def test_system5():
from a_machine.system5 import model
from santa_fe import getData
data = getData('B1.dat')
test = getData('B2.dat')
median = np.median(data[:,:3], axis=0)
std = np.std(data[:,:3], axis=0)
train_size = 1000
sequence_length = 1
gamma_quantile = 100
test_size = 200
train = (( data[:train_size] - median ) / std).astype('float32')
m = model( dimension=0 )
m.train(train)
xN = test_size
#yN = 20
xrange = [train.min(), train.max()]
#yrange = [train[:-1,1].min(), train[:-1,1].max()]
xstep = ((xrange[1]-xrange[0] ) / xN )
#ystep = ((yrange[1]-yrange[0] ) / yN )
#X = np.dstack(np.mgrid[xrange[0]:xrange[1]:xstep,yrange[0]:yrange[1]:ystep]).reshape([ xN *yN,2]).astype('float32')
x = np.arange(xrange[0],xrange[1],xstep)
#y = np.arange(yrange[0],yrange[1],ystep)
Y = m.predict( X )
plt.scatter(train[:-1], train[1:] )
plt.plot( x, Y, 'k', lw=2 )
plt.show()
def test_system4a():
print "Initializing"
from a_machine.system4 import model
from santa_fe import getData
data = getData('B1.dat')
test = getData('B2.dat')
median = np.median(data[:,:2], axis=0)
std = np.std(data[:,:2], axis=0)
train_size = 1000
sequence_length = 1
gamma_quantile = 100
test_size = 200
train = (( data[:train_size,:2] - median ) / std).astype('float32')
labels = (( data[sequence_length:train_size+sequence_length,0] - median[0] ) / std[0]).astype('float32')
#svm = SVR( nu=.1, C=50)
m1 = model( dimension=0, sequence_length=sequence_length )
m2 = model( dimension=0, sequence_length=sequence_length )
#svm.train( kernel_matrix(np.expand_dims(train,1), np.expand_dims(train,1), .5), labels)
m1.train(train[:,:2], train_size, [ [0,[0,1]], [0,[0]] ])
m2.train(train[:,:2], train_size, [ [0,[0,1]], ])
xN = 20
yN = 20
xrange = [train[:,0].min(), train[:,0].max()]
yrange = [train[:,1].min(), train[:,1].max()]
xstep = ((xrange[1]-xrange[0] ) / xN )
ystep = ((yrange[1]-yrange[0] ) / yN )
X = np.dstack(np.mgrid[xrange[0]:xrange[1]:xstep,yrange[0]:yrange[1]:ystep]).reshape([ xN *yN,2]).astype('float32')
x = np.arange(xrange[0],xrange[1],xstep)
y = np.arange(yrange[0],yrange[1],ystep)
#Z = svm.predict( kernel_matrix( np.expand_dims(X,1), np.expand_dims(train,1), .5) )
Z1 = m1.predict( np.expand_dims(X,1) )
Z2 = m2.predict( np.expand_dims(X,1) )
#ax = plt.subplot(111, projection='3d')
#ax.plot( x[:,0], x[:,1], y, 'k,' )
#plt.plot( train[:,0], labels, 'k,', alpha=.2 )
#plt.plot( train[svm.support_,0], labels[svm.support_], 'o', alpha=.15 )
#plt.plot(x[:,0],y, 'r', lw=2)
#plt.show()
mlab.points3d(train[:,0], train[:,1], labels, scale_factor=.05, opacity=.2)
#mlab.points3d(train[m.svm.SV_indices,0], train[m.svm.SV_indices,1], labels[m.svm.SV_indices], scale_factor=.05)
mlab.surf( x,y,Z1.reshape(xN,yN), color=(1,0,0) ) #red, multiple slices
mlab.surf( x,y,Z2.reshape(xN,yN)+.1, color=(0,1,0) ) #green, single slice
print m1.svm.SV_indices
print m2.svm.SV_indices
print "%s SV of %s" % (len(m1.svm.SV_indices), train.shape[0])
print "%s SV of %s" % (len(m2.svm.SV_indices), train.shape[0])
mlab.show()
def run():
from a_machine.system7 import model
from santa_fe import getData
data = getData('B1.dat')[:,1]
test = getData('B2.dat')
median = np.median(data)
std = np.std(data)
train_size = 100
sequence_length = 1
gamma_quantile = 100
test_size = 201
train = (( data[:train_size] - median ) / std).astype('float32')
#train = data[:train_size].astype('float32')
m = model( dimension=0 )
m.train(train)
xN = test_size
#yN = 20
xrange = [train.min(), train.max()]
#yrange = [train[:-1,1].min(), train[:-1,1].max()]
xstep = ((xrange[1]-xrange[0] ) / xN )
#ystep = ((yrange[1]-yrange[0] ) / yN )
#X = np.dstack(np.mgrid[xrange[0]:xrange[1]:xstep,yrange[0]:yrange[1]:ystep]).reshape([ xN *yN,2]).astype('float32')
X = np.arange(xrange[0],xrange[1],xstep)
#y = np.arange(yrange[0],yrange[1],ystep)
print X.shape
print xN
Y = m.predict( X.reshape(xN,1,1) )
plt.plot(train[:-1], train[1:], 'k,')
plt.scatter( m.SVx, m.SVy, train_size*10*(m.beta**2), alpha=.15 )
plt.plot(X, Y, 'r', lw=2)
#plt.axhline(y=0)
plt.show()
def run():
print "Starting"
print "Loading Dataset"
# Retrieve dataset
data = getData('B1.dat')[:100]
#data = list()
#for i in range(100):
# data.append( array( [gauss(2.0,.1), gauss(0.0,.1) ]) )
#for i in range(100):
# data.append( array( [gauss(0.0,.1), gauss(2.0,.1) ]) )
print "Constructing Module"
mod = inference_module(data,gm=2,nu=.1)
print "Parsing Results"
clusters = [ [] , ]*(len(mod.clusters))
bsv = list()
colors = ['b','r','g','c','m','y','w']
for point in data:
vector = mod.induce( data_vector(point),False)
if vector.cluster != None:
if not clusters[vector.cluster]:
clusters[vector.cluster] = [vector,]
else:
clusters[vector.cluster].append(vector)
else:
bsv.append(vector)
print "Formatting Results"
for cluster in clusters:
if cluster:
scatter( [point.data[0] for point in cluster], [point.data[1] for point in cluster],s=10, c=colors[cluster[0].cluster % 7])
for cluster in mod.clusters:
scatter( [SV.data[0] for SV in cluster], [SV.data[1] for SV in cluster], s=30, c=colors[cluster[0].cluster % 7], label="Cluster %s" % cluster[0].cluster )
if bsv:
scatter( [v.data[0] for v in bsv], [v.data[1] for v in bsv], s=10, marker="x" )
title('%s SV in %s clusters from %s points' % (len(mod.SV),len(mod.clusters),len(data)))
show()
def run():
# Retrieve dataset
data = getData('B1.dat')[:20]
#data = array([sin(i/4.) for i in range(33)])
# Construct Variables
K = kernel(data,gamma=.1,sigma_q=.5)
F = estimate(data[:-1],data[1:],K)
# Objective Function
print 'constructing objective function...'
P = mul(K.xx,K.yy)
q = matrix(0.0,(K.l,1))
# Equality Constraint
print 'constructing equality constraints...'
#A = matrix( [ sum( K.xx[ n*K.l:( n+1 )*K.l ] for n in range( K.l ) ) ], ( 1,K.l ) ) / K.l
A = matrix( [ sum( K.xx[ n::K.l ] for n in range( K.l ) ) ], ( 1,K.l ) ) / K.l
b = matrix(1.0)
# Inequality Constraint
print 'constructing inequality constraints...'
G = matrix(0.0, (K.l,K.l))
for m in range(K.l):
print "Inequality (%s,n) of %s calculated" % (m,K.l)
k = K.xx[m::K.l]
for n in range(m,K.l):
if K.n > 1:
t =array( [min(K.x[n] - K.x[i]) > 0 for i in range(K.l)] )
else:
t = array( [K.x[n] - K.x[i] > 0 for i in range(K.l)])
i = K.intg[m,n]
G[n,m] = sum(k*t*i)/K.l - F.xy(K.x[n],K.y[n])
G[m,n] = sum(k*t*i)/K.l - F.xy(K.x[n],K.y[n])
print G
h = matrix(K.sigma, (K.l,1))
# Optimize
#f=open('beta.matrix','r')
#F.beta = fromfile(f)
#f.close()
print 'starting optimization...'
optimized = qp(P, q,G=G, h=h, A=A, b=b)
F.beta = optimized['x']
print F.beta
f=open('beta.matrix','w')
F.beta.tofile(f)
f.close()
print 'beta saved to file'
# test on training data
x_1 = list()
y_1 = list()
for i in range(K.l):
x_1.append( F.r(K.x[i])[0] )
y_1.append( K.y[i][0] )
plot(x_1,label="x'")
plot(y_1,label="y")
legend()
show()
def test_system3():
print "Initializing"
train_size = 500
sequence_length = 2
gamma_quantile = 50
test_size = 500
import a_machine.system3 as system
print "Importing & Normalizing Data"
from santa_fe import getData
data = getData('B1.dat')
test = getData('B2.dat')
median = np.median(data, axis=0)
std = np.std(data, axis=0)
# normalizing to median 0, std deviation 1
data = ( data - median ) / std
print "Initializing Models"
model = system.model(gamma_samples=1000, gamma_quantile=gamma_quantile, sequence_length=sequence_length)
model.train( data, train_size )
print "Generating Predictions"
# [test_point][dimension]
#normed_test = (test[:test_size,:] - median) / std
normed_test = data[:test_size]
predictions, risks = model.predict(normed_test)
hybrid = ( predictions * risks ).sum(1) / risks.sum(1)
# denormalize
predictions = ( std.reshape(1,1,3) * predictions ) + median.reshape(1,1,3)
hybrid = ( std.reshape(1,3) * hybrid ) + median.reshape(1,3)
print "Results!"
errors = np.abs( np.expand_dims( test[sequence_length : test_size], 1) - predictions )
hybrid_error = np.abs( test[sequence_length : test_size] - hybrid )
print hybrid.shape
print hybrid_error.shape
print ( hybrid_error.sum(0) / test_size )
print ( errors.sum(0) / test_size )
print std.astype('int')
x = np.arange(test_size-sequence_length)
for i in range(data.shape[1]):
fig = plt.subplot(data.shape[1],1,i+1)
fig.plot(x, test[sequence_length : test_size,i], 'k--')
for j in range(predictions.shape[1]):
fig.plot(x, predictions[:,j,i] )
fig.plot(x, hybrid[:,i], 'r', lw=2)
plt.show()
def test_system4():
print "Initializing"
train_size = 1000
sequence_length = 1
gamma_quantile = 100
test_size = 200
import a_machine.system4 as system
print "Importing & Normalizing Data"
from santa_fe import getData
data = getData('B1.dat')
test = getData('B2.dat')
median = np.median(data, axis=0)
std = np.std(data, axis=0)
# normalizing to median 0, std deviation 1
normed_data = ( data - median ) / std
print "Initializing Models"
model = system.model(dimension=0, gamma_samples=1000, gamma_quantile=gamma_quantile, sequence_length=sequence_length)
model.train( normed_data, train_size )
print "Generating Predictions"
# [test_point][dimension]
test = test[:test_size+sequence_length,:]
#test = data[:test_size+sequence_length,:]
normed_test = (test - median) / std
predictions = model.predict(normed_test)
# denormalize
#predictions = ( std[0] * predictions ) + median[0]
errors = np.abs( normed_test[sequence_length : predictions.shape[0]+sequence_length, 0] - predictions )
print "Results! Loss/point: %s (in normed space)" % ( errors.sum(0) / test_size )
x = np.arange( predictions.shape[0] )
x_pred = np.dstack( [
np.arange(model.sequences[:,0,0].min(), model.sequences[:,0,0].max(), ( model.sequences[:,0,0].max() - model.sequences[:,0,0].min() ) / 100 ),
np.arange(model.sequences[:,0,1].min(), model.sequences[:,0,1].max(), ( model.sequences[:,0,1].max() - model.sequences[:,0,1].min() ) / 100 ),
np.arange(model.sequences[:,0,2].min(), model.sequences[:,0,2].max(), ( model.sequences[:,0,2].max() - model.sequences[:,0,2].min() ) / 100 ),
]).astype('float32').reshape(100,1,3)
y_pred = model.svm.predict( kernel_matrix(x_pred, model.sequences, model.gammas[-1] ) )
print x_pred[0]
print x_pred[1]
pr = plt.subplot(2,2,1)
pr.plot(x,normed_test[sequence_length : predictions.shape[0]+sequence_length, 0], 'k', alpha=.4)
#for i in range(predictions.shape[1]):
# for j in range(predictions.shape[2]):
# plt.plot(x,predictions[:,i,j])
pr.plot(x,predictions)
reg0 = plt.subplot(2,2,2)
reg0.plot(model.sequences[:,0,0], model.labels, 'k,', alpha=.5)
reg0.plot(model.sequences[model.svm.SV_indices,0,0], model.labels[model.svm.SV_indices], 'o', alpha=.15 )
reg0.plot(x_pred[:,0,0], y_pred, 'r', lw=2)
reg1 = plt.subplot(2,2,3)
reg1.plot(model.sequences[:,0,1], model.labels, 'k,', alpha=.5)
reg1.plot(model.sequences[model.svm.SV_indices,0,1], model.labels[model.svm.SV_indices], 'o', alpha=.15 )
reg1.plot(x_pred[:,0,1], y_pred, 'r',lw=2)
reg2 = plt.subplot(2,2,4)
reg2.plot(model.sequences[:,0,2], model.labels, 'k,', alpha=.5)
reg2.plot(model.sequences[model.svm.SV_indices,0,2], model.labels[model.svm.SV_indices], 'o', alpha=.15 )
reg2.plot(x_pred[:,0,2], y_pred, 'r',lw=2)
plt.show()
return
