Minimax-robust filtering of functionals from periodically correlated random fields

SHIFT OPERATOR FOR PERIODICALLY CORRELATED PROCESSES

The existence of shift for periodically correlated processes and its boundedness are investigated. Spectral criteria for these non-stationary processes to have such shifts are obtained.

Local Functionals and Generalized Random Fields

Spectral Theory for Periodically and Almost Periodically Correlated Random Processes: A Survey

This paper contains a survey of the spectral theory of periodically correlated and almost periodically correlated stochastic processes. These processes are also called cyclostationary and almost cyclostationary, and we give give some remarks concerning the historical development of the two nomenclatures. In this paper we survey the spectral theory of the covariance, the estimation of the Fourie...

Collaborative filtering via sparse Markov random fields

Recommender systems play a central role in providing individualized access to information and services. This paper focuses on collaborative filtering, an approach that exploits the shared structure among mind-liked users and similar items. In particular, we focus on a formal probabilistic framework known as Markov random fields (MRF). We address the open problem of structure learning and introd...

Minimax Estimation of Quadratic Fourier Functionals

We study estimation of (semi-)inner products between two nonparametric probability distributions, given IID samples from each distribution. These products include relatively well-studied classical L and Sobolev inner products, as well as those induced by translation-invariant reproducing kernels, for which we believe our results are the first. We first propose estimators for these quantities, a...