Search Results for author:
Found 5 papers, 2 papers with code
Kernel Learning in Ridge Regression "Automatically" Yields Exact Low Rank Solution
Assuming that the covariates have nonzero explanatory power for the response only through a low dimensional subspace (central mean subspace), we find that the global minimizer of the finite sample kernel learning objective is also low rank with high probability.
On the Self-Penalization Phenomenon in Feature Selection
We describe an implicit sparsity-inducing mechanism based on minimization over a family of kernels: \begin{equation*} \min_{\beta, f}~\widehat{\mathbb{E}}[L(Y, f(\beta^{1/q} \odot X)] + \lambda_n \|f\|_{\mathcal{H}_q}^2~~\text{subject to}~~\beta \ge 0, \end{equation*} where $L$ is the loss, $\odot$ is coordinate-wise multiplication and $\mathcal{H}_q$ is the reproducing kernel Hilbert space based on the kernel $k_q(x, x') = h(\|x-x'\|_q^q)$, where $\|\cdot\|_q$ is the $\ell_q$ norm.
Taming Nonconvexity in Kernel Feature Selection -- Favorable Properties of the Laplace Kernel
Kernel-based feature selection is an important tool in nonparametric statistics.
A Self-Penalizing Objective Function for Scalable Interaction Detection
The trick is to maximize a class of parametrized nonparametric dependence measures which we call metric learning objectives; the landscape of these nonconvex objective functions is sensitive to interactions but the objectives themselves do not explicitly model interactions.
The Alzheimer's Disease Prediction Of Longitudinal Evolution (TADPOLE) Challenge: Results after 1 Year Follow-up
TADPOLE's unique results suggest that current prediction algorithms provide sufficient accuracy to exploit biomarkers related to clinical diagnosis and ventricle volume, for cohort refinement in clinical trials for Alzheimer's disease.
