Package: py-ddspls
mddspls is the python light package of the data-driven sparse PLS algorithmIn the high dimensional settings (large number of variables), one objective is to select the relevant variables and thus to reduce the dimension. That subspace selection is often managed with supervised tools. However, some data can be missing, compromising the validity of the sub-space selection. We propose a PLS, Partial Least Square, based method, calleddd-sPLSfor data-driven-sparse PLS, allowing jointly variable selection and subspace estimation while training and testing missing data imputation through a new algorithm called Koh-Lanta.It contains one main classmddsplsand one associated important method denotepredictpermitting to predict from a new dataset. The function calledperf_mddsPLSpermits to compute cross-validation.Data simulationOne might be interested to simulate data and test the package throughregressionandclassification. Here a spiked model is used:#!/usr/bin/env python

import py_ddspls
import numpy as np
import sklearn.metrics as sklm

n = 100
R_model = 10
R_X_Y = 2
T = 10
L = np.array(np.random.normal(0,1,n*R_model)).reshape((n,R_model))

p_t = 20
q = 5

Xs = {}

for t in range(T):
        Omega_1_2 = np.diag(np.random.uniform(0,1,R_model))
        u,s,vh = np.linalg.svd(np.array(np.random.normal(0,1,p_t*p_t)).reshape((p_t,p_t)))
        U_mod_T = vh[0:R_model,:]
        Xs[t] = L@Omega_1_2@U_mod_T

Omega_y_1_2 = np.diag(np.concatenate((np.ones(R_X_Y),np.zeros(R_model-R_X_Y))))
u,s,vh = np.linalg.svd(np.array(np.random.normal(0,1,R_model*R_model)).reshape((R_model,R_model)))
U_mod_T = vh[:,0:q]
Y = L@Omega_y_1_2@U_mod_T

k_groups = 2
Y_transfor = Y[:,0]
lolo = np.linspace(np.min(Y_transfor),np.max(Y_transfor),k_groups+1)
Y_bin = np.zeros(n)
for ii in range(n):
        for k_i in range(k_groups):
                if (Y_transfor[ii]>=lolo[k_i])&(Y_transfor[ii]<lolo[k_i+1]):
                        Y_bin[ii] = k_i
                if Y_transfor[ii]==lolo[k_groups]:
                        Y_bin[ii] = k_groups-1

pos_0 = np.where(Y_bin==0)[0]
pos_1 = np.where(Y_bin==1)[0]
Y_classif = np.repeat("Class 2",n)
Y_classif[pos_1] = "Class 1"

# Missing values are introduced in blocks 1, 2 and 3
Xs[0][0,:] = None
Xs[1][1:3,:] = None
Xs[2][2:10,:] = NoneThe dd-sPLS regularization parameter is fixed to 0.6:lambd=0.6A train/test dataset is defined for the sack of the example:id_train = range(30,100)
id_test = range(30)
Xtrain = {}
Ytrain = Y[id_train,:]
Xtest = {}Regression analysisLet us produce2axes:R=2Start model building and check results with sklearn tools:mod_0=py_ddspls.model.ddspls(Xtrain,Ytrain,lambd=lambd,R=R,mode="reg",verbose=True)
Y_est_reg = mod_0.predict(Xtest)
print(sklm.mean_squared_error(Y[id_test,:],Y_est_reg))Leave-one-out cross validation can be performed with built tools, the parameterNCORESpermits to fix the number of cores to be used in the processperf_model_reg = py_ddspls.model.perf_ddspls(Xs,Y,R=R,kfolds="loo",n_lambd=10,NCORES=4,mode="reg")
print(perf_model_reg)

fig = plt.figure()
ax = fig.add_subplot(1, 1, 1)
cols = ['r','g','b','y','black','brown']
for jj in range(q):
        ax.plot(perf_model_reg[:,1],perf_model_reg[:,jj+2],cols[jj])

ax.plot(perf_model_reg[:,1],
        np.sqrt((perf_model_reg[:,2:(2+q)]**2).mean(axis=1)),"brown",linewidth=2,ls="--")
plt.legend(np.concatenate((1+np.arange(q),np.array("RMSE of RMSE errors").reshape((1,)))),loc='upper')
plt.title('Leave-One-Out Cross-validation error against $\lambda$')
plt.xlabel('$\lambda$')
plt.ylabel('RMSE')
plt.show()Which returns this kind of graphicsFor 0.9 one can find a minimum of the RMSE of the RMSE of each variable. This
oservation can be mitigated assuming that onlyYvariables 1 and 4 are
well described by theXdataset. In that context, a discussion with
experts, might help to decide the value to give to the parameter.Classification analysisLet us produce1axis since only one group must be discriminated:R=1Start model building and tcheck results with sklearn tools:mod_0_classif=py_ddspls.model.ddspls(Xs,Y_bin,lambd=lambd,R=R,mode="clas",verbose=True)
Y_est = mod_0_classif.predict(Xtest)
print(sklm.classification_report(Y_est, Y_classif[id_test]=='Class 1'))Cross validation can be performed with built tools, the parameterNCORESpermits to use parallellization:perf_model_class = py_ddspls.model.perf_ddspls(Xs,Y_classif,R=R,kfolds="loo",n_lambd=40,NCORES=7,mode="classif")
print(perf_model_class)

fig = plt.figure()
ax = fig.add_subplot(1, 1, 1)
ax.plot(perf_model_class[:,1], perf_model_class[:,2])
plt.title('Leave-One-Out Cross-validation error against $\lambda$')
plt.xlabel('$\lambda$')
plt.ylabel('Classification Error')
plt.show()Which returns this kind of graphicsOne that figure one can see that a parameter approximately equal to 0.45 can bechosen.Enjoy :)