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Lasso estimator for fixed design
Definition
For , a deterministic design , response , and penalty , define the Lasso objective Its minimizer set is . The penalty is strictly positive; no full-rank condition on is imposed. The nonemptiness, compactness, and convexity of this set are proved separately; this page defines the objective and minimizer set but does not select one minimizer.
Depends on
Used by
- Nonunique Lasso coefficients with a unique fitted value Example
- One cyclic coordinate-descent cycle for correlated-design Lasso Example
- One proximal-gradient step for a nonorthogonal Lasso design Example
- The orthogonal-design Lasso is coordinatewise soft thresholding Example
- The zero-feature-column Lasso update Example
- Exact Lasso coordinate update, including a zero column Lemma
- The Lasso objective has a nonempty compact convex minimizer set Lemma
- Lasso basic inequality and cone constraint Theorem
- Lasso prediction and coefficient bounds under incoherence Theorem
Dependency tree · two levels
19 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.
Sources
- Philippe Rigollet and Jan-Christian Hütter, High-Dimensional Statistics: Lecture Notes, Chapter 2, Definition 2.12 (standard reference, not scraped)
- Peter J. Bickel, Ya'acov Ritov and Alexandre B. Tsybakov, Simultaneous Analysis of Lasso and Dantzig Selector, Section 7 (standard reference, not scraped)