2 problems

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Information-theoretic threshold separation conjecture for sparse and high-rank models
Consider planted Gaussian matrix models with an information-theoretic threshold and a spectral threshold, including sparse PCA, submatrix localization, and Gaussian mixture cluster…
Conjectureopenclustering sparse-pca submatrix-localizationarXiv posted 2 days ago
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Computational hardness of submatrix localization below the convexified MLE threshold
Let $Y^*$ denote the true support matrix in the submatrix localization model. Assume $\mu\le 1$ , $n_L=n_R=n$ , $K_L=K_R=K$ , and $K\ge c_1\log n$ . Submatrix localization computationa…
Conjectureopencomputational-complexity statistical-inference submatrix-localizationarXiv posted 2 days ago

Information-theoretic threshold separation conjecture for sparse and high-rank models