py-ddspls 1.0.94

The multi data driven sparse pls package

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Multi (& Mono) Data-Driven Sparse PLS
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*mddspls is the python light package of the data-driven sparse PLS algorithm*

In 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, called **dd-sPLS** for 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 class **mddspls** and one associated important method denote **predict** permitting to predict from a new dataset. The function called **perf_mddsPLS** permits to compute cross-validation.

Data simulation
===============
One might be interested to simulate data and test the package through **regression** and **classification**::

#!/usr/bin/env python

import py_ddspls
import numpy as np
import sklearn.metrics as sklm
n = 100
mean = (0,0,0,0,0,0,0,0,0)
cov = [[1, 0.8,0.8,0.8,0.1,0.1,0.1,0.1,0.1],
[0.8,1, 0.8,0.8,0.1,0.1,0.1,0.1,0.1],
[0.8,0.8,1, 0.8,0.1,0.1,0.1,0.1,0.1],
[0.8,0.8,0.8,1, 0.1,0.1,0.1,0.1,0.1],
[0.1,0.1,0.1,0.1, 0.1,0.1,0.1,0.1,0.1],
[0.1,0.1,0.1,0.1, 0.1,0.1,0.1,0.1,0.1],
[0.1,0.1,0.1,0.1, 0.1,0.1,0.1,0.1,0.1],
[0.1,0.1,0.1,0.1, 0.1,0.1,0.1,0.1,0.1],
[0.1,0.1,0.1,0.1, 0.1,0.1,0.1,0.1,0.1]]
df = np.random.multivariate_normal(mean, cov, n)
Y = df[:,[0]]
k_groups = 2
lolo = np.linspace(min(Y),max(Y),k_groups+1)
Y_bin = np.zeros(n)
for ii in range(n):
for k_i in range(k_groups):
if (Y[ii]>=lolo[k_i])&(Y[ii]<lolo[k_i+1]):
Y_bin[ii] = k_i
if Y[ii]==lolo[k_groups]:
Y_bin[ii] = k_groups-1

Y = df[:,[0,2]]
X0 = df[:,[1,4,5]]
X0[0,:] = None
X1 = df[:,[6,8]]
X1[:,1] = 1
X2 = df[:,[3,7]]
Xs = {0:X0,1:X1,2:X2}
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"

The dd-sPLS regularization parameter is fixed to 0.6::

lambd=0.6

A train/test dataset is defined::

id_train = range(30,100)
id_test = range(30)
Xtrain = {0:X0[id_train,:],1:X1[id_train,:],2:X2[id_train,:]}
Ytrain = Y[id_train,:]
Xtest = {0:X0[id_test,:],1:X1[id_test,:],2:X2[id_test,:]}

Regression analysis
-------------------

Let us produce *2* axes::

R=2

Start model building and tcheck 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))

Cross validation can be performed with built tools, the parameter **NCORES** permits to use parallellization::

perf_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)
ax.plot(perf_model_reg[:,1], perf_model_reg[:,2], 'r',perf_model_reg[:,1], perf_model_reg[:,3],'b')
plt.legend(('Y_1 RMSE', 'Y_2 RMSE'),loc='upper')
plt.title('Leave-One-Out Cross-validation error against $\lambda$')
plt.xlabel('$\lambda$')
plt.ylabel('$RMSE$')
plt.show()

.. image:: images/reg.png
:width: 600

Classification analysis
-----------------------

Let us produce *1* axis:
:
R=1

Start 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 parameter **NCORES** permits to use parallellization::

perf_model_class = py_ddspls.model.perf_ddspls(Xs,Y_classif,R=1,kfolds="loo,n_lambd=10,NCORES=5,mode="classif")
print(perf_model_class)


**Enjoy :)**