# Efficient Leverage Score Sampling for the Analysis of Big Time Series Data

## Seminar/Forum

Evan Williams Theatre
Peter Hall
We use randomized numerical linear algebra techniques to develop a new fast algorithm to estimate the leverage scores of an autoregressive model in big data regimes. We show that the accuracy of approximations lies within $(1 + O{\varepsilon})$ of the true leverage scores with high probability. These theoretical results are exploited to fit an appropriate autoregressive model to big time series data and approximately estimate its parameters by sampling the data matrix based on estimated leverage scores. Empirical results on large-scale synthetic as well as real data highly support the theoretical results and reveal the efficacy of this new approach.