- Series
- Stochastics Seminar
- Time
- Thursday, November 15, 2012 - 3:05pm for 1 hour (actually 50 minutes)
- Location
- Skyles 006
- Speaker
- Cun-Hui Zhang – Rutgers University
- Organizer
- Karim Lounici
This paper concerns the problem of matrix completion, which is to
estimate a matrix from observations in a small subset of indices. We
propose a calibrated spectrum elastic net method with a sum of the
nuclear and Frobenius penalties and develop an iterative algorithm to
solve the convex minimization problem. The iterative algorithm
alternates between imputing the missing entries in the incomplete matrix
by the current guess and estimating the matrix by a scaled
soft-thresholding singular value decomposition of the imputed matrix
until the resulting matrix converges. A calibration step follows to
correct the bias caused by the Frobenius penalty. Under proper coherence
conditions and for suitable penalties levels, we prove that the proposed estimator achieves an error bound of nearly optimal order and in proportion to the noise level. This provides a unified analysis of the noisy and noiseless matrix completion problems.
Tingni Sun and Cun-Hui Zhang, Rutgers University