Online Matrix Completion with Side Information

We give an online algorithm and prove novel mistake and regret bounds for online binary matrix completion with side information. The mistake bounds we prove are of the form $\tilde{O}(D/\gamma^2)$. The term $1/\gamma^2$ is analogous to the usual margin term in SVM (perceptron) bounds. More specifically, if we assume that there is some factorization of the underlying $m \times n$ matrix into $P Q^\intercal$ where the rows of $P$ are interpreted as "classifiers" in $\mathcal{R}^d$ and the rows of $Q$ as "instances" in $\mathcal{R}^d$, then $\gamma$ is the maximum (normalized) margin over all factorizations $P Q^\intercal$ consistent with the observed matrix. The quasi-dimension term $D$ measures the quality of side information. In the presence of vacuous side information, $D= m+n$. However, if the side information is predictive of the underlying factorization of the matrix, then in an ideal case, $D \in O(k + \ell)$ where $k$ is the number of distinct row factors and $\ell$ is the number of distinct column factors. We additionally provide a generalization of our algorithm to the inductive setting. In this setting, we provide an example where the side information is not directly specified in advance. For this example, the quasi-dimension $D$ is now bounded by $O(k^2 + \ell^2)$

Turbulent statistics in the vicinity of an SST front: A north wind case, FASINEX February 16, 1986

The technique of boxcar variances and covariances is used to examine NCAR Electra data from FASINEX (Frontal Air-Sea Interaction EXperiment). This technique was developed to examine changes in turbulent fluxes near a sea surface temperature (SST) front. The results demonstrate the influence of the SST front on the MABL (Marine Atmospheric Boundary Layer). Data shown are for February 16, 1986, when the winds blew from over cold water to warm. The front directly produced horizontal variability in the turbulence. The front also induced a secondary circulation which further modified the turbulence