Oblivious Sketching for Logistic Regression

What guarantees are possible for solving logistic regression in one pass over a data stream? To answer this question, we present the first data oblivious sketch for logistic regression. Our sketch can be computed in input sparsity time over a turnstile data stream and reduces the size of a d-dimensional data set from n to only poly(mu d log n) weighted points, where mu is a useful parameter which captures the complexity of compressing the data. Solving (weighted) logistic regression on the sketch gives an O(log n)-approximation to the original problem on the full data set. We also show how to obtain an O(1)-approximation with slight modifications. Our sketches are fast, simple, easy to implement, and our experiments demonstrate their practicality.