def test_isinstance():
def fun(x):
assert ag_isinstance(x, dict)
assert ag_isinstance(x, ag_dict)
return x['x']
fun({'x': 1.})
grad(fun)({'x': 1.})
def compare_smoother_grads(lds):
init_params, pair_params, node_params = lds
symmetrize = make_unop(lambda x: (x + x.T)/2. if np.ndim(x) == 2 else x, tuple)
messages, _ = natural_filter_forward_general(*lds)
dotter = randn_like(natural_smoother_general(messages, *lds))
def py_fun(messages):
result = natural_smoother_general(messages, *lds)
assert shape(result) == shape(dotter)
return contract(dotter, result)
dense_messages, _ = _natural_filter_forward_general(
init_params, pair_params, node_params)
def cy_fun(messages):
result = _natural_smoother_general(messages, pair_params)
result = result[0][:3], result[1], result[2]
assert shape(result) == shape(dotter)
return contract(dotter, result)
result_py = py_fun(messages)
result_cy = cy_fun(dense_messages)
assert np.isclose(result_py, result_cy)
g_py = grad(py_fun)(messages)
g_cy = unpack_dense_messages(grad(cy_fun)(dense_messages))
assert allclose(g_py, g_cy)
def unwrap(self, output, i, *args, **kwargs):
if not hasattr(output, '__iter__'):
def _wrap(*args, **kwargs):
return self.func(*args, **kwargs)[i]
dfunc = grad(_wrap)
return dfunc(*args, **kwargs)
elif isinstance(output, np.ndarray):
shape = output.shape
J = []
axes = []
for dimen in shape:
axes.append(range(dimen))
for idx in product(*axes):
def _wrap(*args, **kwargs):
return self.func(*args, **kwargs)[i][idx]
dfunc = grad(_wrap)
J.append(dfunc(*args, **kwargs))
if hasattr(J[0], "__iter__"):
return list(map(list, zip(*J)))
else:
return J
def test_fast_conv_grad():
skip = 1
block_size = (11, 11)
depth = 1
img = np.random.randn(51, 51, depth)
filt = np.dstack([cv.gauss_filt_2D(shape=block_size,sigma=2) for k in range(depth)])
filt = cv.gauss_filt_2D(shape=block_size, sigma=2)
def loss_fun(filt):
out = fc.convolve(filt, img)
return np.sum(np.sin(out) + out**2)
loss_fun(filt)
loss_grad = grad(loss_fun)
def loss_fun_slow(filt):
out = auto_convolve(img.squeeze(), filt, mode='valid')
return np.sum(np.sin(out) + out**2)
loss_fun_slow(filt)
loss_grad_slow = grad(loss_fun_slow)
# compare gradient timing
loss_grad_slow(filt)
loss_grad(filt)
## check numerical gradients
num_grad = np.zeros(filt.shape)
for i in xrange(filt.shape[0]):
for j in xrange(filt.shape[1]):
de = np.zeros(filt.shape)
de[i, j] = 1e-4
num_grad[i,j] = (loss_fun(filt + de) - loss_fun(filt - de)) / (2*de[i,j])
assert np.allclose(loss_grad(filt), num_grad), "convolution gradient failed!"
def test_isinstance():
def fun(x):
assert ag_isinstance(x, tuple)
assert ag_isinstance(x, ag_tuple)
return x[0]
fun((1., 2., 3.))
grad(fun)((1., 2., 3.))
def test_isinstance():
def fun(x):
assert ag_isinstance(x, list)
assert ag_isinstance(x, ag_list)
return x[0]
fun([1., 2., 3.])
grad(fun)([1., 2., 3.])
def test_array_creation():
# Will always pass, but will take ages (like a minute) if the complexity of
# array creation is O(N)
N = 100000
def fun(x):
arr = [x for i in range(N)]
return np.sum(np.array(arr))
grad(fun)(1.0)
def test_sub():
fun = lambda x, y : to_scalar(x - y)
d_fun_0 = lambda x, y : to_scalar(grad(fun, 0)(x, y))
d_fun_1 = lambda x, y : to_scalar(grad(fun, 1)(x, y))
for arg1, arg2 in arg_pairs():
check_grads(fun, arg1, arg2)
check_grads(d_fun_0, arg1, arg2)
check_grads(d_fun_1, arg1, arg2)
def peakmem_needless_nodes():
N, M = 1000, 100
def fun(x):
for i in range(M):
x = x + 1
return np.sum(x)
grad(fun)(np.zeros((N, N)))
def check_fft_n(fft_fun, D, n):
def fun(x): return to_scalar(fft_fun(x, D + n))
d_fun = lambda x : to_scalar(grad(fun)(x))
mat = npr.randn(D, D)
mat = match_complex(fft_fun, mat)
assert_array_equal(grad(fun)(mat).shape, mat.shape)
check_grads(fun, mat)
check_grads(d_fun, mat)
def test_return_both():
fun = lambda x : 3.0 * np.sin(x)
d_fun = grad(fun)
f_and_d_fun = grad(fun, return_function_value=True)
test_x = npr.randn()
f, d = f_and_d_fun(test_x)
assert f == fun(test_x)
assert d == d_fun(test_x)
def fan_out_fan_in():
"""The 'Pearlmutter test' """
def fun(x):
for i in range(10**4):
x = (x + x)/2.0
return np.sum(x)
with tictoc():
grad(fun)(1.0)
def test_add():
fun = lambda x, y : to_scalar(x + y)
d_fun_0 = lambda x, y : to_scalar(grad(fun, 0)(x, y))
d_fun_1 = lambda x, y : to_scalar(grad(fun, 1)(x, y))
for arg1, arg2 in arg_pairs():
print(type(arg1), type(arg2))
check_grads(fun, arg1, arg2)
check_grads(d_fun_0, arg1, arg2)
check_grads(d_fun_1, arg1, arg2)
def check_binary_func(fun):
x, y = 0.7, 1.8
a = grad(fun)(x, y)
b = nd(lambda x: fun(x, y), x)
check_close(a, b)
a = grad(fun, 1)(x, y)
b = nd(lambda y: fun(x, y), y)
check_close(a, b)
def test_nested_higher_order():
def outer_fun(x):
def inner_fun(y):
return y[0] * y[1]
return np.sum(np.sin(np.array(grad(inner_fun)(ag_tuple((x,x))))))
check_grads(outer_fun)(5.)
check_grads(grad(outer_fun))(10.)
check_grads(grad(grad(outer_fun)))(10.)
def test_nograd():
# we want this to raise non-differentiability error
fun = lambda x: np.allclose(x, (x*3.0)/3.0)
try:
grad(fun)(np.array([1., 2., 3.]))
except TypeError:
pass
else:
raise Exception('Expected non-differentiability exception')
def test_return_both():
fun = lambda x : 3.0 * x**3.2
d_fun = grad(fun)
f_and_d_fun = grad(fun, return_function_value=True)
test_x = 1.7
f, d = f_and_d_fun(test_x)
assert f == fun(test_x)
assert d == d_fun(test_x)
def test_third_derivative():
fun = lambda x : np.sin(np.sin(x) + np.sin(x))
df = grad(fun)
ddf = grad(fun)
dddf = grad(fun)
check_grads(fun, npr.randn())
check_grads(df, npr.rand())
check_grads(ddf, npr.rand())
check_grads(dddf, npr.rand())
def test_third_derivative_other_args2():
fun = lambda x, y : np.sin(np.sin(x) + np.sin(y))
df = grad(fun, 1)
ddf = grad(fun)
dddf = grad(fun, 1)
check_grads(fun, npr.randn(), npr.randn())
check_grads(df, npr.randn(), npr.randn())
check_grads(ddf, npr.randn(), npr.randn())
check_grads(dddf, npr.randn(), npr.randn())
def check_binary_func(fun, independent=False):
with warnings.catch_warnings(independent) as w:
x, y = 0.7, 1.8
a = grad(fun)(x, y)
b = nd(lambda x: fun(x, y), x)
check_close(a, b)
a = grad(fun, 1)(x, y)
b = nd(lambda y: fun(x, y), y)
check_close(a, b)
def test_power_arg0():
# the +1.'s here are to avoid regimes where numerical diffs fail
make_fun = lambda y: lambda x: np.power(x, y)
fun = make_fun(npr.randn()**2 + 1.)
check_grads(fun)(npr.rand()**2 + 1.)
# test y == 0. as a special case, c.f. #116
fun = make_fun(0.)
assert grad(fun)(0.) == 0.
assert grad(grad(fun))(0.) == 0.
def test_dtypes():
def f(x):
return np.sum(x**2)
# Array y with dtype np.float32
y = np.random.randn(10, 10).astype(np.float32)
assert grad(f)(y).dtype.type is np.float32
y = np.random.randn(10, 10).astype(np.float16)
assert grad(f)(y).dtype.type is np.float16
def test_pow():
fun = lambda x, y : to_scalar(x ** y)
d_fun_0 = lambda x, y : to_scalar(grad(fun, 0)(x, y))
d_fun_1 = lambda x, y : to_scalar(grad(fun, 1)(x, y))
make_positive = lambda x : np.abs(x) + 1.1 # Numeric derivatives fail near zero
for arg1, arg2 in arg_pairs():
arg1 = make_positive(arg1)
check_grads(fun, arg1, arg2)
check_grads(d_fun_0, arg1, arg2)
check_grads(d_fun_1, arg1, arg2)
def test_div():
fun = lambda x, y : to_scalar(x / y)
d_fun_0 = lambda x, y : to_scalar(grad(fun, 0)(x, y))
d_fun_1 = lambda x, y : to_scalar(grad(fun, 1)(x, y))
make_gap_from_zero = lambda x : np.sqrt(x **2 + 0.5)
for arg1, arg2 in arg_pairs():
arg1 = make_gap_from_zero(arg1)
arg2 = make_gap_from_zero(arg2)
check_grads(fun, arg1, arg2)
check_grads(d_fun_0, arg1, arg2)
check_grads(d_fun_1, arg1, arg2)
def test_compute_stats_grad():
F = make_unop(lambda x: np.require(x, np.double, 'F'), tuple)
dotter = F(randn_like(compute_stats(Ex, ExxT, ExnxT, True)))
g1 = grad(lambda x: contract(dotter, compute_stats(*x)))((Ex, ExxT, ExnxT, 1.))
g2 = _compute_stats_grad(dotter)
assert allclose(g1[:3], g2)
dotter = F(randn_like(compute_stats(Ex, ExxT, ExnxT, False)))
g1 = grad(lambda x: contract(dotter, compute_stats(*x)))((Ex, ExxT, ExnxT, 0.))
g2 = _compute_stats_grad(dotter)
assert allclose(g1[:3], g2)
def test_mod():
fun = lambda x, y : to_scalar(x % y)
d_fun_0 = lambda x, y : to_scalar(grad(fun, 0)(x, y))
d_fun_1 = lambda x, y : to_scalar(grad(fun, 1)(x, y))
make_gap_from_zero = lambda x : np.sqrt(x **2 + 0.5)
for arg1, arg2 in arg_pairs():
if not arg1 is arg2: # Gradient undefined at x == y
arg1 = make_gap_from_zero(arg1)
arg2 = make_gap_from_zero(arg2)
check_grads(fun, arg1, arg2)
check_grads(d_fun_0, arg1, arg2)
check_grads(d_fun_1, arg1, arg2)
def test_hess_vector_prod():
npr.seed(1)
randv = npr.randn(10)
def fun(x):
return np.sin(np.dot(x, randv))
df = grad(fun)
def vector_product(x, v):
return np.sin(np.dot(v, df(x)))
ddf = grad(vector_product)
A = npr.randn(10)
B = npr.randn(10)
check_grads(fun, A)
check_grads(vector_product, A, B)
def test_slices():
def f(x):
s = slice(None, -1, None)
y = x[s]
return y[0]
grad(f)([1., 2., 3.])
def f(x):
y = x[1:3]
return y[0]
grad(f)([1., 2., 3.])
def test_checkpoint_correctness():
bar = lambda x, y: 2*x + y + 5
checkpointed_bar = checkpoint(bar)
foo = lambda x: bar(x, x/3.) + bar(x, x**2)
foo2 = lambda x: checkpointed_bar(x, x/3.) + checkpointed_bar(x, x**2)
assert np.allclose(foo(3.), foo2(3.))
assert np.allclose(grad(foo)(3.), grad(foo2)(3.))
baz = lambda *args: sum(args)
checkpointed_baz = checkpoint(baz)
foobaz = lambda x: baz(x, x/3.)
foobaz2 = lambda x: checkpointed_baz(x, x/3.)
assert np.allclose(foobaz(3.), foobaz2(3.))
assert np.allclose(grad(foobaz)(3.), grad(foobaz2)(3.))
def test_jacobian_against_stacked_grads():
scalar_funs = [
lambda x: np.sum(x ** 3),
lambda x: np.prod(np.sin(x) + np.sin(x)),
lambda x: grad(lambda y: np.exp(y) * np.tanh(x[0]))(x[1]),
]
vector_fun = lambda x: np.array([f(x) for f in scalar_funs])
x = npr.randn(5)
jac = jacobian(vector_fun)(x)
grads = [grad(f)(x) for f in scalar_funs]
assert np.allclose(jac, np.vstack(grads))
def burer_monteiro(target_choi,
n_decomp,
rank,
n_qubits,
initial_guess=None,
cfac_tol=1.):
choi_dim = target_choi.shape[0]
# expanding and flattening
entries = choi_dim * rank
def extract_matrix(x):
mat_re = x[0:entries].reshape((rank, choi_dim))
mat_im = x[entries:2 * entries].reshape((rank, choi_dim))
return mat_re + 1j * mat_im
matlen = 2 * entries
def expand(x):
arr_Y_pos = list()
arr_Y_neg = list()
arr_a_pos = list()
arr_a_neg = list()
for i in range(n_decomp):
arr_Y_pos.append(extract_matrix(x[matlen * i:matlen * (i + 1)]))
for i in range(n_decomp):
arr_Y_neg.append(
extract_matrix(x[matlen * (n_decomp + i):matlen *
(n_decomp + i + 1)]))
for i in range(n_decomp):
arr_a_pos.append(x[matlen * 2 * n_decomp + i])
arr_a_neg.append(x[matlen * 2 * n_decomp + n_decomp + i])
return arr_Y_pos, arr_Y_neg, arr_a_pos, arr_a_neg
def flatten_matrix(mat):
mat_re = np.real(mat).flatten()
mat_im = np.imag(mat).flatten()
return [mat_re, mat_im]
def flatten(arr_Y_pos, arr_Y_neg, arr_a_pos, arr_a_neg):
tot_list = list()
for Y in arr_Y_pos:
tot_list += flatten_matrix(Y)
for Y in arr_Y_neg:
tot_list += flatten_matrix(Y)
tot_list += arr_a_pos
tot_list += arr_a_neg
return np.hstack(tot_list)
# optimization function
def loss(x):
arr_Y_pos, arr_Y_neg, arr_a_pos, arr_a_neg = expand(x)
return np.sum(np.abs(arr_a_pos)) + np.sum(np.abs(arr_a_neg))
def constraint(x):
arr_Y_pos, arr_Y_neg, arr_a_pos, arr_a_neg = expand(x)
arr_C_pos = list()
arr_C_neg = list()
def conj(z):
return np.real(z) - 1j * np.imag(z)
for i in range(n_decomp):
arr_C_pos.append(conj(arr_Y_pos[i].T) @ arr_Y_pos[i])
arr_C_neg.append(conj(arr_Y_neg[i].T) @ arr_Y_neg[i])
retvec = np.array([])
# TP constraint
for i in range(n_decomp):
pt = anp_partial_trace(arr_C_pos[i], [2**n_qubits, 2**n_qubits], 1)
vec = (pt - arr_a_pos[i] * np.identity(2**n_qubits)).flatten()
retvec = np.hstack([retvec, vec])
pt = anp_partial_trace(arr_C_neg[i], [2**n_qubits, 2**n_qubits], 1)
vec = (pt - arr_a_neg[i] * np.identity(2**n_qubits)).flatten()
retvec = np.hstack([retvec, vec])
# equality constraint
C_sum = np.zeros_like(target_choi)
for i in range(n_decomp):
C_sum += arr_C_pos[i] - arr_C_neg[i]
vec = (C_sum - target_choi).flatten()
retvec = np.hstack([retvec, vec])
# separate complex and real part
retvec = np.hstack([np.real(retvec), np.imag(retvec)])
return retvec
constraint_jac = autograd.jacobian(constraint)
constraint_hess = autograd.hessian(lambda x, v: np.dot(constraint(x), v),
argnum=0)
# initial guess
res = minimize(
lambda z: np.linalg.norm(
np_partial_trace(target_choi, [2**n_qubits, 2**n_qubits], 1).data -
z * np.eye(2**n_qubits)), [1.])
scale = res.x
#assert res.fun < 1e-6
arr_Y_pos = list()
arr_Y_neg = list()
arr_a_pos = list()
arr_a_neg = list()
if initial_guess is not None:
for i in range(n_decomp):
arr_Y_pos.append(initial_guess["Y_pos"][i])
arr_Y_neg.append(initial_guess["Y_neg"][i])
arr_a_pos.append(initial_guess["a_pos"][i])
arr_a_neg.append(initial_guess["a_neg"][i])
else:
for i in range(n_decomp):
arr_Y_pos.append(scale * np.random.normal(size=(rank, choi_dim)) +
1j * scale *
np.random.normal(size=(rank, choi_dim)))
arr_Y_neg.append(scale * np.random.normal(size=(rank, choi_dim)) +
1j * scale *
np.random.normal(size=(rank, choi_dim)))
arr_a_pos.append(scale * np.random.uniform())
arr_a_neg.append(scale * np.random.uniform())
x0 = flatten(arr_Y_pos, arr_Y_neg, arr_a_pos, arr_a_neg)
len_x0 = x0.shape[0]
# check flatten+expand
Yp, Yn, ap, an = expand(x0)
for i in range(n_decomp):
assert np.linalg.norm(arr_Y_pos[i] - Yp[i]) < 1e-10
assert np.linalg.norm(arr_Y_neg[i] - Yn[i]) < 1e-10
assert np.linalg.norm(arr_a_pos[i] - ap[i]) < 1e-10
assert np.linalg.norm(arr_a_neg[i] - an[i]) < 1e-10
# solve
def new_loss(x):
return np.sum(np.square(constraint(x)))
new_loss_grad = autograd.grad(new_loss)
lc_mat_dense = np.zeros((1, x0.shape[0]))
lc_mat_dense[0, matlen * 2 * n_decomp:] = np.ones((n_decomp * 2))
indices_x = np.zeros((n_decomp * 2))
indices_y = list(range(matlen * 2 * n_decomp, x0.shape[0]))
vals = np.ones((n_decomp * 2))
lc_mat = scipy.sparse.csr_matrix((vals, (indices_x, indices_y)),
shape=(1, x0.shape[0]))
assert np.linalg.norm(lc_mat_dense - lc_mat.toarray()) < 1e-10
if np.max(np.abs(constraint(x0))) < 1e-8 and np.abs(loss(x0) - 1.) < 1e-8:
res = OptimizeResult()
res.x = x0
else:
con = LinearConstraint(lc_mat, 1., cfac_tol)
res = minimize(new_loss,
x0,
jac=new_loss_grad,
constraints=con,
options={
"verbose": 0,
"maxiter": 10000000,
"gtol": 1e-12,
"xtol": 1e-16
},
method='trust-constr')
#assert np.max(np.abs(constraint(res.x))) < 1e-6
# return
arr_Y_pos, arr_Y_neg, arr_a_pos, arr_a_neg = expand(res.x)
arr_C_pos = list()
arr_C_neg = list()
for i in range(n_decomp):
arr_C_pos.append(np.conj(arr_Y_pos[i].T) @ arr_Y_pos[i])
arr_C_neg.append(np.conj(arr_Y_neg[i].T) @ arr_Y_neg[i])
return arr_a_pos + arr_a_neg, arr_C_pos + arr_C_neg
def gradient(objective, argument):
"""
Compute the gradient of 'objective' with respect to the first
argument and return as a function.
"""
return ad.grad(objective)
#etas = np.arange(-0.8, 1.2, 0.4)
#pts = np.array((3.,7.,15.,20.))
etas = np.array((-0.8, 0.8))
pts = np.array((3., 20.))
#phis = np.arange(-np.pi, np.pi+2.*np.pi/6.,2.*np.pi/6.)
#etas = np.array((-0.8,-0.4))
phis = np.array((-np.pi, np.pi))
x = defineState(len(etas) - 1, len(phis) - 1, datasetJ)
print "minimising"
xtol = np.finfo('float64').eps
grad = grad(nllJ)
hess = hessian(nllJ)
btol = 1.e-8
#lb = [0.999,0.999,0.999,0.999,-0.01,-0.01,-0.01,-0.01,-1e-4,-1e-4,-1e-4,-1e-4,0.]
lb = [0.999, -0.01, -1e-4, 0., 0.]
#ub = [1.001,1.001,1.001,1.001,0.01,0.01,0.01,0.01,1e-4,1e-4,1e-4,1e-4,100]
ub = [1.001, 0.01, 1e-4, 100., 1e9]
constraints = LinearConstraint(A=np.eye(x.shape[0]),
lb=lb,
ub=ub,
keep_feasible=True)
def fit(self, X, B, T, W=None):
'''Fits the model.
:param X: numpy matrix of shape :math:`k \\cdot n`
:param B: numpy vector of shape :math:`n`
:param T: numpy vector of shape :math:`n`
:param W: (optional) numpy vector of shape :math:`n`
'''
if W is None:
W = numpy.ones(len(X))
X, B, T, W = (Z if type(Z) == numpy.ndarray else numpy.array(Z)
for Z in (X, B, T, W))
keep_indexes = (T > 0) & (B >= 0) & (B <= 1) & (W >= 0)
if sum(keep_indexes) < X.shape[0]:
n_removed = X.shape[0] - sum(keep_indexes)
warnings.warn('Warning! Removed %d/%d entries from inputs where '
'T <= 0 or B not 0/1 or W < 0' % (n_removed, len(X)))
X, B, T, W = (Z[keep_indexes] for Z in (X, B, T, W))
n_features = X.shape[1]
# scipy.optimize and emcee forces the the parameters to be a vector:
# (log k, log p, log sigma_alpha, log sigma_beta,
# a, b, alpha_1...alpha_k, beta_1...beta_k)
# Generalized Gamma is a bit sensitive to the starting point!
x0 = numpy.zeros(6 + 2 * n_features)
x0[0] = +1 if self._fix_k is None else log(self._fix_k)
x0[1] = -1 if self._fix_p is None else log(self._fix_p)
args = (X, B, T, W, self._fix_k, self._fix_p, self._hierarchical,
self._flavor)
# Set up progressbar and callback
bar = progressbar.ProgressBar(widgets=[
progressbar.Variable('loss', width=15, precision=9), ' ',
progressbar.BouncingBar(), ' ',
progressbar.Counter(width=6), ' [',
progressbar.Timer(), ']'
])
def callback(LL, value_history=[]):
value_history.append(LL)
bar.update(len(value_history), loss=LL)
# Define objective and use automatic differentiation
f = lambda x: -generalized_gamma_loss(x, *args, callback=callback)
jac = autograd.grad(lambda x: -generalized_gamma_loss(x, *args))
# Find the maximum a posteriori of the distribution
res = scipy.optimize.minimize(f,
x0,
jac=jac,
method='SLSQP',
options={'maxiter': 9999})
if not res.success:
raise Exception('Optimization failed with message: %s' %
res.message)
result = {'map': res.x}
# TODO: should not use fixed k/p as search parameters
if self._fix_k:
result['map'][0] = log(self._fix_k)
if self._fix_p:
result['map'][1] = log(self._fix_p)
# Make sure we're in a local minimum
gradient = jac(result['map'])
gradient_norm = numpy.dot(gradient, gradient)
if gradient_norm >= 1e-2 * len(X):
warnings.warn('Might not have found a local minimum! '
'Norm of gradient is %f' % gradient_norm)
# Let's sample from the posterior to compute uncertainties
if self._ci:
dim, = res.x.shape
n_walkers = 5 * dim
sampler = emcee.EnsembleSampler(
nwalkers=n_walkers,
dim=dim,
lnpostfn=generalized_gamma_loss,
args=args,
)
mcmc_initial_noise = 1e-3
p0 = [
result['map'] + mcmc_initial_noise * numpy.random.randn(dim)
for i in range(n_walkers)
]
n_burnin = 100
n_steps = numpy.ceil(2000. / n_walkers)
n_iterations = n_burnin + n_steps
bar = progressbar.ProgressBar(max_value=n_iterations,
widgets=[
progressbar.Percentage(), ' ',
progressbar.Bar(),
' %d walkers [' % n_walkers,
progressbar.AdaptiveETA(), ']'
])
for i, _ in enumerate(sampler.sample(p0, iterations=n_iterations)):
bar.update(i + 1)
result['samples'] = sampler.chain[:, n_burnin:, :] \
.reshape((-1, dim)).T
if self._fix_k:
result['samples'][0, :] = log(self._fix_k)
if self._fix_p:
result['samples'][1, :] = log(self._fix_p)
self.params = {
k: {
'k': exp(data[0]),
'p': exp(data[1]),
'a': data[4],
'b': data[5],
'alpha': data[6:6 + n_features].T,
'beta': data[6 + n_features:6 + 2 * n_features].T,
}
for k, data in result.items()
}
def get_batch_lower_bound(cur_params, iter):
encoder_weights = combined_parser.get(cur_params, 'encoder weights')
flow_params = combined_parser.get(cur_params, 'flow params')
decoder_weights = combined_parser.get(cur_params, 'decoder weights')
cur_data = train_images[batch_idxs[iter]]
mus, log_sigs = encoder(encoder_weights, cur_data)
samples, entropy_estimates = flow_sampler(flow_params, mus, np.exp(log_sigs), rs)
loglikes = decoder_log_like(decoder_weights, samples, cur_data)
print "Iter", iter, "loglik:", np.mean(loglikes).value, \
"entropy:", np.mean(entropy_estimates).value, "marg. like:", np.mean(entropy_estimates + loglikes).value
return np.mean(entropy_estimates + loglikes)
lb_grad = grad(get_batch_lower_bound)
def callback(weights, iter, grad):
#Generate samples
num_samples = 100
zs = rs.randn(num_samples, latent_dimension)
samples = decoder(combined_parser.get(weights, 'decoder weights'), zs)
fig = plt.figure(1)
fig.clf()
ax = fig.add_subplot(111)
plot_images(samples, ax, ims_per_row=10)
plt.savefig('samples.png')
final_params = adam(lb_grad, combined_params, num_training_iters, callback=callback)
finish_time = time.time()
def test_angle_real():
fun = lambda x: np.angle(x)
d_fun = lambda x: grad(fun)(x)
check_grads(fun)(npr.rand())
check_grads(d_fun)(npr.rand())
def build_branin_objective(D=100):
obj_grad = grad(branin)
obj_hvp = sliced_hvp(obj_grad)
return D, branin, obj_grad, obj_hvp, {}
def test_abs_complex():
fun = lambda x: np.abs(x)
d_fun = lambda x: grad(fun)(x)
check_grads(fun)(1.1 + 1.2j)
check_grads(d_fun)(1.1 + 1.3j)
t2 = targets * 2 - 1
t2 = t2[:, np.newaxis, :]
# Now t2 is -1 or 1, which makes the following form nice
label_probabilities = -np.logaddexp(0, -unnormalized_logprobs * t2)
return np.sum(label_probabilities, axis=-1) # Sum across pixels.
def batched_loss(params, iter):
data_idx = batch_indices(iter)
return neglogprob(params, train_images[data_idx, :])
def neglogprob(params, data):
return np.log(K) - logsumexp(bernoulli_log_density(data, params),
axis=-1).mean()
# Get gradient of objective using autograd.
objective_grad = grad(batched_loss)
def print_perf(params, iter, gradient):
if iter % 30 == 0:
save_images(sigmoid(params),
'results/4/thetas.png',
vmin=0.0,
vmax=1.0)
print(batched_loss(params, iter))
# The optimizers provided by autograd can optimize lists, tuples, or dicts of parameters.
# You may use these optimizers for Q4, but implement your own gradient descent optimizer for Q3!
optimized_params = adam(objective_grad,
theta,
step_size=0.2,
num_iters=10000,
def test_polygamma():
x = npr.randn()
fun = lambda x: to_scalar(autograd.scipy.special.polygamma(0, x))
d_fun = grad(fun)
check_grads(fun, x)
check_grads(d_fun, x)
def test_yn():
x = npr.randn()**2 + 0.2
fun = lambda x: to_scalar(autograd.scipy.special.yn(2, x))
d_fun = grad(fun)
check_grads(fun, x)
check_grads(d_fun, x)
network_size = [2, 128, 128, 128, 1]
A = [sigmoid, sigmoid, sigmoid, identity]
network = simple_MLP(network_size, A)
layer_data = network.layer_data
L = network.L
# trial solution
def v(x, t, layer_data):
input = np.array([x, t])
return np.sin(np.pi * x) + x * (x - 1) * t * network.input_to_output(
input, layer_data)
# applying the operator D := Dxx - Dt to the trial solution
v_xx = grad(grad(v, 0), 0)
v_t = grad(v, 1)
def Dv(x, t, layer_data):
return v_xx(x, t, layer_data) - v_t(x, t, layer_data)
# cost function
def cost_function(domain, layer_data):
x, t = domain[0], domain[1]
Dv_eval = np.array([Dv(x_, t_, layer_data) for t_ in t for x_ in x])
cost = np.dot(Dv_eval, Dv_eval)
return cost / np.size(x) / np.size(x)
print ('b1', params[2][1][2])
# print ('b', params[2][2])
plt.cla()
target_distribution = lambda x: np.exp(log_density(x))
var_distribution = lambda x: np.exp(variational_log_density(params, x))
plot_isocontours(ax, target_distribution)
plot_isocontours(ax, var_distribution, cmap=plt.cm.bone)
ax.set_autoscale_on(False)
# rs = npr.RandomState(0)
# samples = variational_sampler(params, num_plotting_samples, rs)
# plt.plot(samples[:, 0], samples[:, 1], 'x')
plt.draw()
plt.pause(1.0/30.0)
print("Optimizing variational parameters...")
variational_params = adam(grad(objective), init_var_params(D), step_size=0.1,
num_iters=2000, callback=callback)
def distance_from_target_image(smoke):
return np.mean((target - smoke)**2)
def convert_param_vector_to_matrices(params):
vx = np.reshape(params[:(rows * cols)], (rows, cols))
vy = np.reshape(params[(rows * cols):], (rows, cols))
return vx, vy
def objective(params):
init_vx, init_vy = convert_param_vector_to_matrices(params)
final_smoke = simulate(init_vx, init_vy, init_smoke,
simulation_timesteps)
return distance_from_target_image(final_smoke)
# Specify gradient of objective function using autograd.
objective_with_grad = grad(objective, return_function_value=True)
fig = plt.figure(figsize=(8, 8))
ax = fig.add_subplot(111, frameon=False)
def callback(params):
init_vx, init_vy = convert_param_vector_to_matrices(params)
simulate(init_vx, init_vy, init_smoke, simulation_timesteps, ax)
print "Optimizing initial conditions..."
result = minimize(objective_with_grad,
init_dx_and_dy,
jac=True,
method='CG',
options={
'maxiter': 25,
def d_fun(input_list):
g = grad(fun)(input_list)
A = np.sum(g[0])
B = np.sum(np.sin(g[0]))
C = np.sum(np.sin(g[1]))
return A + B + C
def flow_eq_grad1(self, mf, pu, pd):
return grad(self.flow_eq, 0)(mf, pu,
pd), -1., 1., self.flow_eq(mf, pu, pd)
def test_real_type():
fun = lambda x: np.sum(np.real(x))
df = grad(fun)
assert np.isrealobj(df(2.0))
assert np.iscomplexobj(df(1.0j))
def logistic_predictions(weights, inputs):
# Outputs probability of a label being true according to logistic model.
return sigmoid(np.dot(inputs, weights))
def training_loss(weights):
# Training loss is the negative log-likelihood of the training labels.
preds = logistic_predictions(weights, inputs)
label_probabilities = preds * targets + (1 - preds) * (1 - targets)
return -np.sum(np.log(label_probabilities))
# Build a toy dataset.
inputs = np.array([[0.52, 1.12, 0.77], [0.88, -1.08, 0.15],
[0.52, 0.06, -1.30], [0.74, -2.49, 1.39]])
targets = np.array([True, True, False, True])
# Build a function that returns gradients of training loss using autograd.
training_gradient_fun = grad(training_loss)
# Check the gradients numerically, just to be safe.
weights = np.array([0.0, 0.0, 0.0])
quick_grad_check(training_loss, weights)
# Optimize weights using gradient descent.
print("Initial loss:", training_loss(weights))
for i in range(100):
weights -= training_gradient_fun(weights) * 0.01
print("Trained loss:", training_loss(weights))
def test_abs_real():
fun = lambda x: np.abs(x)
d_fun = lambda x: grad(fun)(x)
check_grads(fun)(1.1)
check_grads(d_fun)(2.1)
def __init__(self,
point_estimate,
demo_func,
data,
mut_rate=None,
length=1,
regime="long",
psd_rtol=1e-8,
**kwargs):
"""
Parameters
----------
point_estimate : array
a statistically consistent estimate for the true parameters.
confidence regions and hypothesis tests are computed for a (shrinking)
neighborhood around this point.
demo_func : function that returns a Demography from parameters
data : SegSites (or Sfs, if regime="many")
regime : the limiting regime for the asymptotic confidence region
if "long", number of loci is fixed, and the length of the loci -> infinity.
* uses time series information to estimate covariance structure
* requires isinstance(data, SegSites)
* loci should be independent. they don't have to be identically distributed
if "many", the number of loci -> infinity
* loci should be independent, and roughly identically distributed
psd_rtol: for checking if certain matrices (e.g. covariance matrices) are positive semidefinite
if psd_rtol = epsilon, then we will consider a matrix positive semidefinite if its most
negative eigenvalue has magnitude less than epsilon * most positive eigenvalue.
**kwargs : additional arguments passed into composite_log_likelihood
"""
if regime not in ("long", "many"):
raise ValueError("Unrecognized regime '%s'" % regime)
try:
data = data.seg_sites
except AttributeError:
data = data
if mut_rate is not None:
mut_rate = mut_rate * length
self.point = np.array(point_estimate)
self.demo_func = demo_func
self.data = data
self.regime = regime
self.kwargs = dict(kwargs)
self.psd_rtol = psd_rtol
self.score = autograd.grad(self.lik_fun)(self.point)
self.score_cov = _observed_score_covariance(self.regime,
self.point,
self.data,
self.demo_func,
psd_rtol=self.psd_rtol,
mut_rate=mut_rate,
**self.kwargs)
self.fisher = _observed_fisher_information(self.point,
self.data,
self.demo_func,
psd_rtol=self.psd_rtol,
assert_psd=False,
mut_rate=mut_rate,
**self.kwargs)
def test_angle_complex():
fun = lambda x: np.angle(x)
d_fun = lambda x: grad(fun)(x)
check_grads(fun)(npr.rand() + 1j * npr.rand())
check_grads(d_fun)(npr.rand() + 1j * npr.rand())
def test_drift_force(X, alpha):
psi = SimpleGaussian(alpha)
pool = SumPooling(psi)
expected = 2 * grad(sum_pool_np, 0)(X, alpha) / sum_pool_np(X, alpha)
assert_close(expected.ravel(), pool.drift_force(X))
def main():
num_iters = 10
X, y = make_classification(
100,
n_classes=3,
n_informative=3,
n_redundant=0,
n_clusters_per_class=2,
n_features=20,
)
model = lgb.LGBMClassifier(
boosting_type="gbdt", objective="binary", n_estimators=3, random_state=1
)
model.fit(X, y)
model_dump = model.booster_.dump_model()
trees_ = [m["tree_structure"] for m in model_dump["tree_info"]]
# needs to infer from model.predict_proba? or labelbinarizer
lb = LabelBinarizer()
y_ohe = lb.fit_transform(y)
nclass = y_ohe.shape[1]
if nclass == 2:
y_ohe = y
if nclass > 2:
trees = split_trees_by_classes(trees_, nclass)
trees_params = multiclass_trees_to_param(X, y, trees)
model_ = gbm_gen(
trees_params[0], X, trees_params[2], trees_params[1], True, nclass
)
def training_loss(weights, idx=0):
# Training loss is the negative log-likelihood of the training labels.
preds = model_(weights, X)
loglik = -np.sum(np.log(preds + 1e-7) * y_ohe)
return loglik
else:
trees_params = multi_tree_to_param(X, y, trees_)
model_ = gbm_gen(trees_params[0], X, trees_params[2], trees_params[1], False, 2)
def training_loss(weights, idx=0):
# Training loss is the negative log-likelihood of the training labels.
preds = sigmoid(model_(weights, X))
label_probabilities = preds * y + (1 - preds) * (1 - y)
loglik = -np.sum(np.log(label_probabilities))
return loglik
# training the model and outputting results
training_gradient_fun = grad(training_loss)
param_ = adam(
training_gradient_fun,
trees_params[0],
callback=simple_callback,
step_size=0.05,
num_iters=num_iters,
)
lgb_predict = model.predict_proba(X)
if lgb_predict.shape[1] == 2:
lgb_predict = lgb_predict[:, 1]
results = {
"train_base": roc_auc_score(y_ohe, model_(trees_params[0], X)),
"train_nnet": roc_auc_score(y_ohe, model_(param_, X)),
"train_lgb": roc_auc_score(y_ohe, lgb_predict),
}
return results
def optimize_latent_weighting_stochastic(self,
exp_buffer,
wb,
task_steps,
state_diffs=False,
use_all_exp=False):
"""Learn the latent weights using gradients of the energy function with respect to the latent weights
and performing minibatch updates via SGD (ADAM).
Arguments:
exp_buffer -- Either an ExperienceReplay object, or a list of transitions of a single instance;
if use_all_exp==False, then an ExperienceReplay object must be supplied;
otherwise, a list of transitions must be supplied (where each transition is a numpy array)
wb -- the latent weights for the specific instance
task_steps --total steps taken in environment
Keyword Arguments:
state_diffs -- boolean indicating if the BNN should predict state differences rather than the next state (default: False)
use_all_exp -- boolean indicating whether updates should be performed using all experiences
"""
# Create gradient functional of the energy function wrt wb
energy_grad = grad(self.simple_loss, argnum=2)
# energy_grad = grad(self.energy, argnum=2)
cur_latent_weights = wb
m1 = 0
m2 = 0
beta1 = 0.9
beta2 = 0.999
epsilon = 1e-8
t = 0
# With linear top latent weights, use a single sample of the BNN network weights to compute gradients
if self.linear_latent_weights:
tmp_num_weight_samples = self.num_weight_samples
self.num_weight_samples = 1
for epoch in range(self.wb_opt_epochs):
# Gather a sample of data from the experience buffer, convert to input and target arrays
if use_all_exp:
batch = exp_buffer
else:
batch, __, indices = exp_buffer.sample(task_steps)
# batch: [state,self.__encode_action(action),reward,next_state]
X = np.array([
np.hstack([batch[tt, 0], batch[tt, 1]])
for tt in range(len(batch))
])
y = np.array([batch[tt, 3] for tt in range(len(batch))])
if state_diffs:
y = y - X[:, :batch[0, 0].shape[0]]
self.N = X.shape[0]
batch_idxs = self.__make_batches__()
# Permute the indices of the training inputs for SGD purposes
#permutation = np.random.permutation(X.shape[0])
permutation = np.random.choice(range(X.shape[0]),
X.shape[0],
replace=False)
for idxs in batch_idxs:
t += 1
grad_wb = energy_grad(self.weights, X[permutation[idxs]],
cur_latent_weights, y[permutation[idxs]])
# m1 = beta1*m1 + (1-beta1)*grad_wb
# m2 = beta2*m2 + (1-beta2)*grad_wb**2
# m1_hat = m1 / (1-beta1**t)
# m2_hat = m2 / (1-beta2**t)
# cur_latent_weights -= self.wb_learning_rate * m1_hat / (np.sqrt(m2_hat)+epsilon)
cur_latent_weights -= self.wb_learning_rate * grad_wb
# Re-queue sampled data with updated TD-error calculations
X_latent_weights = np.vstack(
[cur_latent_weights[0] for i in range(X.shape[0])])
if not use_all_exp and exp_buffer.mem_priority:
td_loss = self.get_td_error(np.hstack([X, X_latent_weights]),
y, 0.0, 1.0)
exp_buffer.update_priorities(
np.hstack((np.reshape(td_loss, (len(td_loss), -1)),
np.reshape(indices, (len(indices), -1)))))
if self.linear_latent_weights:
self.num_weight_samples = tmp_num_weight_samples
return cur_latent_weights
def gradient_function(point):
return projector(point, grad(cost)(point))
def fit_network(self,
exp_buffer,
task_weights,
task_steps,
state_diffs=False,
use_all_exp=False):
"""Learn BNN network weights using gradients of the energy function with respect to the network weights
and performing minibatch updates via SGD (ADAM).
Arguments:
exp_buffer -- Either an ExperienceReplay object, or a list of transitions;
if use_all_exp==False, then an ExperienceReplay object must be supplied;
otherwise, a list of transitions must be supplied (where each transition is a numpy array)
task_weights -- the latent weights: a numpy array of with dimensions (number of instances x number of latent weights)
task_steps --total steps taken in environment
Keyword Arguments:
state_diffs -- boolean indicating if the BNN should predict state differences rather than the next state (default: False)
use_all_exp -- boolean indicating whether updates should be performed using all experiences
"""
# Create gradient functional of the energy function wrt W
energy_grad = grad(self.simple_loss, argnum=0)
# energy_grad = grad(self.energy, argnum=0)
weights = np.copy(self.weights)
m1 = 0
m2 = 0
beta1 = 0.9
beta2 = 0.999
epsilon = 1e-8
t = 0
for epoch in range(self.train_epochs):
# Gather a sample of data from the experience buffer, convert to input and target arrays
if use_all_exp:
batch = exp_buffer
else:
batch, __, indices = exp_buffer.sample(task_steps)
# batch: [state,self.__encode_action(action),reward,next_state]
X = np.array([
np.hstack([batch[tt, 0], batch[tt, 1]])
for tt in range(len(batch))
])
wb = np.array(
[task_weights[batch[tt, 4], :] for tt in range(len(batch))])
y = np.array([batch[tt, 3] for tt in range(len(batch))])
if state_diffs:
y = y - X[:, :batch[0, 0].shape[0]]
self.N = X.shape[0]
batch_idxs = self.__make_batches__()
# Permute the indices of the training inputs for SGD purposes
permutation = np.random.permutation(X.shape[0])
for idxs in batch_idxs:
t += 1
grad_w = energy_grad(weights, X[permutation[idxs]],
wb[permutation[idxs]],
y[permutation[idxs]])
print("GRAD = ", grad_w)
# m1 = beta1*m1 + (1-beta1)*grad_w
# m2 = beta2*m2 + (1-beta2)*grad_w**2
# m1_hat = m1 / (1-beta1**t)
# m2_hat = m2 / (1-beta2**t)
# weights = weights - self.learning_rate*m1_hat/(np.sqrt(m2_hat)+epsilon)
weights = weights - self.learning_rate * grad_w
# Re-queue sampled data with updated TD-error calculations
self.weights = weights
if (not use_all_exp) and exp_buffer.mem_priority:
td_loss = self.get_td_error(np.hstack([X, wb]), y, 0.0, 1.0)
exp_buffer.update_priorities(
np.hstack((np.reshape(td_loss, (len(td_loss), -1)),
np.reshape(indices, (len(indices), -1)))))
def hamiltonian_monte_carlo(
n_samples,
negative_log_prob,
initial_position,
tune=500,
path_len=1,
initial_step_size=0.1,
):
"""Run Hamiltonian Monte Carlo sampling.
Parameters
----------
n_samples : int
Number of samples to return
negative_log_prob : callable
The negative log probability to sample from
initial_position : np.array
A place to start sampling from.
tune: int
Number of iterations to run tuning
path_len : float
How long each integration path is. Smaller is faster and more correlated.
initial_step_size : float
How long each integration step is. This will be tuned automatically.
Returns
-------
np.array
Array of length `n_samples`.
"""
initial_position = np.array(initial_position)
# autograd magic
dVdq = grad(negative_log_prob)
# collect all our samples in a list
samples = [initial_position]
# Keep a single object for momentum resampling
momentum = st.norm(0, 1)
step_size = initial_step_size
step_size_tuning = DualAveragingStepSize(step_size)
# If initial_position is a 10d vector and n_samples is 100, we want 100 x 10 momentum draws
# we can do this in one call to np.random.normal, and iterate over rows
size = (n_samples + tune, ) + initial_position.shape[:1]
for idx, p0 in tqdm(enumerate(momentum.rvs(size=size)), total=size[0]):
# Integrate over our path to get a new position and momentum
q_new, p_new = leapfrog(
samples[-1],
p0,
dVdq,
path_len=2 * np.random.rand() *
path_len, # We jitter the path length a bit
step_size=step_size,
)
# Check Metropolis acceptance criterion
start_log_p = np.sum(momentum.logpdf(p0)) - negative_log_prob(
samples[-1])
new_log_p = np.sum(momentum.logpdf(p_new)) - negative_log_prob(q_new)
p_accept = min(1, np.exp(new_log_p - start_log_p))
if np.random.rand() < p_accept:
samples.append(q_new)
else:
samples.append(np.copy(samples[-1]))
if idx < tune - 1:
step_size, _ = step_size_tuning.update(p_accept)
elif idx == tune - 1:
_, step_size = step_size_tuning.update(p_accept)
return np.array(samples[1 + tune:])
def map_gpp_bnn(layer_sizes, nonlinearity=np.tanh,
n_data=200, N_samples=10,
L2_reg=0.1, noise_var=0.1):
shapes = list(zip(layer_sizes[:-1], layer_sizes[1:]))
N_weights = sum((m+1)*n for m, n in shapes)
def unpack_params(params):
mean, log_std = params[:N_weights], params[N_weights:]
return mean, log_std
def unpack_layers(weights):
""" iterable that unpacks the weights into relevant tensor shapes for each layer"""
num_weight_sets = len(weights)
for m, n in shapes:
yield weights[:, :m*n] .reshape((num_weight_sets, m, n)),\
weights[:, m*n:m*n+n].reshape((num_weight_sets, 1, n))
weights = weights[:, (m+1)*n:]
def predictions(weights, inputs):
""" implements the forward pass of the bnn
weights | dim = [N_weight_samples, N_weights]
inputs | dim = [N_data]
outputs | dim = [N_weight_samples, N_data, 1] """
inputs = np.expand_dims(inputs, 0)
for W, b in unpack_layers(weights):
outputs = np.einsum('mnd,mdo->mno', inputs, W) + b
inputs = nonlinearity(outputs)
return outputs
def sample_gpp(x, n_samples):
""" Samples from the gp prior x = inputs with shape [N_data]
returns : samples from the gp prior [N_data, N_samples] """
x = np.ravel(x)
n_data = len(x)
K = covariance(x[:, None], x[:, None])
L = cholesky(K + 1e-7 * np.eye(n_data))
e = rs.randn(n_data, n_samples)
return np.dot(L, e)
def log_gp_prior(y_bnn, x):
""" computes: the expectation value of the log of the gp prior :
E [ log p_gp(f) ] where p_gp(f) = N(f|0,K) where f ~ p_BNN(f)
= -0.5 * E [ (L^-1f)^T(L^-1f) ] + const; K = LL^T (cholesky decomposition)
(we ignore constants for now as we are not optimizing the covariance hyper-params)
bnn_weights | dim = [N_weights_samples, N_weights]
K = covariance/Kernel matrix | dim = [N_data, N_data] ; dim L = dim K
y_bnn output of a bnn | dim = [N_data, N_weights_samples]
returns : E[log p_gp(y)] | dim = [N_function_samples] """
K = covariance(x, x)+noise_var*np.eye(len(x)) # shape [N_data, N_data]
L = cholesky(K) # K = LL^T ; shape L = shape K
a = solve(L, y_bnn) # a = L^-1 y_bnn ; shape L^-1 y_bnn =
log_gp = -0.5*np.mean(a**2, axis=0) # Compute E [a^2]
return log_gp
def log_prob(weights, inputs, targets):
""" computes log p(y,w) = log p(y|w)+ log p(w) with p(w) = N(w|0,I)
weights: | dim = [N_weight_samples, N_weights]
preds = f | dim = [N_weight_samples, N_data, 1]
targets = y | dim = [N_data]
log_prior = log p(w) | dim = [N_weights_samples]
log_lik = log(y|w) | dim = [N_weights_samples] """
log_prior = -L2_reg * np.sum(weights ** 2, axis=1)
preds = predictions(weights, inputs)
log_lik = -np.sum((preds - targets)**2, axis=1)[:, 0] / noise_var
return log_prior + log_lik
def gaussian_entropy(log_std):
return 0.5 * N_weights * (1.0 + np.log(2*np.pi)) + np.sum(log_std)
def elbo(var_param, x, y):
""" Provides a stochastic estimate of the evidence lower bound
ELBO = E_r(w) [log p(y,w)-r(w)]
params | dim = [2*N_weights]
mean, log_std | dim = [N_weights]
ws | dim = [N_samples, N_weights]
returns : ELBO | dim = [1] """
mean, log_std = unpack_params(var_param)
ws = rs.randn(N_samples, N_weights) * np.exp(log_std) + mean # sample weights from r(w)
return gaussian_entropy(log_std) + np.mean(log_prob(ws, x, y)) # ELBO
def log_pys(thetas, ys, x):
""" creates an array of log p(y) for each y in ys
which are estimated by using the ELBO
log p(y) => E_r(w) [ log p(y,w)-log r(w)]
ys has shape [y_samples, N_data] """
# get E_r(w)[p(y,w) - r(w)] for each w, y
elbos = np.array([elbo(theta, x, y) for theta, y in zip(thetas, ys)])
return elbos
def kl_objective(params_phi, params_theta, t):
"""
Provides a stochastic estimate of the kl divergence
kl[p(y)|p_GP(y)] = E_p(y) [log p(y) -log p_gp(y)]
= -H[ p(y) ] -E_p(y) [log p_gp(y)]
using :
params_phi dim = [2*N_weights]
params_theta list of [2*N_weights] : the var params of each r(w|theta)
phi_mean, phi_log_std | dim = [N_weights]
w_phi | dim = [N_samples, N_weights]
y_bnn | dim = [N_data, N_weights_samples]
kl | dim = [1] """
phi_mean, phi_log_std = unpack_params(params_phi)
w_phi = rs.randn(N_samples, N_weights) * np.exp(phi_log_std) + phi_mean
x = np.random.uniform(low=-10, high=10, size=(n_data, 1)) # X ~ p(X)
f_bnn = predictions(w_phi, x)[:, :, 0].T # shape [N_data, N_weights_samples] f ~ p(f)
y_bnn = f_bnn + 3*noise_var*rs.randn(n_data, N_samples) # y = f + e ; y ~ p(y)
# use monte carlo to approx H[p(y)] = E_p(y)[ log p(y)]
entropy = np.mean(log_pys(params_theta, y_bnn.T, x))
# use monte carlo to approx E_p(y) [log p_gp(y)]
expected_log_gpp = np.mean(log_gp_prior(y_bnn, x))
kl_div = entropy - expected_log_gpp
return kl_div # the KL
grad_kl = grad(kl_objective, argnum=(0, 1))
return N_weights, predictions, sample_gpp, unpack_params, kl_objective, grad_kl
def prepare_loss_node(loss, opt_args_ls=None):
if global_settings.backend == 'autograd':
return ag.grad(loss, opt_args_ls)
elif global_settings.backend == 'pytorch':
return loss
ub_sigma = np.full((nEtaBins, nEtaBins, nPtBins, nPtBins), 10).flatten()
ub_nsig = np.full((nEtaBins, nEtaBins, nPtBins, nPtBins), 20.).flatten()
ub_scale[idx] = np.full(len(idx), 1.)
ub_sigma[idx] = np.full(len(idx), -3.5)
ub_nsig[idx] = np.full(len(idx), 6.9)
lb = np.concatenate((lb_scale, lb_sigma, lb_nsig), axis=None)
ub = np.concatenate((ub_scale, ub_sigma, ub_nsig), axis=None)
constraints = LinearConstraint(A=np.eye(x.shape[0]),
lb=lb,
ub=ub,
keep_feasible=True)
grad = grad(nll)
hess = hessian(nll)
res = minimize(nll, x, args=(nEtaBins,nPtBins,datasetJ,datasetJgen),\
method = 'trust-constr',jac = grad, hess=SR1(), constraints = constraints,\
options={'verbose':3,'disp':True,'maxiter' : 100000, 'gtol' : 0., 'xtol' : xtol, 'barrier_tol' : btol})
print res
good_idx = np.where((np.sum(datasetJgen, axis=2) > 1000.).flatten())[0]
sep = nEtaBins * nEtaBins * nPtBins * nPtBins
good_idx = np.concatenate((good_idx, good_idx + sep, good_idx + 2 * sep),
axis=None)
fitres = res.x[good_idx]