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Found 11 papers, 0 papers with code
Private graphon estimation via sum-of-squares
We develop the first pure node-differentially-private algorithms for learning stochastic block models and for graphon estimation with polynomial running time for any constant number of blocks.
Reaching Kesten-Stigum Threshold in the Stochastic Block Model under Node Corruptions
We study robust community detection in the context of node-corrupted stochastic block model, where an adversary can arbitrarily modify all the edges incident to a fraction of the $n$ vertices.
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.
On the well-spread property and its relation to linear regression
In this paper, we show that there exists a family of design matrices lacking well-spreadness such that consistent recovery of the parameter vector in the above robust linear regression model is information-theoretically impossible.
A Ihara-Bass Formula for Non-Boolean Matrices and Strong Refutations of Random CSPs
Strong refutation results based on current approaches construct a certificate that a certain matrix associated to the k-CSP instance is quasirandom.
Fast algorithm for overcomplete order-3 tensor decomposition
We develop the first fast spectral algorithm to decompose a random third-order tensor over $\mathbb{R}^d$ of rank up to $O(d^{3/2}/\text{polylog}(d))$.
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.
The Complexity of Sparse Tensor PCA
Even in the restricted case of sparse PCA, known algorithms only recover the sparse vectors for $\lambda \geq \tilde{\mathcal{O}}(k \cdot r)$ while our algorithms require $\lambda \geq \tilde{\mathcal{O}}(k)$.
Sparse PCA: Algorithms, Adversarial Perturbations and Certificates
Despite a long history of prior works, including explicit studies of perturbation resilience, the best known algorithmic guarantees for Sparse PCA are fragile and break down under small adversarial perturbations.
Consistent regression when oblivious outliers overwhelm
Concretely, we show that the Huber loss estimator is consistent for every sample size $n= \omega(d/\alpha^2)$ and achieves an error rate of $O(d/\alpha^2n)^{1/2}$.
