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The Performance Analysis of Generalized Margin Maximizers on Separable Data
The performance of hard-margin SVM has been recently analyzed in~\cite{montanari2019generalization, deng2019model}.
The Performance Analysis of Generalized Margin Maximizer (GMM) on Separable Data
We also provide a detailed study for three special cases: ($1$) $\ell_2$-GMM that is the max-margin classifier, ($2$) $\ell_1$-GMM which encourages sparsity, and ($3$) $\ell_{\infty}$-GMM which is often used when the parameter vector has binary entries.
The Impact of Regularization on High-dimensional Logistic Regression
In both cases, we obtain explicit expressions for various performance metrics and can find the values of the regularizer parameter that optimizes the desired performance.
Learning without the Phase: Regularized PhaseMax Achieves Optimal Sample Complexity
The problem of estimating an unknown signal, $\mathbf x_0\in \mathbb R^n$, from a vector $\mathbf y\in \mathbb R^m$ consisting of $m$ magnitude-only measurements of the form $y_i=|\mathbf a_i\mathbf x_0|$, where $\mathbf a_i$'s are the rows of a known measurement matrix $\mathbf A$ is a classical problem known as phase retrieval.
LASSO with Non-linear Measurements is Equivalent to One With Linear Measurements
In this work, we considerably strengthen these results by obtaining explicit expressions for $\|\hat x-\mu x_0\|_2$, for the regularized Generalized-LASSO, that are asymptotically precise when $m$ and $n$ grow large.
