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kmm.py
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kmm.py
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import math, numpy, sklearn.metrics.pairwise as sk, sys
from sklearn import linear_model
from cvxopt import matrix, solvers
#DENSITY ESTIMATION
#KMM solving the quadratic programming problem to get betas (weights) for each training instance
def kmm(Xtrain, Xtest, sigma):
n_tr = len(Xtrain)
n_te = len(Xtest)
#calculate Kernel
print 'Computing kernel for training data ...'
K_ns = sk.rbf_kernel(Xtrain, Xtrain, sigma)
#make it symmetric
K = 0.5*(K_ns + K_ns.transpose())
#calculate kappa
print 'Computing kernel for kappa ...'
kappa_r = sk.rbf_kernel(Xtrain, Xtest, sigma)
ones = numpy.ones(shape=(n_te, 1))
kappa = numpy.dot(kappa_r, ones)
kappa = -(float(n_tr)/float(n_te)) * kappa
#calculate eps
eps = (math.sqrt(n_tr) - 1)/math.sqrt(n_tr)
#constraints
A0 = numpy.ones(shape=(1,n_tr))
A1 = -numpy.ones(shape=(1,n_tr))
A = numpy.vstack([A0, A1, -numpy.eye(n_tr), numpy.eye(n_tr)])
b = numpy.array([[n_tr*(eps+1), n_tr*(eps-1)]])
b = numpy.vstack([b.T, -numpy.zeros(shape=(n_tr,1)), numpy.ones(shape=(n_tr,1))*1000])
print 'Solving quadratic program for beta ...'
P = matrix(K, tc='d')
q = matrix(kappa, tc='d')
G = matrix(A, tc='d')
h = matrix(b, tc='d')
beta = solvers.qp(P,q,G,h)
return [i for i in beta['x']]
#KMM PARAMETER TUNING
#Train a linear regression model with Lasso (L1 regularization).
#Model parameter selection via cross validation
#Predict the target (Beta) for a given test dataset
def regression(XTrain, betaTrain, XTest):
model = linear_model.LassoCV(cv=10, alphas=[0.001,0.005,0.01,0.05,0.1,0.5,1,5,10])
model.fit(XTrain, betaTrain)
Beta = model.predict(XTest)
return [i for i in Beta]
#KMM PARAMETER TUNING
#Compute J score for parameter tuning of KMM
def computeJ(betaTrain, betaTest):
tr = sum([i ** 2 for i in betaTrain])
te = sum(betaTest)
return ((1/float(len(betaTrain)))*tr) - ((2/float(len(betaTest)))*te)
#I/O OPERATIONS
#Read input csv file
def getData(filename):
data = []
with open(filename) as f:
content = f.readlines()
for line in content:
line = line.strip()
data.append(map(float,line.split(",")))
return data
#I/O OPERATIONS
#Write Output to file
def writeFile(filename, data):
if len(data) == 0:
return
with open(filename, 'w') as f:
for i in data:
f.write(str(i) + '\n')
#MAIN ALGORITHM
#compute beta
def getBeta(traindata, testdata, gammab):
Jmin = 0
beta = []
for g in gammab:
betaTrain = kmm(traindata, testdata, g)
betaTest = regression(traindata, betaTrain, testdata)
J = computeJ(betaTrain,betaTest)
#print betaTrain
#print betaTest
#print J
if len(beta) == 0:
Jmin = J
beta = list(betaTrain)
elif Jmin > J:
Jmin = J
beta = list(betaTrain)
return beta
#MAIN METHOD
def main():
#traindata = [[1,2,3],[4,7,4],[3,3,3],[4,4,4],[5,5,5],[3,4,5],[1,2,3],[4,7,4],[3,3,3],[4,4,4],[5,5,5],[3,4,5],[1,2,3],[4,7,4],[3,3,3],[4,4,4],[5,5,5],[3,4,5],[1,2,3],[4,7,4],[3,3,3],[4,4,4],[5,5,5],[3,4,5]]
#testdata = [[5,9,10],[4,5,6],[10,20,30],[1,2,3],[3,4,5],[5,6,7],[7,8,9],[100,100,100],[11,22,33],[12,11,5],[5,9,10],[4,5,6],[10,20,30],[1,2,3],[3,4,5],[5,6,7],[7,8,9],[100,100,100],[11,22,33],[12,11,5]]
#gammab = [0.001]
if len(sys.argv) != 4:
print 'Incorrect number of arguments.'
print 'Arg: training_file, test_file, output_file.'
return
traindata = getData(sys.argv[1])
testdata = getData(sys.argv[2])
gammab = [1/float(len(traindata)),0.0001,0.0005,0.001,0.005,0.01,0.05,0.1,0.5,1,5,10]
print 'Got training and test data.'
beta = getBeta(traindata, testdata, gammab)
writeFile(sys.argv[3], beta)
if __name__ == '__main__':
main()