Interaction Terms Aware Sparse Grids

This example compares standard sparse grids with sparse grids that only contain a subset of all possible interaction terms.

It uses the optical digits dataset as an example.

import numpy as np
import pysgpp as sg; sg.omp_set_num_threads(4)
import pandas as pd
import sklearn.preprocessing as pre

This function scales all predictors so that they are suitable for sparse grids.

def scale(df, scaler=None):
Y = df.ix[:,-1] # save Y (don't need to transform it/useless for cat. data!)
X = df.values
if scaler:
X = scaler.transform(X)
scaler = pre.MinMaxScaler()
X = scaler.fit_transform(X)
index = df.index
columns = df.columns
df = pd.DataFrame(data=X, index=index, columns=columns)
df.ix[:,-1] = Y
return scaler, df

This function downloads the optical digits dataset and performs the necessary preprocessing steps.

def get_dataset():
train_url = ""
test_url = ''
print "Loading dataset from UCI repository."
columns = ["x{}".format(i) for i in range(0, 64)] + ['digit']
df_train = pd.read_csv(train_url, header=None, index_col=None)
df_test = pd.read_csv(train_url, header=None, index_col=None)
print "Preprocessing dataset."
df_complete = df_train.append(df_test, ignore_index=True)
scaler , _ = scale(df_complete)
_, df_train = scale(df_train, scaler)
_, df_test = scale(df_test, scaler)
return df_train, df_test

This function evaluates a sparse grid learner for a different set of interaction terms. To do this, it first trains a classification learner with the training set and then evaluates it using the testing part of the dataset.

def evaluate(X_tr, y_tr, X_te, y_te, interactions=None):
grid = sg.RegularGridConfiguration()
grid.dim_ = 64
grid.level_ = 2
grid.type_ = sg.GridType_ModLinear
adapt = sg.AdpativityConfiguration()
adapt.numRefinements_ = 0
adapt.noPoints_ = 0
solv = sg.SLESolverConfiguration()
solv.maxIterations_ = 50
solv.eps_ = 10e-6
solv.threshold_ = 10e-6
solv.type_ = sg.SLESolverType_CG
final_solv = solv
final_solv.maxIterations = 200
regular = sg.RegularizationConfiguration()
regular.type_ = sg.RegularizationType_Identity
regular.exponentBase_ = 1.0
regular.lambda_ = 0.1
X_tr = sg.DataMatrix(X_tr)
y_tr = sg.DataVector(y_tr)
X_te = sg.DataMatrix(X_te)
y_te = sg.DataVector(y_te)
if interactions is None:
estimator = sg.ClassificationLearner(grid, adapt, solv, final_solv,regular)
estimator = sg.ClassificationLearner(grid, adapt, solv, final_solv,regular, interactions)
return estimator.getAccuracy(X_te,y_te)
def main():
df_tr, df_te = get_dataset()
X_tr = np.array(df_tr.ix[:,0:-1])
y_tr = (df_tr.ix[:,-1]).values
X_te = np.array(df_te.ix[:,0:-1])
y_te = (df_te.ix[:,-1]).values

We first create all possible interactions between pixels whose pairwise \(L_2\) distance is smaller than \(\sqrt{2}\).

nn = sg.NearestNeighbors(8,8)
interactions = nn.getAllInteractions(3, 2**0.5)

We then compare a standard sparse grid with a sparse grid learner that only contains the aforementioned interaction terms.

standard_accuracy = evaluate(X_tr, y_tr, X_te, y_te)
print "The standard sparse grid achieved an accuracy of {:2.3f}".format(standard_accuracy)
ia_accuracy = evaluate(X_tr, y_tr, X_te, y_te, interactions)
print "The interaction aware grid achieved an accuracy of {:2.3f}".format(ia_accuracy)
if __name__ == '__main__':