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This paper concerns the problem of estimating a vector \beta, from /-1 measurements y_i which depend statistically on linear functions x_i, \beta, where the x_i are Gaussian random vectors. This model is general enough to capture compressed sensing and phase retrieval problems with binary measurements. The paper assumes that f is completely unknown ahead of time, but that it satisfies certain moment conditions. The paper shows how, under these moment conditions, to reduce the problem of estimating \beta to a sparse PCA problem, with covariance matrix generated by pairs of observations. The idea is to look at differences of x_i - x_{i'} and y_i - y_{i'}; the paper proves that the population covariance matrix of \delta_y \delta_x is a spiked identity matrix, where the spike is of the form \beta* \beta* T. This clever reduction appears to be the main contribution of the work.