Mistake Bounds for Binary Matrix Completion

Doubly Aggressive Selective Sampling Algorithms for Classification

Online selective sampling algorithms learn to perform binary classification, and additionally they decided whether to ask, or query, for a label of any given example. We introduce two stochastic linear algorithms and analyze them in the worst-case mistake-bound framework. Even though stochastic, for some inputs, our algorithms query with probability 1 and make an update even if there is no mist...

1-Bit Matrix Completion

In this paper we develop a theory of matrix completion for the extreme case of noisy 1-bit observations. Instead of observing a subset of the real-valued entries of a matrix M , we obtain a small number of binary (1-bit) measurements generated according to a probability distribution determined by the realvalued entries of M . The central question we ask is whether or not it is possible to obtai...

PU Learning for Matrix Completion

In this paper, we consider the matrix completion problem when the observations are one-bit measurements of some underlying matrix M , and in particular the observed samples consist only of ones and no zeros. This problem is motivated by modern applications such as recommender systems and social networks where only “likes” or “friendships” are observed. The problem is an instance of PU (positive...

Lower bounds of Copson type for the transpose of matrices on weighted sequence spaces

Coherent Matrix Completion

ij of a certain matrix Y 0, which gives rise to the standard and joint incoherence conditions involving uniform bounds by μ 0 and μ str . Here, we derive a new bound using the weighted `1,2 norm of Y 0, which is the maximum of the weighted row and column norms of Y 0. These bounds lead to a tighter bound of kY k and hence less restrictive conditions for matrix completion. We now turn to the det...