Research map / Learning theory and algorithms / Kernels and regression theory
First order expansion of convex regularized estimators
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Construct a first-order expansion using the expected Hessian and the empirical score | Convex regularized estimators · High-dimensional regression with random designs | distance to estimator relative to estimation error: o_p(1) | Helped |
| Include the estimator difference η−β̂ in the low-dimensional set | Lasso, squared loss · Linear regression | expansion approximation error rate: r_n^{3/2} -> r_n^{2} | Helped |
| Use a first-order expansion to represent risk by a Gaussian-sequence proximal estimator | Convex regularized estimators · Linear regression with Gaussian identity-covariance design | risk characterization: 1 + o_p(1) | Helped |
| Apply the first-order expansion-based de-biasing result | Lasso · Inference for a linear coefficient functional | sparsity range for confidence intervals: s = o(n^{2/3}) | Helped |
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