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Found 13 papers, 2 papers with code
Model-adapted Fourier sampling for generative compressed sensing
We study generative compressed sensing when the measurement matrix is randomly subsampled from a unitary matrix (with the DFT as an important special case).
A coherence parameter characterizing generative compressed sensing with Fourier measurements
In Bora et al. (2017), a mathematical framework was developed for compressed sensing guarantees in the setting where the measurement matrix is Gaussian and the signal structure is the range of a generative neural network (GNN).
PLUGIn: A simple algorithm for inverting generative models with recovery guarantees
We prove that, when weights are Gaussian and layer widths $n_i \gtrsim 5^i n_0$ (up to log factors), the algorithm converges geometrically to a neighbourhood of $x$ with high probability.
Beyond Independent Measurements: General Compressed Sensing with GNN Application
When the structure is given as a possibly non-convex cone $T \subset \mathbb{R}^{n}$, an approximate empirical risk minimizer is proven to be a robust estimator if the effective number of measurements is sufficient, even in the presence of a model mismatch.
PLUGIn-CS: A simple algorithm for compressive sensing with generative prior
After a sufficient number of iterations, the estimation errors for both $x$ and $\mathcal{G}(x)$ are at most in the order of $\sqrt{4^dn_0/m} \|\epsilon\|$.
NBIHT: An Efficient Algorithm for 1-bit Compressed Sensing with Optimal Error Decay Rate
The Binary Iterative Hard Thresholding (BIHT) algorithm is a popular reconstruction method for one-bit compressed sensing due to its simplicity and fast empirical convergence.
Information Theory Numerical Analysis Information Theory Numerical Analysis 94-XX
Sub-Gaussian Matrices on Sets: Optimal Tail Dependence and Applications
In many applications, e. g., compressed sensing, this norm may be large, or even growing with dimension, and thus it is important to characterize this dependence.
Tight Analyses for Non-Smooth Stochastic Gradient Descent
We prove that after $T$ steps of stochastic gradient descent, the error of the final iterate is $O(\log(T)/T)$ with high probability.
Nearly tight sample complexity bounds for learning mixtures of Gaussians via sample compression schemes
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.
Learning tensors from partial binary measurements
In this paper we generalize the 1-bit matrix completion problem to higher order tensors.
Statistics Theory Information Theory Information Theory Optimization and Control Statistics Theory 62B10, 94A17, 15A69, 62D05 H.3.3; I.2.6
Near-optimal sample complexity for convex tensor completion
In this paper, we show that by using an atomic-norm whose atoms are rank-$1$ sign tensors, one can obtain a sample complexity of $O(dN)$.
Near-optimal Sample Complexity Bounds for Robust Learning of Gaussians Mixtures via Compression Schemes
We prove that $\tilde{\Theta}(k d^2 / \varepsilon^2)$ samples are necessary and sufficient for learning a mixture of $k$ Gaussians in $\mathbb{R}^d$, up to error $\varepsilon$ in total variation distance.
Average-case Hardness of RIP Certification
The restricted isometry property (RIP) for design matrices gives guarantees for optimal recovery in sparse linear models.
