We study finite-sample parameter estimation in logistic regression with Gaussian design, where the goal is to estimate $\mathbf{\theta}^*\in \mathbb{R}^d$ with $R=\|\mathbf{\theta}^*\|_2\ge 1$ from i.i.d. samples $\{(\mathbf{x}_i,y_i)\}_{i=1}^n,$ $\mathbf{x}_i \sim N(0,\mathbf{I}_d)$, $y_i\mid \mathbf{x}_i \sim \mathrm...
The main technical component is to show that the gradient of the logistic loss satisfies a certain approximate invertibility condition (AIC) and uniformly control the deviation of the gradient from its population counterpart by covering and peeling arguments, and then show that the population GD is a contraction by a d...
This paper proposes adaptive and non-adaptive schemes that significantly improve upon prior results by simultaneously reducing the number of measurements and achieving sublinear decoding time in mixture models.
This paper provides the first near-optimal lower bounds for one-bit compressed sensing of approximately sparse signals lying in a scaled $\ell_1$ ball, which is a commonly adopted relaxation of the exactly $k$-sparse assumption. In prior works, the best known upper bounds on uniform Euclidean error are of order $\widet...
Junren Chen, Arya Mazumdar, Ming Yuan· 0 citations
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