
OneBit ExpanderSketch for OneBit Compressed Sensing
Is it possible to obliviously construct a set of hyperplanes H such that...
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Recovery of Sparse Signals from a Mixture of Linear Samples
Mixture of linear regressions is a popular learning theoretic model that...
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An Approach to OneBit Compressed Sensing Based on Probably Approximately Correct Learning Theory
In this paper, the problem of onebit compressed sensing (OBCS) is formu...
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Robust onebit compressed sensing with partial circulant matrices
We present optimal sample complexity estimates for onebit compressed se...
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Sample Complexity of Learning Mixtures of Sparse Linear Regressions
In the problem of learning mixtures of linear regressions, the goal is t...
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VectorMatrixVector Queries for Solving Linear Algebra, Statistics, and Graph Problems
We consider the general problem of learning about a matrix through vecto...
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A modelfree approach to linear least squares regression with exact probabilities
In a regression setting with observation vector y ∈ R^n and given finite...
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Recovery of sparse linear classifiers from mixture of responses
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 belongs to. This model provides a rich representation of 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 1bit compressed sensing. Suppose we have a set of ℓ unknown ksparse vectors. We can query the set with another vector a, to obtain the sign of the inner product of a and a randomly chosen vector from the ℓset. How many queries are sufficient to identify all the ℓ unknown vectors? This question is significantly more challenging than both the basic 1bit compressed sensing problem (i.e., ℓ=1 case) and the analogous regression problem (where the value instead of the sign is provided). We provide rigorous query complexity results (with efficient algorithms) for this problem.
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