Linear Predictions and Occam's Razor

A time series is, mathematically, a sequence of real numbers which is revealed to us one element at a time. Examples abound: stock prices, temperature readings, medical data, an audio stream, etc. In many cases, we are interested in learning a pattern among a set of many time series, such as among prices in a stock market. In this talk, we will explore the possibility of learning linear identities among time series. In particular, we will focus on the discovery of _sparse_ linear identities --- those which depend on only a small number of time series (hence Occam's Razor). We will see theoretical evidence that sparsity is indeed a good indicator of predictive power in our model, as well as an efficient incremental algorithm for updating predictions as the time series evolve.