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regressionalgorithms.py
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regressionalgorithms.py
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from __future__ import division # floating point division
import numpy as np
import math
import utilities as utils
def l2err(prediction,ytest):
""" l2 error (i.e., root-mean-squared-error) """
return np.linalg.norm(np.subtract(prediction,ytest))
def geterror(predictions, ytest):
# Can change this to other error values
return l2err(predictions,ytest)/ytest.shape[0]
class Regressor:
"""
Generic regression interface; returns random regressor
Random regressor randomly selects w from a Gaussian distribution
"""
def __init__( self, params={}):
""" Params can contain any useful parameters for the algorithm """
self.weights = None
self.params = {}
def reset(self, params):
""" Can pass parameters to reset with new parameters """
try:
utils.update_dictionary_items(self.params,params)
except AttributeError:
# Variable self.params does not exist, so not updated
# Create an empty set of params for future reference
self.params = {}
# Could also add re-initialization of weights, so that does not use previously learned weights
# However, current learn always initializes the weights, so we will not worry about that
def getparams(self):
return self.params
def learn(self, Xtrain, ytrain):
""" Learns using the traindata """
self.weights = np.random.rand(Xtrain.shape[1])
def predict(self, Xtest):
""" Most regressors return a dot product for the prediction """
ytest = np.dot(Xtest, self.weights)
return ytest
class RangePredictor(Regressor):
"""
Random predictor randomly selects value between max and min in training set.
"""
def __init__( self, params={} ):
""" Params can contain any useful parameters for the algorithm """
self.min = 0
self.max = 1
self.params = {}
def learn(self, Xtrain, ytrain):
""" Learns using the traindata """
self.min = np.amin(ytrain)
self.max = np.amax(ytrain)
def predict(self, Xtest):
ytest = np.random.rand(Xtest.shape[0])*(self.max-self.min) + self.min
return ytest
class MeanPredictor(Regressor):
"""
Returns the average target value observed; a reasonable baseline
"""
def __init__( self, params={} ):
self.mean = None
def learn(self, Xtrain, ytrain):
""" Learns using the traindata """
self.mean = np.mean(ytrain)
def predict(self, Xtest):
return np.ones((Xtest.shape[0],))*self.mean
class FS_SC_LinearRegression(Regressor):
"""
Linear Regression with feature selection
"""
def __init__( self, params={} ):
self.weights = None
self.params = {'features': [1,2,3,4,5]}
self.reset(params)
def stoch_descent(self, x, y, w):
alpha = .01
self.epoch_error = []
for epoch in range(0,9):
self.epoch_error.append(np.linalg.norm(np.dot(x,w) - y)/np.shape(x)[0])
state = np.random.get_state()
np.random.shuffle(x)
np.random.set_state(state)
np.random.shuffle(y)
for t in range(0, np.shape(x)[0]):
alpha = alpha
w = w - alpha * np.dot((np.dot(x[t,:],w) - y[t]),x[t,:])
return w
def learn(self, Xtrain, ytrain):
""" Learns using the traindata """
# Dividing by numsamples before adding ridge regularization
# to make the regularization parameter not dependent on numsamples
numsamples = Xtrain.shape[0]
Xless = Xtrain[:,self.params['features']]
w0 = np.array(list(range(0, np.shape(Xless)[1])))
self.weights = self.stoch_descent(Xless, ytrain, w0)
def predict(self, Xtest):
Xless = Xtest[:,self.params['features']]
ytest = np.dot(Xless, self.weights)
return ytest
class FS_B_LinearRegression(Regressor):
"""
Linear Regression with feature selection
"""
def __init__( self, params={} ):
self.weights = None
self.params = {'features': [1,2,3,4,5]}
self.reset(params)
def batch_descent(self, x, y, w):
alpha = 1
self.epoch_error = []
new_error = 3
Ew = 1
while np.abs(new_error-Ew)>0.01:
Ew = np.sum((np.dot(x, w) - y)**2)/x.shape[0]
new_w = w-alpha*np.dot(x.T,(np.dot(x,w)-y))
new_error = np.sum((np.dot(x, new_w) - y)**2)/x.shape[0]
while new_error>=Ew:
alpha = .5*alpha
new_w = w-alpha*np.dot(x.T,(np.dot(x,w)-y))
new_error = np.sum((np.dot(x, new_w) - y)**2)/x.shape[0]
w = w-alpha*np.dot(x.T,(np.dot(x,w)-y))
new_error = np.sum((np.dot(x, w) - y)**2)/x.shape[0]
self.epoch_error.append(np.linalg.norm(np.dot(x,w) - y)/np.shape(x)[0])
return(w)
def learn(self, Xtrain, ytrain):
""" Learns using the traindata """
# Dividing by numsamples before adding ridge regularization
# to make the regularization parameter not dependent on numsamples
numsamples = Xtrain.shape[0]
Xless = Xtrain[:,self.params['features']]
w0 = np.array(list(range(0, np.shape(Xless)[1])))
self.weights = self.batch_descent(Xless, ytrain, w0)
def predict(self, Xtest):
Xless = Xtest[:,self.params['features']]
ytest = np.dot(Xless, self.weights)
return ytest
class FSLinearRegression(Regressor):
"""
Linear Regression with feature selection
"""
def __init__( self, params={} ):
self.weights = None
self.params = {'features': [1,2,3,4,5]}
self.reset(params)
def learn(self, Xtrain, ytrain):
""" Learns using the traindata """
# Dividing by numsamples before adding ridge regularization
# to make the regularization parameter not dependent on numsamples
numsamples = Xtrain.shape[0]
Xless = Xtrain[:,self.params['features']]
self.weights = np.dot(np.dot(np.linalg.inv(np.dot(Xless.T,Xless)), Xless.T),ytrain)
def predict(self, Xtest):
Xless = Xtest[:,self.params['features']]
ytest = np.dot(Xless, self.weights)
return ytest
class FS_pinv_LinearRegression(Regressor):
"""
Linear Regression with feature selection
"""
def __init__( self, params={} ):
self.weights = None
self.params = {'features': [1,2,3,4,5]}
self.reset(params)
def learn(self, Xtrain, ytrain):
""" Learns using the traindata """
# Dividing by numsamples before adding ridge regularization
# to make the regularization parameter not dependent on numsamples
numsamples = Xtrain.shape[0]
Xless = Xtrain[:,self.params['features']]
self.weights = np.dot(np.dot(np.linalg.pinv(np.dot(Xless.T,Xless)), Xless.T),ytrain)
def predict(self, Xtest):
Xless = Xtest[:,self.params['features']]
ytest = np.dot(Xless, self.weights)
return ytest
class FSRidgeRegression(Regressor):
"""
Linear Regression with feature selection
"""
def __init__( self, params={} ):
self.weights = None
self.params = {'features': [1,2,3,4,5], 'lambda': 0}
self.reset(params)
#self.lambda = lambda
def learn(self, Xtrain, ytrain):
""" Learns using the traindata """
# Dividing by numsamples before adding ridge regularization
# to make the regularization parameter not dependent on numsamples
numsamples = Xtrain.shape[0]
Xless = Xtrain[:,self.params['features']]
self.weights = np.dot(np.dot(np.linalg.inv(np.dot(Xless.T,Xless)+(self.params['lambda']*np.identity(np.shape(Xless)[1]))), Xless.T),ytrain)
def predict(self, Xtest):
Xless = Xtest[:,self.params['features']]
ytest = np.dot(Xless, self.weights)
return ytest
class MPLinearRegression(Regressor):
"""
Linear Regression with feature selection
"""
def __init__( self, params={} ):
self.weights = None
self.params = {'features': [1,2,3,4,5]}
self.reset(params)
#self.lambda = lambda
def learn(self, Xtrain, ytrain):
""" Learns using the traindata """
# Dividing by numsamples before adding ridge regularization
# to make the regularization parameter not dependent on numsamples
numsamples = Xtrain.shape[0]
xless = Xtrain[:,self.params['features']]
#Starting with adding constant feature
x = np.ones(np.shape(xless)[0])
self.weights = np.array([np.sum(ytrain)/np.shape(ytrain)[0]])
residuals = ytrain - x*self.weights
self.select_cols = []
self.highest_corr = []
self.errors_for = []
self.max_col_corr = 1
while self.max_col_corr>=.05:
col_corr = [np.abs(np.corrcoef(residuals,col)[0,1]) for col in xless.T]
self.max_col_corr = max(col_corr)
highest_corr_index = col_corr.index(max(col_corr))
self.select_cols.append(highest_corr_index)
self.highest_corr.append(max(col_corr))
x = np.column_stack((x, xless[:,highest_corr_index]))
self.weights = np.dot(np.dot(np.linalg.inv(np.dot(x.T,x)), x.T),ytrain)
self.errors_for.append(geterror(np.dot(x,self.weights),ytrain))
#print(geterror(np.dot(x,weights),ytrain))
residuals = ytrain - np.dot(x,self.weights)
def predict(self, Xtest):
xless = Xtest[:,self.params['features']]
x = np.ones(np.shape(xless)[0])
x = np.column_stack((x, xless[:,self.select_cols]))
ytest = np.dot(x, self.weights)
return ytest