def _evaluate(self, ctx, deps):
V, M, U = deps['V'], deps['M'], deps['U']
strata = _compute_strata(V)
util.log_info('Start eval')
for i, stratum in enumerate(strata):
util.log_info('Processing stratum: %d of %d (size = %d)', i, len(strata), len(stratum))
#for ex in stratum: print ex
worklist = set(stratum)
expr.shuffle(V, sgd_netflix_mapper,
kw={'V' : lazify(V), 'M' : lazify(M), 'U' : lazify(U),
'worklist' : worklist }).force()
util.log_info('Eval done.')
def test_sparse_sum(self):
x = expr.sparse_diagonal(ARRAY_SIZE).force()
y = x.glom()
print y.todense()
x = expr.lazify(x)
for axis in [None, 0, 1]:
y = x.sum(axis)
val = y.glom()
print val
def test_sparse_sum(self):
x = expr.sparse_diagonal(ARRAY_SIZE).force()
y = x.glom()
print y.todense()
x = expr.lazify(x)
for axis in [None, 0, 1]:
y = x.sum(axis)
val = y.glom()
print val
def examine_example(self, i, N, labels, kernel_results):
''' Check if the alpha_i can be optimized. It should satisfy the KKT condition.
If so, choose it as one parameter to be optimized.
Args:
i(int): index of the alpha to be checked
N(int): the number of features
labels(Expr): the labels of the training data
kernel_results(Expr): the result of the kernel function on the training data
'''
Ei = self.E[i, 0]
ai = self.alpha[i, 0]
r = labels[i, 0] * Ei
# check if satisfy KKT condition
if r < -self.tol and ai < self.C or r > self.tol and ai > self.tol:
alpha_expr = expr.lazify(self.alpha)
active_set_mask = (alpha_expr > self.tol) * (alpha_expr < self.C)
active_set = active_set_mask.glom().nonzero()[0]
#print 'actives:', active_set
# first check the jth example that maximize the |Ei - Ej|
idxj = -1
if active_set.shape[0] > 1:
active_E = expr.abs(expr.lazify(self.E) - Ei)[active_set_mask -
True]
idxj = np.argmax(active_E.glom())
if self.take_step(idxj, i, N, labels, kernel_results): return 1
# then check the examples in active_set
for j in active_set:
if j != idxj and self.take_step(j, i, N, labels,
kernel_results):
return 1
# finally check the other examples
for j in xrange(N):
if j not in active_set and self.take_step(
j, i, N, labels, kernel_results):
return 1
return 0
def examine_example(self, i, N, labels, kernel_results):
""" Check if the alpha_i can be optimized. It should satisfy the KKT condition.
If so, choose it as one parameter to be optimized.
Args:
i(int): index of the alpha to be checked
N(int): the number of features
labels(Expr): the labels of the training data
kernel_results(Expr): the result of the kernel function on the training data
"""
Ei = self.E[i, 0]
ai = self.alpha[i, 0]
r = labels[i, 0] * Ei
# check if satisfy KKT condition
if r < -self.tol and ai < self.C or r > self.tol and ai > self.tol:
alpha_expr = expr.lazify(self.alpha)
active_set_mask = (alpha_expr > self.tol) * (alpha_expr < self.C)
active_set = active_set_mask.glom().nonzero()[0]
# print 'actives:', active_set
# first check the jth example that maximize the |Ei - Ej|
idxj = -1
if active_set.shape[0] > 1:
active_E = expr.abs(expr.lazify(self.E) - Ei)[active_set_mask - True]
idxj = np.argmax(active_E.glom())
if self.take_step(idxj, i, N, labels, kernel_results):
return 1
# then check the examples in active_set
for j in active_set:
if j != idxj and self.take_step(j, i, N, labels, kernel_results):
return 1
# finally check the other examples
for j in xrange(N):
if j not in active_set and self.take_step(j, i, N, labels, kernel_results):
return 1
return 0
def _evaluate(self, ctx, deps):
V, M, U = deps['V'], deps['M'], deps['U']
strata = _compute_strata(V)
util.log_info('Start eval')
for i, stratum in enumerate(strata):
util.log_info('Processing stratum: %d of %d (size = %d)', i,
len(strata), len(stratum))
#for ex in stratum: print ex
worklist = set(stratum)
expr.shuffle(V,
sgd_netflix_mapper,
kw={
'V': lazify(V),
'M': lazify(M),
'U': lazify(U),
'worklist': worklist
}).evaluate()
util.log_info('Eval done.')
def _get_norm_of_each_item(self, rating_table):
"""Get norm of each item vector.
For each Item, caculate the norm the item vector.
Parameters
----------
rating_table : Spartan matrix of shape(M, N).
Each column represents the rating of the item.
Returns
---------
item_norm: Spartan matrix of shape(N,).
item_norm[i] equals || rating_table[:,i] ||
"""
ctx = blob_ctx.get()
if isinstance(rating_table, array.distarray.DistArray):
rating_table = expr.lazify(rating_table)
res = expr.sqrt(expr.sum(expr.multiply(rating_table, rating_table), axis=0,
tile_hint=(rating_table.shape[1] / ctx.num_workers, )))
return res.force()
def train_smo_2005(self, data, labels):
'''
Train an SVM model using the SMO (2005) algorithm.
Args:
data(Expr): points to be trained
labels(Expr): the correct labels of the training data
'''
N = data.shape[0] # Number of instances
D = data.shape[1] # Number of features
self.b = 0.0
alpha = expr.zeros((N,1), dtype=np.float64, tile_hint=[N/self.ctx.num_workers, 1]).force()
# linear kernel
kernel_results = expr.dot(data, expr.transpose(data), tile_hint=[N/self.ctx.num_workers, N])
gradient = expr.ones((N, 1), dtype=np.float64, tile_hint=[N/self.ctx.num_workers, 1]) * -1.0
expr_labels = expr.lazify(labels)
util.log_info("Starting SMO")
pv1 = pv2 = -1
it = 0
while it < self.maxiter:
util.log_info("Iteration:%d", it)
minObj = 1e100
expr_alpha = expr.lazify(alpha)
G = expr.multiply(labels, gradient) * -1.0
v1_mask = ((expr_labels > self.tol) * (expr_alpha < self.C) + (expr_labels < -self.tol) * (expr_alpha > self.tol))
v1 = expr.argmax(G[v1_mask-True]).glom().item()
maxG = G[v1,0].glom()
print 'maxv1:', v1, 'maxG:', maxG
v2_mask = ((expr_labels > self.tol) * (expr_alpha > self.tol) + (expr_labels < -self.tol) * (expr_alpha < self.C))
min_v2 = expr.argmin(G[v2_mask-True]).glom().item()
minG = G[min_v2,0].glom()
#print 'minv2:', min_v2, 'minG:', minG
set_v2 = v2_mask.glom().nonzero()[0]
#print 'actives:', set_v2.shape[0]
v2 = -1
for v in set_v2:
b = maxG - G[v,0].glom()
if b > self.tol:
na = (kernel_results[v1,v1] + kernel_results[v,v] - 2*kernel_results[v1,v]).glom()[0][0]
if na < self.tol: na = 1e12
obj = -(b*b)/na
if obj <= minObj and v1 != pv1 or v != pv2:
v2 = v
a = na
minObj = obj
if v2 == -1: break
if maxG - minG < self.tol: break
print 'opt v1:', v1, 'v2:', v2
pv1 = v1
pv2 = v2
y1 = labels[v1,0]
y2 = labels[v2,0]
oldA1 = alpha[v1,0]
oldA2 = alpha[v2,0]
# Calculate new alpha values, to reduce the objective function...
b = y2*expr.glom(gradient[v2,0]) - y1*expr.glom(gradient[v1,0])
if y1 != y2:
a += 4 * kernel_results[v1,v2].glom()
newA1 = oldA1 + y1*b/a
newA2 = oldA2 - y2*b/a
# Correct for alpha being out of range...
sum = y1*oldA1 + y2*oldA2;
if newA1 < self.tol: newA1 = 0.0
elif newA1 > self.C: newA1 = self.C
newA2 = y2 * (sum - y1 * newA1)
if newA2 < self.tol: newA2 = 0.0;
elif newA2 > self.C: newA2 = self.C
newA1 = y1 * (sum - y2 * newA2)
# Update the gradient...
dA1 = newA1 - oldA1
dA2 = newA2 - oldA2
gradient += expr.multiply(labels, kernel_results[:,v1]) * y1 * dA1 + expr.multiply(labels, kernel_results[:,v2]) * y2 * dA2
alpha[v1,0] = newA1
alpha[v2,0] = newA2
#print 'alpha:', alpha.glom().T
it += 1
#print 'gradient:', gradient.glom().T
self.w = expr.zeros((D, 1), dtype=np.float64).force()
for i in xrange(D):
self.w[i,0] = expr.reduce(alpha, axis=None, dtype_fn=lambda input: input.dtype,
local_reduce_fn=margin_mapper,
accumulate_fn=np.add,
fn_kw=dict(label=labels, data=expr.force(data[:,i]))).glom()
self.b = 0.0
E = (labels - self.margins(data)).force()
minB = -1e100
maxB = 1e100
actualB = 0.0
numActualB = 0
for i in xrange(N):
ai = alpha[i,0]
yi = labels[i,0]
Ei = E[i,0]
if ai < 1e-3:
if yi < self.tol:
maxB = min((maxB,Ei))
else:
minB = max((minB,Ei))
elif ai > self.C - 1e-3:
if yi < self.tol:
minB = max((minB,Ei))
else:
maxB = min((maxB,Ei))
else:
numActualB += 1
actualB += (Ei - actualB) / float(numActualB)
if numActualB > 0:
self.b = actualB
else:
self.b = 0.5*(minB + maxB)
self.usew_ = True
print 'iteration finish:', it
print 'b:', self.b
print 'w:', self.w.glom()
def train_smo_2005(self, data, labels):
'''
Train an SVM model using the SMO (2005) algorithm.
Args:
data(Expr): points to be trained
labels(Expr): the correct labels of the training data
'''
N = data.shape[0] # Number of instances
D = data.shape[1] # Number of features
self.b = 0.0
alpha = expr.zeros((N, 1),
dtype=np.float64,
tile_hint=[N / self.ctx.num_workers, 1]).force()
# linear kernel
kernel_results = expr.dot(data,
expr.transpose(data),
tile_hint=[N / self.ctx.num_workers, N])
gradient = expr.ones(
(N, 1), dtype=np.float64, tile_hint=[N / self.ctx.num_workers, 1
]) * -1.0
expr_labels = expr.lazify(labels)
util.log_info("Starting SMO")
pv1 = pv2 = -1
it = 0
while it < self.maxiter:
util.log_info("Iteration:%d", it)
minObj = 1e100
expr_alpha = expr.lazify(alpha)
G = expr.multiply(labels, gradient) * -1.0
v1_mask = ((expr_labels > self.tol) * (expr_alpha < self.C) +
(expr_labels < -self.tol) * (expr_alpha > self.tol))
v1 = expr.argmax(G[v1_mask - True]).glom().item()
maxG = G[v1, 0].glom()
print 'maxv1:', v1, 'maxG:', maxG
v2_mask = ((expr_labels > self.tol) * (expr_alpha > self.tol) +
(expr_labels < -self.tol) * (expr_alpha < self.C))
min_v2 = expr.argmin(G[v2_mask - True]).glom().item()
minG = G[min_v2, 0].glom()
#print 'minv2:', min_v2, 'minG:', minG
set_v2 = v2_mask.glom().nonzero()[0]
#print 'actives:', set_v2.shape[0]
v2 = -1
for v in set_v2:
b = maxG - G[v, 0].glom()
if b > self.tol:
na = (kernel_results[v1, v1] + kernel_results[v, v] -
2 * kernel_results[v1, v]).glom()[0][0]
if na < self.tol: na = 1e12
obj = -(b * b) / na
if obj <= minObj and v1 != pv1 or v != pv2:
v2 = v
a = na
minObj = obj
if v2 == -1: break
if maxG - minG < self.tol: break
print 'opt v1:', v1, 'v2:', v2
pv1 = v1
pv2 = v2
y1 = labels[v1, 0]
y2 = labels[v2, 0]
oldA1 = alpha[v1, 0]
oldA2 = alpha[v2, 0]
# Calculate new alpha values, to reduce the objective function...
b = y2 * expr.glom(gradient[v2, 0]) - y1 * expr.glom(gradient[v1,
0])
if y1 != y2:
a += 4 * kernel_results[v1, v2].glom()
newA1 = oldA1 + y1 * b / a
newA2 = oldA2 - y2 * b / a
# Correct for alpha being out of range...
sum = y1 * oldA1 + y2 * oldA2
if newA1 < self.tol: newA1 = 0.0
elif newA1 > self.C: newA1 = self.C
newA2 = y2 * (sum - y1 * newA1)
if newA2 < self.tol: newA2 = 0.0
elif newA2 > self.C: newA2 = self.C
newA1 = y1 * (sum - y2 * newA2)
# Update the gradient...
dA1 = newA1 - oldA1
dA2 = newA2 - oldA2
gradient += expr.multiply(
labels, kernel_results[:, v1]) * y1 * dA1 + expr.multiply(
labels, kernel_results[:, v2]) * y2 * dA2
alpha[v1, 0] = newA1
alpha[v2, 0] = newA2
#print 'alpha:', alpha.glom().T
it += 1
#print 'gradient:', gradient.glom().T
self.w = expr.zeros((D, 1), dtype=np.float64).force()
for i in xrange(D):
self.w[i, 0] = expr.reduce(alpha,
axis=None,
dtype_fn=lambda input: input.dtype,
local_reduce_fn=margin_mapper,
accumulate_fn=np.add,
fn_kw=dict(label=labels,
data=expr.force(
data[:, i]))).glom()
self.b = 0.0
E = (labels - self.margins(data)).force()
minB = -1e100
maxB = 1e100
actualB = 0.0
numActualB = 0
for i in xrange(N):
ai = alpha[i, 0]
yi = labels[i, 0]
Ei = E[i, 0]
if ai < 1e-3:
if yi < self.tol:
maxB = min((maxB, Ei))
else:
minB = max((minB, Ei))
elif ai > self.C - 1e-3:
if yi < self.tol:
minB = max((minB, Ei))
else:
maxB = min((maxB, Ei))
else:
numActualB += 1
actualB += (Ei - actualB) / float(numActualB)
if numActualB > 0:
self.b = actualB
else:
self.b = 0.5 * (minB + maxB)
self.usew_ = True
print 'iteration finish:', it
print 'b:', self.b
print 'w:', self.w.glom()