Mary Wootters

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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(More)
A fundamental fact about polynomial interpolation is that k evaluations of a degree-(k-1) polynomial f are sufficient to determine f. This is also necessary in a strong sense: given k-1 evaluations, we learn nothing about the value of f on any k'th point. In this paper, we study a variant of the polynomial interpolation problem. Instead of querying(More)
Binary measurements arise naturally in a variety of statistics and engineering applications. They may be inherent to the problem—for example, in determining the relationship between genetics and the presence or absence of a disease—or they may be a result of extreme quantization. A recent influx of literature has suggested that using prior(More)
Machine learning relies on the assumption that unseen test instances of a classification problem follow the same distribution as observed training data. However, this principle can break down when machine learning is used to make important decisions about the welfare (employment, education, health) of strategic individuals. Knowing information about the(More)
In compressed sensing, the restricted isometry property (RIP) is a sufficient condition for the efficient reconstruction of a nearly k-sparse vector x ∈ C from m linear measurements Φx. It is desirable for m to be small, and for Φ to support fast matrix-vector multiplication. In this work, we give a randomized construction of RIP matrices Φ ∈ Cm×d,(More)
The primary goal of compressed sensing and (non-adaptive) combinatorial group testing is to recover a sparse vector x from an underdetermined set of linear equations Φx = y. Both problems entail solving Φx = y given Φ and y but they use different models of arithmetic, different models of randomness models for F, and different guarantees(More)
We show that any <i>q</i>-ary code with sufficiently good distance can be randomly punctured to obtain, with high probability, a code that is list decodable up to radius 1 --- 1/<i>q</i> --- <i>&#949;</i> with near-optimal rate and list sizes. Our results imply that "most" Reed-Solomon codes are list decodable beyond the Johnson bound, settling the(More)
In order to overcome the limitations imposed by DNA barcoding when multiplexing a large number of samples in the current generation of high-throughput sequencing instruments, we have recently proposed a new protocol that leverages advances in combinatorial pooling design (group testing) [9]. We have also demonstrated how this new protocol would enable de(More)
In this work, we present the first local-decoding algorithm for expander codes. This yields a new family of constant-rate codes that can recover from a constant fraction of errors in the codeword symbols, and where any symbol of the codeword can be recovered with high probability by reading N symbols from the corrupted codeword, where N is the block-length(More)