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Found 7 papers, 3 papers with code
Optimal Strategies Against Generative Attacks
Are there optimal strategies for the attacker or the authenticator?
LOCA: LOcal Conformal Autoencoder for standardized data coordinates
We propose a deep-learning based method for obtaining standardized data coordinates from scientific measurements. Data observations are modeled as samples from an unknown, non-linear deformation of an underlying Riemannian manifold, which is parametrized by a few normalized latent variables.
Optimal Shrinkage of Singular Values Under Random Data Contamination
A low rank matrix X has been contaminated by uniformly distributed noise, missing values, outliers and corrupt entries.
ReFACTor: Practical Low-Rank Matrix Estimation Under Column-Sparsity
Various problems in data analysis and statistical genetics call for recovery of a column-sparse, low-rank matrix from noisy observations.
Optimal Shrinkage of Singular Values
For a variety of loss functions, including Mean Square Error (MSE - square Frobenius norm), the nuclear norm loss and the operator norm loss, we show that in this framework there is a well-defined asymptotic loss that we evaluate precisely in each case.
Statistics Theory Statistics Theory
The Maximum Entropy Relaxation Path
We show existence and a geometric description of the relaxation path.
The Optimal Hard Threshold for Singular Values is 4/sqrt(3)
In our asymptotic framework, this thresholding rule adapts to unknown rank and to unknown noise level in an optimal manner: it is always better than hard thresholding at any other value, no matter what the matrix is that we are trying to recover, and is always better than ideal Truncated SVD (TSVD), which truncates at the true rank of the low-rank matrix we are trying to recover.
Methodology
