Nearly optimal stochastic approximation for online principal subspace estimation

Nearly Optimal Competitive Online Replacement Policies

This paper studies the following online replacement problem. There is a real function f(t), called the ow rate, deened over a nite time horizon 0; T]. It is known that m f(t) M for some reals 0 m < M. At time 0 an online player starts to pay money at the rate f(0). At each time 0 < t T the player may changeover and continue paying money at the rate f(t). The complication is that each such chang...

Approximation Results for Preemptive Stochastic Online Scheduling

We present first constant performance guarantees for preemptive stochastic scheduling to minimize the sum of weighted completion times. For scheduling jobs with release dates on identical parallel machines we derive policies with a guaranteed performance ratio of 2 which matches the currently best known result for the corresponding deterministic online problem. Our policies apply to the recentl...

Nearly Optimal Robust Subspace Tracking and Dynamic Robust PCA

In this work, we study the robust subspace tracking (RST) problem and obtain one of the first two provable guarantees for it. The goal of RST is to track sequentially arriving data vectors that lie in a slowly changing low-dimensional subspace, while being robust to corruption by additive sparse outliers. It can also be interpreted as a dynamic (time-varying) extension of robust PCA (RPCA), wit...

Sinusoidal frequency estimation by signal subspace approximation

Eigenvector-based methods such as multiple signal classification (MUSIC) are currently popular in sinusoidal frequency estimation due to their high resolution. A problem with these methods is the often high cost of estimating the eigenvectors of the autocorrelation matrix spanning the signal (or noise) subspace. In this work, we propose an efficient Fourier transform-based method avoiding eigen...

Optimal and nearly optimal online and semi-online algorithms for some scheduling problems