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Found 6 papers, 0 papers with code
The staircase property: How hierarchical structure can guide deep learning
This paper identifies a structural property of data distributions that enables deep neural networks to learn hierarchically.
Statistical Query Algorithms and Low-Degree Tests Are Almost Equivalent
Researchers currently use a number of approaches to predict and substantiate information-computation gaps in high-dimensional statistical estimation problems.
Reducibility and Statistical-Computational Gaps from Secret Leakage
Inference problems with conjectured statistical-computational gaps are ubiquitous throughout modern statistics, computer science and statistical physics.
Average-Case Lower Bounds for Learning Sparse Mixtures, Robust Estimation and Semirandom Adversaries
This paper develops several average-case reduction techniques to show new hardness results for three central high-dimensional statistics problems, implying a statistical-computational gap induced by robustness, a detection-recovery gap and a universality principle for these gaps.
Optimal Average-Case Reductions to Sparse PCA: From Weak Assumptions to Strong Hardness
We also show the surprising result that weaker forms of the PC conjecture up to clique size $K = o(N^\alpha)$ for any given $\alpha \in (0, 1/2]$ imply tight computational lower bounds for sparse PCA at sparsities $k = o(n^{\alpha/3})$.
Universality of Computational Lower Bounds for Submatrix Detection
In the general submatrix detection problem, the task is to detect the presence of a small $k \times k$ submatrix with entries sampled from a distribution $\mathcal{P}$ in an $n \times n$ matrix of samples from $\mathcal{Q}$.
