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2dim_search.py
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2dim_search.py
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#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Fri Jul 12 09:19:55 2019
@author: luna
"""
import os
import numpy as np
import pandas as pd
import math
#import matplotlib.pyplot as plt
from sklearn.linear_model import LassoCV, Lasso, RidgeCV
from sklearn.metrics import confusion_matrix
def norm2(x):
return np.sqrt((x**2).sum())
class SmoothingSubgroupAnalysis():
def __init__(self, X, Y, K, beta, tolerance = 10**-3, lambdaPercent=500,num_lambda1=10,weight = 'lasso'):
'''
initiate: X: independent variables
Y: dependent variables
K: K-fold cv
tolerance: convergence condition
selection_type: model(lambda) selection evaluation type: bic/aic/cv
train_n: sample size used for training (only for cv)
test_n: sample size used for testing (only for cv)
'''
self.X = X
self.Y = Y
self.K = K
self.n = X.shape[0]
self.p = X.shape[1]
self.tolerance = tolerance
self.lambdaPercent = lambdaPercent
self.num_lambda1 = num_lambda1
self.w = weight
self.beta = beta
def calDD(self):
self.D = np.zeros((self.n-2,self.n))
for i in range(self.n-2):
self.D[i,i:(i+3)] = np.array([1,-2,1])
self.DTD = self.D.T@self.D
def Weight(self):
if self.w == 'lasso':
model_lasso = LassoCV(cv=10, max_iter=10000).fit(self.X,self.Y)
self.weight = abs(model_lasso.coef_)+0.00001
elif self.w == 'ridge':
model_ridge = RidgeCV(cv=10).fit(self.X,self.Y)
self.weight = abs(model_ridge.coef_)
elif self.w == 'ols':
self.weight = np.zeros(self.p)
for i in range(self.X.shape[1]):
self.weight[i] = abs(1/self.X[:,i].T.dot(self.X[:,i])*self.X[:,i].T.dot(self.Y))
def SSA(self, x, y, lambdaa1, lambdaa2, beta_hat = None):
#iteration times k
k = 0
n = x.shape[0]
p = x.shape[1]
#initialize beta, beta for k-1, beta for k-2
if beta_hat is None:
#star = np.ones((n,p))
#beta_hat = model_lasso.coef_.T*star
beta_hat = np.zeros((n,p))
old_beta = beta_hat.copy() #k-1
older_beta = old_beta.copy() #k-2
#iterate till convergence
while True:
k += 1
for j in range(self.p):
t = 1
while True:
#cal grad_f(beta0)
grad_beta0 = -x[:,j]*(y-(x*beta_hat).sum(axis=1))/n + lambdaa2 * self.DTD@beta_hat[:,j]
#cal f(beta0)
f_beta0 = norm2(y-(x*beta_hat).sum(axis=1))**2/2/n + lambdaa2/2*norm2(self.D@beta_hat[:,j])**2
#cal G(beta0,t)
temp = beta_hat[:,j] - t*grad_beta0
G_beta0 = temp*(1-t*lambdaa1/self.weight[j]/norm2(temp))*((1-t*lambdaa1/self.weight[j]/norm2(temp))>0)
#cal f(beta_new,t)
t_beta_hat = beta_hat.copy()
t_beta_hat[:,j] = G_beta0
f_beta_new = norm2(y-(x*t_beta_hat).sum(axis=1))**2/2/n + lambdaa2/2*norm2(self.D@G_beta0)**2
#break condition
if f_beta_new <= f_beta0 + (grad_beta0*(G_beta0-beta_hat[:,j])).sum() + norm2(G_beta0-beta_hat[:,j])**2/2/t:
break
#else update t
t *= 0.8
#update parameter
#cal v
v = beta_hat[:,j] + (k-2)/(k+1)*(beta_hat[:,j]-older_beta[:,j])
#cal G(v,t)
t_beta_hat[:,j] = v
#cal grad_v
grad_v = -x[:,j]*(y-(x*t_beta_hat).sum(axis=1))/n + lambdaa2 * self.DTD@v
temp = v - t*grad_v
G_v = temp*(1-t*lambdaa1/self.weight[j]/norm2(temp))*((1-t*lambdaa1/self.weight[j]/norm2(temp))>0)
#update beta
beta_hat[:,j] = G_v
#max change
delta = np.abs(beta_hat - old_beta).max()
if k % 50 == 0:
print('iteration: ' + str(k) + ' ========== max change: ' + str(delta))
if delta < self.tolerance or k >69999:
break
#else update beta_k-1 adn beta_k-2
older_beta = old_beta.copy()
old_beta = beta_hat.copy()
return beta_hat
def step2_CD(self, X, Y, lambdaa2):
k = 0
n = X.shape[0]
p = X.shape[1]
beta_hat = np.zeros((n,p))
old_beta = beta_hat.copy()
D = np.zeros((n-2,n))
for i in range(n-2):
D[i,i:(i+3)] = np.array([1,-2,1])
DTD = D.T@D
while True:
k += 1
for j in range(p):
X_j = np.delete(X,j,axis=1)
beta_j = np.delete(beta_hat,j,axis=1)
fac1 = lambdaa2*DTD + np.diag(X[:,j]**2)/n
fac2 = X[:,j]*(Y-(X_j*beta_j).sum(axis=1))/n
beta_hat[:,j] = np.linalg.inv(fac1)@fac2
delta = np.abs(beta_hat - old_beta).max()
#if k % 50 == 0:
#print('step 2 iteration: ' + str(k) + ' ========== max change: ' + str(delta))
if delta < self.tolerance or k > 29999:
break
#else update beta_k-1
old_beta = beta_hat.copy()
return beta_hat
def calMaxlambda1(self):
corr = np.apply_along_axis(lambda x:x*self.Y, 0, self.X)
#self.max_lambda1 = max(np.apply_along_axis(norm2, 0 , corr)/self.n)*max(self.weight)
self.max_lambda1 = max(self.weight*np.apply_along_axis(norm2, 0 , corr)/self.n)
def lambda1Interval(self):
self.min_lambda1 = self.max_lambda1 / self.lambdaPercent
#self.lambda1_interval = np.linspace(self.max_lambda1,self.min_lambda1,self.num_lambda1)
self.lambda1_interval = np.geomspace(self.max_lambda1,self.min_lambda1,self.num_lambda1)
#self.lambda1 = list(map(lambda x: math.log(x), np.linspace(math.e**self.max_lambda1,math.e**self.min_lambda1,self.num_lambda1)))
def evaluate(self, beta_hat, q):
beta_indic = np.concatenate((np.ones(q),np.zeros(self.p-q)))
beta_hat_indic = np.sign(np.apply_along_axis(norm2, 0, beta_hat))
confu = confusion_matrix(beta_indic, beta_hat_indic)
fp_n = confu[0][1]
fn_n = confu[1][0]
tp_n = confu[1][1]
precision = tp_n/(tp_n+fp_n)
recall = tp_n/(tp_n+fn_n)
f_score = 2*precision*recall/(precision+recall)
#TruePositve.append(tp_n)
#FalsePositive.append(fp_n)
#F_score.append(f_score)
indic_path = (np.apply_along_axis(norm2, 0, beta_hat)!=0)
beta_mse = np.sqrt(norm2(self.beta-beta_hat)**2/self.p)
y_mse = np.sqrt(norm2(self.Y-(self.X*beta_hat).sum(axis = 1))**2/self.n)
#beta_loss.append(beta_mse)
return tp_n, fp_n, f_score, indic_path, beta_mse, y_mse
def train(self):
self.score_lambda = np.zeros((self.num_lambda1, len(lambda2)))
self.best_score = 10000000
self.Path = np.zeros((self.num_lambda1,(self.p+1)))
self.TruePositive = []
self.FalsePositive = []
self.F_score = []
self.Beta_mse = []
self.pool = pd.DataFrame(columns = ['lambda1','TruePositive','FalsePositive','F_score','Beta_rmse','Y_rpe'])
X_sig_ind_old = []
for i,lambdaa1 in enumerate(self.lambda1_interval):
print('========= lambda1: round: '+ str(i+1) + ' =========')
if i == 0:
res = self.SSA(self.X, self.Y, lambdaa1, 0.1)
else:
res = self.SSA(self.X, self.Y, lambdaa1, 0.1,res)
X_sig_ind = np.where(np.apply_along_axis(norm2, 0, res)!=0)[0]
X_sig = self.X[:,X_sig_ind]
if set(X_sig_ind)-set(X_sig_ind_old)==set():
print('stop step 2')
continue
for j,lambdaa2 in enumerate(lambda2):
print('==== current lambda2:'+ str(lambdaa2) +' lambda1:'+ str(lambdaa1) + ' ====')
X_sig_ind_old = X_sig_ind.copy()
res_sig = self.step2_CD(X_sig, self.Y, lambdaa2)
score = self.cross_validation(X_sig, self.Y, lambdaa2)
self.score_lambda[i][j]=score
#cal confusionmatrix & F_score
tp_n, fp_n, f_score, indic_path,_,_ = self.evaluate(res, q)
beta_mse1 = norm2(self.beta[:,np.apply_along_axis(norm2, 0, res)!=0]-res_sig)**2
beta_mse2 = (self.beta[:,np.apply_along_axis(norm2, 0, res)==0]**2).sum()
beta_mse = np.sqrt((beta_mse1 + beta_mse2)/self.p)
y_mse = np.sqrt(norm2(self.Y-(X_sig*res_sig).sum(axis = 1))**2/self.n)
self.TruePositive.append(tp_n)
self.FalsePositive.append(fp_n)
self.F_score.append(f_score)
self.Beta_mse.append(beta_mse)
self.Path[i,0] = lambdaa1
self.Path[i,1:] = indic_path
poo = pd.DataFrame({'lambda2':lambdaa2,'lambda1':lambdaa1,'score': self.score_lambda[i][j],'TruePositive': tp_n,'FalsePositive':fp_n, 'F_score':f_score, 'Beta_rmse':beta_mse,'Y_rpe':y_mse},index=["0"])
self.pool = self.pool.append(poo,ignore_index=True)
if score < self.best_score:
self.best_score = score
self.best_lambda = {'lambda1':lambdaa1, 'lambda2':lambdaa2}
self.best_res = res
self.best_res_fina = res_sig
self.X_sig =X_sig
self.beta_mse_ic = beta_mse
# if tp_n == q or fp_n > 40:
# break
self.Path = np.delete(self.Path,np.where(self.Path.sum(axis=1)==0)[0],axis=0)
print('best_estimate')
#self.best_res_fina = self.step2_CD(self.X_sig, self.Y, self.best_lambda['lambda2'])
self.tp_n_ic, self.fp_n_ic, self.f_score_ic, self.indic_path_ic,_,_ = self.evaluate(self.best_res, q)
#self.beta_mse_ic = norm2(self.beta[:,np.apply_along_axis(norm2, 0, self.best_res)!=0]-self.best_res_fina)**2/self.n + (self.beta[:,np.apply_along_axis(norm2, 0, self.best_res)==0]**2).sum()/self.n
self.y_mse_ic = norm2(self.Y-(self.X_sig*self.best_res_fina).sum(axis = 1))**2/self.n
self.poo_bst_ic = pd.DataFrame({'lambda1_bst':self.best_lambda['lambda1'],'lambda2_bst':self.best_lambda['lambda2'],'score_bst': self.best_score,'TruePositive': self.tp_n_ic,'FalsePositive':self.fp_n_ic, 'F_score':self.f_score_ic, 'Beta_mse':self.beta_mse_ic,'Y_mse':self.y_mse_ic},index=["0"])
def cross_validation(self,x,y,lambdaa2):
test_n = int(self.n/self.K)
cv_ind = np.arange(0,self.n,1).reshape(test_n,self.K)
cv_c = cv_ind.shape[1]
p = x.shape[1]
self.score_lambda = np.zeros((self.num_lambda1, len(lambda2)))
y_mse = []
for l in range(cv_c):
print('+++++++ cv_group: '+ str(l) + ' +++++++++')
test_x = x[cv_ind[:,l]]
test_y = y[cv_ind[:,l]]
train_x = np.delete(x,cv_ind[:,l],axis = 0)
train_y = np.delete(y,cv_ind[:,l],axis = 0)
res = self.step2_CD(train_x, train_y, lambdaa2)
#cal beta_test_hat
beta_test_hat = np.zeros(test_n*p).reshape(test_n,p)
for m in range(test_n):
if cv_ind[m,l] == 0:
beta_test_hat[m,:] = res[0,:]
elif cv_ind[m,l] == self.n-1:
beta_test_hat[m,:] = res[-1,:]
else:
train_neibor_ori = cv_ind[m,l]-1
train_neibor = train_neibor_ori - (train_neibor_ori//self.K+train_neibor_ori//(l+1+self.K*m))
beta_test_hat[m,:] = res[train_neibor,:]
y_mse.append(norm2(test_y-(test_x*beta_test_hat).sum(axis = 1))**2/test_n)
mean_score = np.array(y_mse).mean()
return mean_score
def compare_lasso(self):
model_lasso = LassoCV(cv=10, max_iter=10000).fit(self.X,self.Y)
self.lambda_lasso = model_lasso.alphas_
self.coef_lasso = model_lasso.coef_
self.lasso_best_lambda = model_lasso.alpha_
self.lasso_best_beta = model_lasso.coef_*np.ones((self.n,self.p))
self.Path_lasso = np.zeros((len(self.lambda_lasso),(self.p+1)))
self.pool_lasso = pd.DataFrame(columns = ['lambda_lasso','TruePositve_lasso','FalsePositive_lasso','F_score_lasso','Beta_rmse_lasso','Y_rpe_lasso'])
###iteration for each lambda_lasso
for i, la_lambda in enumerate(self.lambda_lasso):
model_lasso_iter = Lasso(la_lambda).fit(self.X,self.Y)
model_lasso_iter_beta = model_lasso_iter.coef_*np.ones((self.n,self.p))
tp_n_lasso, fp_n_lasso, f_score_lasso, indic_path_lasso, beta_mse_lasso, y_mse_lasso = self.evaluate(model_lasso_iter_beta, q)
self.Path_lasso[i,0] = la_lambda
self.Path_lasso[i,1:(self.p+1)] = indic_path_lasso
la_poo = pd.DataFrame({'lambda_lasso':la_lambda,'TruePositve_lasso': tp_n_lasso,'FalsePositive_lasso':fp_n_lasso, 'F_score_lasso':f_score_lasso, 'Beta_rmse_lasso':beta_mse_lasso,'Y_rpe_lasso':y_mse_lasso},index=["0"])
self.pool_lasso = self.pool_lasso.append(la_poo,ignore_index=True)
q = 20
lambda2 = [10, 200, 500]
import sys
sys.path.append(r'/pathway/of/gen_data.py')
import gen_data
#data generation
beta, beta_begin = gen_data.gen_beta(100,50,20,'sin')
Y,X = gen_data.simuGenerator(100,50,0.3,beta)
##SSA
fina2 = SmoothingSubgroupAnalysis(X, Y, 5, beta, weight = 'lasso',lambdaPercent=500,num_lambda1=3)
fina2.calDD()
fina2.Weight()
fina2.calMaxlambda1()
fina2.lambda1Interval()
fina2.train() #where algorithm starts
evaluate_result = fina2.pool #evaluation results for all candidate tuning parameters
best_beta_est = fina2.best_res_fina #coefficient estimation results under the best parameter sets
path = fina2.Path #entering pathway of significant coefficients for each lambda1
best_result = fina2.poo_bst_ic # evaluation results under the best parameter sets