Learning Linear Dynamical Systems via Spectral Filtering

We present an efficient and practical algorithm for the online prediction of discrete-time linear dynamical systems with a symmetric transition matrix. We circumvent the non-convex optimization problem using improper learning: carefully overparameterize the class of LDSs by a polylogarithmic factor, in exchange for convexity of the loss functions. From this arises a polynomial-time algorithm with a near-optimal regret guarantee, with an analogous sample complexity bound for agnostic learning. Our algorithm is based on a novel filtering technique, which may be of independent interest: we convolve the time series with the eigenvectors of a certain Hankel matrix.Comment: Published as a conference paper at NIPS 201

Downlink Resource Scheduling in an LTE System

The problem of allocating resources to multiple users on the downlink of a Long Term Evolution (LTE) cellular communication system is discussed. An optimal (maximum throughput) multiuser scheduler is proposed and its performance is evaluated. Numerical results show that the system performance improves with increasing correlation among OFDMA subcarriers. It is found that a limited amount of feedback information can provide a relatively good performance. A sub-optimal scheduler with a lower computational complexity is also proposed, and shown to provide good performance. The sub-optimal scheme is especially attractive when the number of users is large, as the complexity of the optimal scheme may then be unacceptably high in many practical situations. The performance of a scheduler which addresses fairness among users is also presented

A combined spectroscopic and photometric stellar activity study of Epsilon Eridani

We present simultaneous ground-based radial velocity (RV) measurements and space-based photometric measurements of the young and active K dwarf Epsilon Eridani. These measurements provide a data set for exploring methods of identifying and ultimately distinguishing stellar photospheric velocities from Keplerian motion. We compare three methods we have used in exploring this data set: Dalmatian, an MCMC spot modeling code that fits photometric and RV measurements simultaneously; the FF$'$ method, which uses photometric measurements to predict the stellar activity signal in simultaneous RV measurements; and H$\alpha$ analysis. We show that our H$\alpha$ measurements are strongly correlated with photometry from the Microvariability and Oscillations of STars (MOST) instrument, which led to a promising new method based solely on the spectroscopic observations. This new method, which we refer to as the HH$'$ method, uses H$\alpha$ measurements as input into the FF$'$ model. While the Dalmatian spot modeling analysis and the FF$'$ method with MOST space-based photometry are currently more robust, the HH$'$ method only makes use of one of the thousands of stellar lines in the visible spectrum. By leveraging additional spectral activity indicators, we believe the HH$'$ method may prove quite useful in disentangling stellar signals