first establish some fundamental limit theorems connecting these beautiful potentially useful notions. Furthermore, based upon our proposed techniques, Korovkin-type approximation with algebraic test functions. Finally, present ...