我正在尝试使用950个样本和大约5000个功能对数据进行套索优化。套索函数是$（1 /（2 * numberofsamples））* || y - Xw || ^ 2_2 + alpha * || w || _1 $。一旦我通过初始化尝试最小化，我会得到完全不同的w这是奇怪的，因为套索是凸的，初始化不应该影响结果。这是套索的结果，有或没有初始化。 tol是容忍度。如果w的变化变得低于容差，就会发生收敛。
tol=0.00000001
##### lasso model errors #####
gene: 5478 matrix error: 0.069611732213
with initialization: alpha: 1e-20 promotion: -3.58847815733e-13
coef: [-0.00214732 -0.00509795 0.00272167 -0.00651548 -0.00164646 -0.00115342
0.00553346 0.01047653 0.00139832]
without initialization: alpha: 1e-20 promotion: -19.0735249749
coef: [-0.03650629 0.08992003 -0.01287155 0.03203973 0.1567577 -0.03708655
-0.13710957 -0.01252736 -0.21710334]
with initialization: alpha: 1e-15 promotion: 1.06179081478e-10
coef: [-0.00214732 -0.00509795 0.00272167 -0.00651548 -0.00164646 -0.00115342
0.00553346 0.01047653 0.00139832]
without initialization: alpha: 1e-15 promotion: -19.0735249463
coef: [-0.03650629 0.08992003 -0.01287155 0.03203973 0.1567577 -0.03708655
-0.13710957 -0.01252736 -0.21710334]
Warning (from warnings module):
File "/usr/local/lib/python2.7/site-packages/sklearn/linear_model/coordinate_descent.py", line 491
ConvergenceWarning)
ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Fitting data with very small alpha may cause precision problems.
with initialization: alpha: 1e-10 promotion: 0.775144987537
coef: [-0.00185139 -0.0048819 0.00218349 -0.00622618 -0.00145647 -0.00115857
0.0055919 0.01072924 0.00043773]
without initialization: alpha: 1e-10 promotion: -17.8649603301
coef: [-0.03581581 0.0892119 -0.01232829 0.03151441 0.15606195 -0.03734093
-0.13604286 -0.01247732 -0.21233529]
with initialization: alpha: 1e-08 promotion: -5.87121366314
coef: [-0. 0. -0. -0.01064477 0. -0.00116167
-0. 0.01114746 0. ]
without initialization: alpha: 1e-08 promotion: 4.05593555389
coef: [ 0. 0.04505117 0.00668611 0. 0.07731668 -0.03537848
-0.03151995 0. -0.00310122]
max promote:
4.05593555389
对于实现，我使用了python包sklearn.linear_model的lasso函数。我也改变了数据，但新数据的结果也随初始化而改变。我认为这很奇怪，但我无法分析并找到解释。
这是我的代码的一部分，它与套索有关。我的数据是基因表达。我在标准化和非标准化数据上测试代码。在这两个方面，最初的观点都有所不同。
alpha_lasso = [1e-20,1e-15, 1e-10, 1e-8, 1e-7,1e-6,1e-5,1e-4, 1e-3,1e-2, 1, 5 ,20]
lassoreg = Lasso(alpha=alpha_lasso[i],warm_start=True,tol=0.00000001,max_iter=100000)
lassoreg.coef_ = mybeta[:,j-c]
lassoreg.fit(train[:,predictors],train[:,y])
y_train_pred = lassoreg.predict(A)#train[:,predictors])
y_test_pred = lassoreg.predict(C)#test[:,predictors])
这也是我的全部代码：
import pandas as pd
import random
import tensorflow as tf
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.gridspec as gridspec
import os
from GEOparse.GEOTypes import (GSE, GSM, GPL, GDS,
GDSSubset, GEODatabase,
DataIncompatibilityException,
NoMetadataException,
)
import GEOparse as GEO
import numpy as np
import copy
import sys
import math
from sklearn import linear_model
from sklearn.linear_model import Lasso
from sklearn.linear_model import LassoLars
from sklearn.linear_model import MultiTaskLassoCV
from sklearn.linear_model import coordinate_descent
from sklearn.linear_model import lasso_path, enet_path
import numpy as np
from sklearn.base import BaseEstimator, RegressorMixin
from copy import deepcopy
miss_percent = 0.1
alpha_lasso = [1e-20,1e-15, 1e-10, 1e-8, 1e-7,1e-6,1e-5,1e-4, 1e-3,1e-2, 1, 5 ,20]
mins=[]
maxs=[]
mean_err=[]
alphas=[]
mins1=[]
maxs1=[]
mean_err1=[]
alphas1=[]
#mnist = input_data.read_data_sets('../../MNIST_data', one_hot=True)
def getdata(percent):
gsd = GEO.get_GEO(geo="GDS4971")
ngsd = gsd.table.replace('null', np.NaN)
ngsd = ngsd.dropna(axis=0, how='any')
ngsd =ngsd.transpose()
dataarray = ngsd.values
data = np.delete(dataarray, [0,1], 0)
x = data.astype(np.float)
r_df = x.shape[0]
c_df = x.shape[1]
r = int(r_df-math.sqrt((1-percent)*r_df))
c = int(c_df-math.sqrt((1-percent)*c_df))
train = x[0:r,:]
test = x[r:r_df,:]
return x,train,test,r_df,c_df,r,c
genedata,train,test,r_df,c_df,r,c = getdata(miss_percent)
predictors = range(0,c)
promotion =[[0.001 for x in range(len(alpha_lasso))] for y in range(c_df-c)]
promotion = np.asmatrix(promotion)
#error of ax-b
error_aw_b = [[0.001 for x in range(len(alpha_lasso))] for y in range(c_df-c)]
error_aw_b = np.asmatrix(error_aw_b)
#error of cw-x
error_cw_x = [[0.001 for x in range(len(alpha_lasso))] for y in range(c_df-c)]
error_cw_x = np.asmatrix(error_cw_x)
#error of lasso function
error_lasso = [[0.001 for x in range(len(alpha_lasso))] for y in range(c_df-c)]
error_lasso = np.asmatrix(error_lasso)
promotion1 =[[0.001 for x in range(len(alpha_lasso))] for y in range(c_df-c)]
promotion1 = np.asmatrix(promotion)
#error of ax-b
error_aw_b1 = [[0.001 for x in range(len(alpha_lasso))] for y in range(c_df-c)]
error_aw_b1 = np.asmatrix(error_aw_b)
#error of cw-x
error_cw_x1 = [[0.001 for x in range(len(alpha_lasso))] for y in range(c_df-c)]
error_cw_x1 = np.asmatrix(error_cw_x)
#error of lasso function
error_lasso1 = [[0.001 for x in range(len(alpha_lasso))] for y in range(c_df-c)]
error_lasso1 = np.asmatrix(error_lasso)
mybeta = #any initialization
###################### LASSO #####################
print("##### lasso model errors #####")
for j in range(c,c+1):
mean_err=[]
print("\n")
y=j
eachMeanError= math.sqrt((np.power(errorC[:,j-c],2)).sum()/(r_df-r))
print("gene: "+str(j)+ " matrix error: "+ str(eachMeanError))
for i in range(0,4):#len(alpha_lasso)):
lassoreg = Lasso(alpha=alpha_lasso[i],warm_start=True,tol=0.00000001,max_iter=100000)
lassoreg.coef_ = mybeta[:,j-c]
lassoreg.fit(train[:,predictors],train[:,y])
y_train_pred = lassoreg.predict(A)#train[:,predictors])
y_test_pred = lassoreg.predict(C)#test[:,predictors])
y_lasso_func = (1/(2*r))*sum(y_train_pred)+sum(abs(lassoreg.coef_))
################## RMS ##################
error_aw_b[j-c,i] = math.sqrt(sum((y_train_pred-train[:,y])**2)/r)
error_lasso[j-c,i] = y_lasso_func
error_cw_x[j-c,i] = math.sqrt(sum((y_test_pred-test[:,y])**2)/(r_df-r))
mins.extend([(error_cw_x.min())])
maxs.extend([(error_cw_x.max())])
promotion[j-c,i] = (((eachMeanError-error_cw_x[j-c,i])/eachMeanError)*100)
print("alpha: "+str(alpha_lasso[i])+ " error_aw_b: "+str(error_aw_b[j-c,i]) + " error_cw_x: " + str(error_cw_x[j-c,i])+" error_lasso: "+str(error_lasso[j-c,i]) + " promotion: " + str(promotion[j-c,i]) )
print("coef: " + str(lassoreg.coef_[1:10]))
lassoreg1 = Lasso(alpha=alpha_lasso[i],tol=0.00000001,max_iter=100000)
lassoreg1.fit(train[:,predictors],train[:,y])
y_train_pred1 = lassoreg1.predict(A)#train[:,predictors])
y_test_pred1 = lassoreg1.predict(C)#test[:,predictors])
y_lasso_func1 = (1/(2*r))*sum(y_train_pred1)+sum(abs(lassoreg1.coef_))
################## RMS ##################
error_aw_b1[j-c,i] = math.sqrt(sum((y_train_pred1-train[:,y])**2)/r)
error_lasso1[j-c,i] = y_lasso_func1
error_cw_x1[j-c,i] = math.sqrt(sum((y_test_pred1-test[:,y])**2)/(r_df-r))
mins1.extend([(error_cw_x1.min())])
maxs1.extend([(error_cw_x1.max())])
promotion1[j-c,i] = (((eachMeanError-error_cw_x1[j-c,i])/eachMeanError)*100)
print("alpha: "+str(alpha_lasso[i])+ " error_aw_b: "+str(error_aw_b1[j-c,i]) + " error_cw_x: " + str(error_cw_x1[j-c,i])+" error_lasso: "+str(error_lasso1[j-c,i]) + " promotion: " + str(promotion1[j-c,i]) )
print("coef: " + str(lassoreg1.coef_[1:10]))
print("\n")
print("max promote:")
print((promotion[j-c,:].max()))
f = open('analyse_col', 'wb')
np.save(f, [promotion,alphas,error_cw_x,mins,maxs])
f.close()
plt.plot(promotion[:,j-c])
plt.ylabel('coef for ')
plt.xlabel('each gene')
plt.show()
答案 0 :(得分：1)
您获得了M个样本和N个要素，M=950 , N=5000。
这里的内容是：但是当p> n时，套索标准不是严格凸的，因此它可能没有唯一的最小值。 Documentation。
这使得优化变得复杂（请记住：它不是所有问题中最简单的，因为它本质上是非平滑的！）并且大多数求解器将针对其他情况进行调整。
在您的情况下，有一个明确的警告和建议：增加迭代次数！并确保您的 alphas 不会太小。不确定，你是如何开始后者的，但是如果那些1e-15量级是手工制作的，那就重新考虑一下你的问题制定了！
警告足以不将这些解决方案作为优化的解决方案（因此：我的套索针对不同的inits有不同的解决方案在技术上不正确;只有你的近似解决方案表现得那样）。