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Found 4 papers, 0 papers with code
Higher degree sum-of-squares relaxations robust against oblivious outliers
Using a reduction from the planted clique problem, we provide evidence that the quasipolynomial time is likely to be necessary for sparse PCA with symmetric noise.
Optimal SQ Lower Bounds for Learning Halfspaces with Massart Noise
Further, this continues to hold even if the information-theoretically optimal error $\mathrm{OPT}$ is as small as $\exp\left(-\log^c(d)\right)$, where $d$ is the dimension and $0 < c < 1$ is an arbitrary absolute constant, and an overwhelming fraction of examples are noiseless.
Robust recovery for stochastic block models
We develop an efficient algorithm for weak recovery in a robust version of the stochastic block model.
Consistent Estimation for PCA and Sparse Regression with Oblivious Outliers
For sparse regression, we achieve consistency for optimal sample size $n\gtrsim (k\log d)/\alpha^2$ and optimal error rate $O(\sqrt{(k\log d)/(n\cdot \alpha^2)})$ where $n$ is the number of observations, $d$ is the number of dimensions and $k$ is the sparsity of the parameter vector, allowing the fraction of inliers to be inverse-polynomial in the number of samples.
