Reviews: Dimensionality Reduction for Stationary Time Series via Stochastic Nonconvex Optimization

Summary: The paper consider the setting of streaming PCA for time series data which contains two challenging ingredients: data stream dependence and a non-convex optimization manifold. The authors address this setting via downsampled version of Oja's algorithm. By closely inspecting the optimization manifold and using tools from the theory of stochastic differential equations, the authors provide a rather detailed analysis of the convergence behavior, along with confirming experiments on synthetic and real data. Evaluation: Streaming PCA is a fundamental setting in a topic which becomes increasingly important for the ML community, namely, time series analysis. Both data dependence and non-convex optimization are still at their anecdotal preliminary stage, and the algorithm and the analysis provided in the paper form an interesting contribution in this respect.