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| (ns ml-clj.lasso | |
| (:require [clojure.algo.generic.math-functions :as math] | |
| [clojure.core.matrix :as m] | |
| [clojure.core.matrix.operators :as M])) | |
| (defn max-lambda | |
| [Y X] | |
| (second | |
| (apply max-key second | |
| (map-indexed vector | |
| (map (fn [x] | |
| (/ (m/mget (m/dot x (m/transpose Y)) 0) | |
| (m/row-count X))) | |
| X))))) | |
| (defn soft-thresholding | |
| [s lambda] | |
| (* (math/sgn s) | |
| (max 0 (- (math/abs s) lambda)))) | |
| (defn active-set | |
| [B] | |
| (filter (complement nil?) | |
| (map (fn [b i] (if (not (= 0 b)) i nil)) | |
| B | |
| (range 0 (count B))))) | |
| (defn convergenced? | |
| [Bnew Bold] | |
| (= (active-set Bnew) | |
| (active-set Bold))) | |
| (defn coordinate-descent | |
| ([f Bold converged? j] | |
| (coordinate-descent f 1 Bold converged? j)) | |
| ([f n Bold converged? j] | |
| (let [Bold-snapshot Bold | |
| Bnew (f Bold j)] | |
| (if (converged? | |
| Bnew | |
| Bold-snapshot) | |
| {:betas Bnew :iterations n} | |
| (recur f (+ n 1) Bnew converged? j))))) | |
| (defn mae | |
| [Y X B] | |
| (/ (reduce + | |
| (flatten | |
| (m/emap math/abs | |
| (M/- Y (map #(reduce + (m/emul % B)) X))))) | |
| (m/row-count X))) | |
| (defn init-coefs | |
| [X] | |
| (vec (repeat (m/column-count X) 0))) | |
| (defn lasso | |
| [Y X Bold lambda precision] | |
| (let [inner (fn [Blast j] | |
| (let [Xj (m/slice X j) | |
| Rj (M/+ | |
| (M/- Y (map #(reduce + (m/emul % Blast)) X)) | |
| (M/* Xj (get Blast j))) | |
| Bj* (/ (m/dot (m/transpose Xj) | |
| (flatten Rj)) ; Rj must be a vector | |
| (m/row-count X)) | |
| Bjnew (soft-thresholding Bj* lambda) | |
| Blast (assoc Blast j Bjnew)] | |
| (if (zero? j) | |
| Blast | |
| (recur Blast (dec 1))))) | |
| coefs (coordinate-descent inner Bold convergenced? | |
| (dec (m/column-count X)))] | |
| (-> coefs | |
| (assoc :lambda lambda) | |
| (assoc :mae (mae Y X | |
| (coefs :betas (init-coefs X))))))) | |
| (defn lasso-cv | |
| [Y X & {:keys [precision step] | |
| :or {precision 0.0001 step 0.0001}}] | |
| (let [lambda (max-lambda Y X)] | |
| (apply min-key :mae | |
| (pmap #(lasso Y X (init-coefs X) % precision) | |
| (range 0 lambda step))))) |
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