| #------------------------------------------------------------- |
| # |
| # Licensed to the Apache Software Foundation (ASF) under one |
| # or more contributor license agreements. See the NOTICE file |
| # distributed with this work for additional information |
| # regarding copyright ownership. The ASF licenses this file |
| # to you under the Apache License, Version 2.0 (the |
| # "License"); you may not use this file except in compliance |
| # with the License. You may obtain a copy of the License at |
| # |
| # http://www.apache.org/licenses/LICENSE-2.0 |
| # |
| # Unless required by applicable law or agreed to in writing, |
| # software distributed under the License is distributed on an |
| # "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY |
| # KIND, either express or implied. See the License for the |
| # specific language governing permissions and limitations |
| # under the License. |
| # |
| #------------------------------------------------------------- |
| |
| # Builtin function for the SpaRSA algorithm to perform lasso regression |
| # (SpaRSA .. Sparse Reconstruction by Separable Approximation) |
| # |
| # INPUTS: |
| # --------------------------------------------------------------------------------------------- |
| # NAME TYPE DEFAULT MEANING |
| # --------------------------------------------------------------------------------------------- |
| # X Double --- input feature matrix |
| # y Double --- matrix Y columns of the design matrix |
| # tol Double 1e-15 target convergence tolerance |
| # M Integer 5 history length |
| # tau Double 1 regularization component |
| # maxi Integer 100 maximum number of iterations until convergence |
| # --------------------------------------------------------------------------------------------- |
| # OUTPUTS |
| # w Double --- model matrix |
| |
| |
| m_lasso = function(Matrix[Double] X, Matrix[Double] y, Double tol = 10^(-15), |
| Integer M = 5, Double tau = 1, Integer maxi = 100, Boolean verbose = TRUE) |
| return(Matrix[Double] w) |
| { |
| n = nrow(X) |
| m = ncol(X) |
| |
| #constants |
| eta = 2 |
| sigma = 0.01 |
| alpha_min = 10^(-30) |
| alpha_max = 10^(30) |
| |
| #init |
| alpha = 1 |
| w = Rand(rows=m, cols=1, min=0, max=1, pdf="uniform") |
| history = -1e30 * matrix(1, rows=M, cols=1) |
| |
| r = X %*% w - y |
| g = t(X) %*% r |
| obj = 0.5 * sum(r*r) + tau*sum(abs(w)) |
| |
| if( verbose ) |
| print("Initial OBJ=" + obj) |
| |
| history[M,1] = obj |
| |
| inactive_set = matrix(1, rows=m, cols=1) |
| iter = 0 |
| continue = TRUE |
| while(iter < maxi & continue) { |
| dw = matrix(0, rows=m, cols=1) |
| dg = matrix(0, rows=m, cols=1) |
| relChangeObj = -1.0 |
| |
| inner_iter = 0 |
| inner_continue = TRUE |
| inner_maxiter = 100 |
| while(inner_iter < inner_maxiter & inner_continue) { |
| u = w - g/alpha |
| lambda = tau/alpha |
| |
| wnew = sign(u) * (abs(u) - lambda) * ((abs(u) - lambda) > 0) |
| dw = wnew - w |
| dw2 = sum(dw*dw) |
| |
| r = X %*% wnew - y |
| gnew = t(X) %*% r |
| objnew = 0.5 * sum(r*r) + tau*sum(abs(wnew)) |
| obj_threshold = max(history) - 0.5*sigma*alpha*dw2 |
| |
| if(objnew <= obj_threshold) { |
| w = wnew |
| dg = gnew - g |
| g = gnew |
| inner_continue = FALSE |
| |
| history[1:(M-1),] = history[2:M,] |
| history[M,1] = objnew |
| relChangeObj = abs(objnew - obj)/obj |
| obj = objnew |
| } |
| else |
| alpha = eta*alpha |
| |
| inner_iter = inner_iter + 1 |
| } |
| |
| if(inner_continue) |
| print("Inner loop did not converge") |
| |
| alphanew = sum(dw*dg)/sum(dw*dw) |
| alpha = max(alpha_min, min(alpha_max, alphanew)) |
| |
| old_inactive_set = inactive_set |
| inactive_set = w != 0 |
| diff = sum(abs(old_inactive_set - inactive_set)) |
| continue = (diff != 0 | relChangeObj >= tol) |
| |
| num_inactive = sum(w != 0) |
| if( verbose ) |
| print("ITER=" + iter + " OBJ=" + obj + " relative change=" + relChangeObj + " num_inactive=" + num_inactive) |
| iter = iter + 1 |
| } |
| } |