Michael Busch

Michael Busch, Jeff Moehlis

We use statistical learning methods to construct an adaptive state estimator for nonlinear stochastic systems. Optimal state estimation, in the form of a Kalman filter, requires knowledge of the system's process and measurement uncertainty. We propose that these uncertainties can be estimated from (conditioned on) past observed data, and without making any assumptions of the system's prior distribution. The system's prior distribution at each time step is constructed from an ensemble of least-squares estimates on sub-sampled sets of the data via jackknife sampling. As new data is acquired, the state estimates, process uncertainty, and measurement uncertainty are updated accordingly, as described in this manuscript.

Nima Asadi, Jimmy Lin, Michael Busch

We explore a real-time Twitter search application where tweets are arriving at a rate of several thousands per second. Real-time search demands that they be indexed and searchable immediately, which leads to a number of implementation challenges. In this paper, we focus on one aspect: dynamic postings allocation policies for index structures that are completely held in main memory. The core issue can be characterized as a "Goldilocks Problem". Because memory remains today a scare resource, an allocation policy that is too aggressive leads to inefficient utilization, while a policy that is too conservative is slow and leads to fragmented postings lists. We present a dynamic postings allocation policy that allocates memory in increasingly-larger "slices" from a small number of large, fixed pools of memory. Through analytical models and experiments, we explore different settings that balance time (query evaluation speed) and space (memory utilization).