3 accepted papers
We consider the problem of recovering an unknown latent code vector under a known generative model. For a $d$-layer deep generative network $\mathcal{G}:\mathbb{R}^{n_0}\rightarrow \mathbb{R}^{n_d}$ with ReLU activation functions, let the observation be $\mathcal{G}(x)+\epsilon$ where $\epsilon$ is…
We prove that ϴ(k d^2 / ε^2) samples are necessary and sufficient for learning a mixture of k Gaussians in R^d, up to error ε in total variation distance. This improves both the known upper bounds and lower bounds for this problem. For mixtures of axis-aligned Gaussians, we show that O(k d / ε^2) sa…
The restricted isometry property (RIP) for design matrices gives guarantees for optimal recovery in sparse linear models. It is of high interest in compressed sensing and statistical learning. This property is particularly important for computationally efficient recovery methods. As a consequence,…