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import numpy as np;

import matplotlib.pyplot as plt;

import mpl_toolkits.mplot3d as p3d;

import DataHelper;

from UnaryLinearRegression import *;

from MultipleLinearRegression import *;

def __run(X, y):

lr = MultipleLinearRegression();

lr.fit(X, y);

lr.sigLevel = None;

return lr;

def __show(X, y, line):

predictY = line.predictValue(X);

plt.figure(1, (16, 10));

plt.scatter(predictY.A.flatten(), (y - predictY).A.flatten(), marker = "x");

plt.show(block = True);

def __vif(X):

p = X.shape[1];

y, X1 = None, None;

for i in range(0, p):

y = X[:, i];

if i == 0:

X1 = X[:, 1:];

elif i == p - 1:

X1 = X[:, :-1];

else:

X1 = np.hstack((X[:, :i], X[:, i + 1:]));

lr = MultipleLinearRegression();

lr.fit(X1, y);

print("VIF of {0} attribute: {1}".format(i + 1, 1 / (1 - lr.r2)));

def __loadData():

data = np.mat(np.loadtxt("data/hitters.csv", delimiter = ",", dtype = np.object));

names = np.mat(data[0, 1:], dtype = np.str).A.flatten().tolist();

names.remove(names[-2]);

names = np.array(names);

r = (data[:, -1] == '"N"').A.flatten();

data[r, -1] = 1;

data[~r, -1] = 0;

r = (data[:, -6] == '"W"').A.flatten();

data[r, -6] = 1;

data[~r, -6] = 0;

r = (data[:, -7] == '"N"').A.flatten();

data[r, -7] = 1;

data[~r, -7] = 0;

r = (data[:, -2] != 'NA').A.flatten();

X = np.mat(np.hstack((data[r, 1:-2], data[r, -1]))[1:, :], dtype = np.float);

y = np.mat(data[r, -2][1:, :], dtype = np.float);

return names, X, y;

def testMultipleLinearRegression():

data = np.mat(np.loadtxt("data/advertising.txt", delimiter = ","));

y = data[:, -1];

X = data[:, 1:-1];

model = __run(X, y);

model.predictValue(X[0, :]);

model.predictInterval(X);

__show(X, y, model);

print("original: ");

print(model);

__vif(X);

print("");

X = np.hstack((X[:, :-1], np.multiply(X[:, 0], X[:, 1])));

model = __run(X, y);

model.predictValue(X[0, :]);

model.predictInterval(X);

__show(X, y, model);

print("interaction: ");

print(model);

__vif(X);

print("");

def testOptimalSubset():

names, X, y = __loadData();

p = X.shape[1];

models = [];

for i in range(0, p):

layerModels = [];

for j in DataHelper.combinations(p, i + 1):

model = MultipleLinearRegression();

model.fit(X[:, j], y);

layerModels.append((j, model));

models.append(layerModels[np.argmin([item[1].rss for item in layerModels])]);

for indices, model in models:

print("variables: {0}, rss: {1}, r^2: {2}, aic: {3}, bic: {4}, adjusted-r^2: {5}".format(

", ".join(names[indices]), model.rss, model.r2, model.aic, model.bic, model.adjustedR2));

print("");

print("selected model: {0}\r\n".format(np.argmin([item[1].bic for item in models])));

print("\r\n\r\n".join([item[1].__str__() for item in models]));

def testForwardSelection():

names, X, y = __loadData();

n, p = X.shape;

models = [];

selectedFeatures = [];

remainFeatures = list(range(0, p));

previousX = np.mat(np.zeros((n, 0)));

for i in range(0, p):

layerModels = [];

for j in range(0, len(remainFeatures)):

model = MultipleLinearRegression();

model.fit(np.hstack((previousX, X[:, remainFeatures[j]])), y);

layerModels.append((remainFeatures[j], model));

index = np.argmin([item[1].rss for item in layerModels]);

selectedFeatures = selectedFeatures + [layerModels[index][0]];

remainFeatures.remove(layerModels[index][0]);

previousX = np.hstack((previousX, X[:, layerModels[index][0]]));

models.append((selectedFeatures, layerModels[index][1]));

for j, model in models:

print("variables: {0}, rss: {1}, r^2: {2}, aic: {3}, bic: {4}, adjusted-r^2: {5}".format(

", ".join(names[j]), model.rss, model.r2, model.aic, model.bic, model.adjustedR2));

print("");

print("selected model: {0}\r\n".format(np.argmin([item[1].bic for item in models])));

print("\r\n\r\n".join([item[1].__str__() for item in models]));

def testBackwardSelection():

names, X, y = __loadData();

n, p = X.shape;

models = [];

model = MultipleLinearRegression();

model.fit(X, y);

models.append((list(range(0, p)), model));

remainFeatures = list(range(0, p));

for i in range(0, p - 1):

layerModels = [];

for j in range(0, len(remainFeatures)):

model = MultipleLinearRegression();

model.fit(X[:, remainFeatures[0:j] + remainFeatures[j+1:]], y);

layerModels.append((remainFeatures[j], model));

index = np.argmin([item[1].rss for item in layerModels]);

remainFeatures.remove(layerModels[index][0]);

models.append((remainFeatures[:], layerModels[index][1]));

for j, model in models:

print("variables: {0}, rss: {1}, r^2: {2}, aic: {3}, bic: {4}, adjusted-r^2: {5}".format(

", ".join(names[j]), model.rss, model.r2, model.aic, model.bic, model.adjustedR2));

print("");

print("selected model: {0}\r\n".format(np.argmin([item[1].bic for item in models])));

print("\r\n\r\n".join([item[1].__str__() for item in models]));