In the problem of learning a mixture of linear classifiers, the aim is to learn a collection of hyperplanes from a sequence of binary responses. Each response is a result of querying with a vector and indicates the side of a randomly chosen hyperplane from the collection the query vector belong to. This model is quite rich while dealing with heterogeneous data with categorical labels and has only been studied in some special settings. We look at a hitherto unstudied problem of query complexity upper bound of recovering all the hyperplanes, especially for the case when the hyperplanes are sparse. This setting is a natural generalization of the extreme quantization problem known as 1-bit compressed sensing.

First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. This paper proposes an incremental but very sensible and practical modification to'curriculum learning'. Given a partition of the training examples into classes, they propose an additional regularising term (and an additional parameter) to ensure that the'easy' examples selected during learning are spread across the classes, and not from one class. The partition into classes can come from a clustering algorithm, or from a priori knowledge. The idea is straightforward and sensible, and the authors propose an algorithm that looks efficient and correct.

Summary and Contributions: This work initiates the study of the following generalization of 1-bit compressed sensing. There are some unknown k-sparse vectors w_1,...,w_{ell} in R d, and one can query any vector v and get back sgn( v,w_i) for random index i. The goal is to recover the w_i's while minimizing the number of queries. This problem should not be confused with the problem of learning mixtures of halfspaces in the sense of distribution learning, as here the learner gets to pick the design vectors. A similar model in the context of regression has been studied before by Krishnamurthy et al. and Yin et al., as the authors acknowledge.

In the problem of learning a mixture of linear classifiers, the aim is to learn a collection of hyperplanes from a sequence of binary responses. Each response is a result of querying with a vector and indicates the side of a randomly chosen hyperplane from the collection the query vector belong to. This model is quite rich while dealing with heterogeneous data with categorical labels and has only been studied in some special settings. We look at a hitherto unstudied problem of query complexity upper bound of recovering all the hyperplanes, especially for the case when the hyperplanes are sparse. This setting is a natural generalization of the extreme quantization problem known as 1-bit compressed sensing.