def optimize_params(self, p0, num_iters, step_size, tolerance, verbose):
"""
Perform gradient descent using JAX optimizers.
"""
opt_init, opt_update, get_params = optimizers.adam(step_size=step_size)
opt_state = opt_init(p0)
@jit
def step(i, opt_state):
p = get_params(opt_state)
g = grad(self.negative_log_evidence)(p)
return opt_update(i, g, opt_state)
cost_list = []
params_list = []
if verbose:
self.print_progress_header(p0)
for i in range(num_iters):
opt_state = step(i, opt_state)
params_list.append(get_params(opt_state))
cost_list.append(self.negative_log_evidence(params_list[-1]))
if verbose:
if i % verbose == 0:
self.print_progress(i, params_list[-1], cost_list[-1])
if len(params_list) > tolerance:
if np.all(
(np.array(cost_list[1:])) - np.array(cost_list[:-1]) > 0):
params = params_list[0]
if verbose:
print(
'Stop: cost has been monotonically increasing for {} steps.'
.format(tolerance))
break
elif np.all(
np.array(cost_list[:-1]) -
np.array(cost_list[1:]) < 1e-5):
params = params_list[-1]
if verbose:
print(
'Stop: cost has been stop changing for {} steps.'.
format(tolerance))
break
else:
params_list.pop(0)
cost_list.pop(0)
else:
params = params_list[-1]
if verbose:
print('Stop: reached {0} steps, final cost={1:.5f}.'.format(
num_iters, cost_list[-1]))
return params
def cond_fn(curr):
return jnp.bitwise_and(
curr.i < SineBivariateVonMises.max_sample_iter,
jnp.logical_not(jnp.all(curr.done)),
)
def initialize_model(rng_key,
model,
init_strategy=init_to_uniform,
dynamic_args=False,
model_args=(),
model_kwargs=None):
"""
(EXPERIMENTAL INTERFACE) Helper function that calls :func:`~numpyro.infer.util.get_potential_fn`
and :func:`~numpyro.infer.util.find_valid_initial_params` under the hood
to return a tuple of (`init_params_info`, `potential_fn`, `postprocess_fn`, `model_trace`).
:param jax.random.PRNGKey rng_key: random number generator seed to
sample from the prior. The returned `init_params` will have the
batch shape ``rng_key.shape[:-1]``.
:param model: Python callable containing Pyro primitives.
:param callable init_strategy: a per-site initialization function.
See :ref:`init_strategy` section for available functions.
:param bool dynamic_args: if `True`, the `potential_fn` and
`constraints_fn` are themselves dependent on model arguments.
When provided a `*model_args, **model_kwargs`, they return
`potential_fn` and `constraints_fn` callables, respectively.
:param tuple model_args: args provided to the model.
:param dict model_kwargs: kwargs provided to the model.
:return: a namedtupe `ModelInfo` which contains the fields
(`param_info`, `potential_fn`, `postprocess_fn`, `model_trace`), where
`param_info` is a namedtuple `ParamInfo` containing values from the prior
used to initiate MCMC, their corresponding potential energy, and their gradients;
`postprocess_fn` is a callable that uses inverse transforms
to convert unconstrained HMC samples to constrained values that
lie within the site's support, in addition to returning values
at `deterministic` sites in the model.
"""
model_kwargs = {} if model_kwargs is None else model_kwargs
substituted_model = substitute(seed(
model, rng_key if jnp.ndim(rng_key) == 1 else rng_key[0]),
substitute_fn=init_strategy)
inv_transforms, replay_model, has_enumerate_support, model_trace = _get_model_transforms(
substituted_model, model_args, model_kwargs)
# substitute param sites from model_trace to model so
# we don't need to generate again parameters of `numpyro.module`
model = substitute(model,
data={
k: site["value"]
for k, site in model_trace.items()
if site["type"] in ["param", "plate"]
})
constrained_values = {
k: v['value']
for k, v in model_trace.items() if v['type'] == 'sample'
and not v['is_observed'] and not v['fn'].is_discrete
}
if has_enumerate_support:
from numpyro.contrib.funsor import config_enumerate, enum
if not isinstance(model, enum):
max_plate_nesting = _guess_max_plate_nesting(model_trace)
_validate_model(model_trace)
model = enum(config_enumerate(model), -max_plate_nesting - 1)
potential_fn, postprocess_fn = get_potential_fn(model,
inv_transforms,
replay_model=replay_model,
enum=has_enumerate_support,
dynamic_args=dynamic_args,
model_args=model_args,
model_kwargs=model_kwargs)
init_strategy = init_strategy if isinstance(init_strategy,
partial) else init_strategy()
if (init_strategy.func is init_to_value) and not replay_model:
init_values = init_strategy.keywords.get("values")
unconstrained_values = transform_fn(inv_transforms,
init_values,
invert=True)
init_strategy = _init_to_unconstrained_value(
values=unconstrained_values)
prototype_params = transform_fn(inv_transforms,
constrained_values,
invert=True)
(init_params, pe, grad), is_valid = find_valid_initial_params(
rng_key,
model,
init_strategy=init_strategy,
enum=has_enumerate_support,
model_args=model_args,
model_kwargs=model_kwargs,
prototype_params=prototype_params)
if not_jax_tracer(is_valid):
if device_get(~jnp.all(is_valid)):
with numpyro.validation_enabled(), trace() as tr:
# validate parameters
substituted_model(*model_args, **model_kwargs)
# validate values
for site in tr.values():
if site['type'] == 'sample':
with warnings.catch_warnings(record=True) as ws:
site['fn']._validate_sample(site['value'])
if len(ws) > 0:
for w in ws:
# at site information to the warning message
w.message.args = ("Site {}: {}".format(site["name"], w.message.args[0]),) \
+ w.message.args[1:]
warnings.showwarning(w.message,
w.category,
w.filename,
w.lineno,
file=w.file,
line=w.line)
raise RuntimeError(
"Cannot find valid initial parameters. Please check your model again."
)
return ModelInfo(ParamInfo(init_params, pe, grad), potential_fn,
postprocess_fn, model_trace)
def all(self, boolean_tensor, axis=None, keepdims=False):
if isinstance(boolean_tensor, (tuple, list)):
boolean_tensor = jnp.stack(boolean_tensor)
return jnp.all(boolean_tensor, axis=axis, keepdims=keepdims)
def multi_errors(x):
checkify.check(jnp.all(x < 0), "must be negative!") # ASSERT
x = x / 0 # DIV
x = jnp.sin(x) # NAN
x = x[500] # OOB
return x
def testAlphaDerivativeIsPositive(self):
# Assert that d_loss / d_alpha > 0.
_, _, _, alpha, _, _, d_alpha, _ = self._precompute_lossfun_inputs()
mask = jnp.isfinite(alpha)
self.assertTrue(
jnp.all(d_alpha[mask] > (-300. * jnp.finfo(jnp.float32).eps)))
def __eq__(self, other):
assert False, "not yet implemented checking equality of reduce"
return (isinstance(other, self.__class__)
and np.all(other.insp_pts == self.insp_pts)
and other.k == self.k)
def solve(self, result:FiniteVec):
if np.all(self.outp_feat.inspace_points == result.inspace_points):
s = np.linalg.solve(self.matr @ inner(self.inp_feat, self.inp_feat), result.prefactors)
return FiniteVec.construct_RKHS_Elem(result.k, result.inspace_points, s)
else:
assert()
def neighbor_list(displacement_or_metric: DisplacementOrMetricFn,
box_size: Box,
r_cutoff: float,
dr_threshold: float,
capacity_multiplier: float = 1.25,
cell_size: float = None,
disable_cell_list: bool = False,
mask_self: bool = True,
**static_kwargs) -> NeighborFn:
"""Returns a function that builds a list neighbors for collections of points.
Neighbor lists must balance the need to be jit compatable with the fact that
under a jit the maximum number of neighbors cannot change (owing to static
shape requirements). To deal with this, our `neighbor_list` returns a
function `neighbor_fn` that can operate in two modes: 1) create a new
neighbor list or 2) update an existing neighbor list. Case 1) cannot be jit
and it creates a neighbor list with a maximum neighbor count of the current
neighbor count times capacity_multiplier. Case 2) is jit compatable, if any
particle has more neighbors than the maximum, the `did_buffer_overflow` bit
will be set to `True` and a new neighbor list will need to be created.
Here is a typical example of a simulation loop with neighbor lists:
>>> init_fn, apply_fn = simulate.nve(energy_fn, shift, 1e-3)
>>> exact_init_fn, exact_apply_fn = simulate.nve(exact_energy_fn, shift, 1e-3)
>>>
>>> nbrs = neighbor_fn(R)
>>> state = init_fn(random.PRNGKey(0), R, neighbor_idx=nbrs.idx)
>>>
>>> def body_fn(i, state):
>>> state, nbrs = state
>>> nbrs = neighbor_fn(state.position, nbrs)
>>> state = apply_fn(state, neighbor_idx=nbrs.idx)
>>> return state, nbrs
>>>
>>> step = 0
>>> for _ in range(20):
>>> new_state, nbrs = lax.fori_loop(0, 100, body_fn, (state, nbrs))
>>> if nbrs.did_buffer_overflow:
>>> nbrs = neighbor_fn(state.position)
>>> else:
>>> state = new_state
>>> step += 1
Args:
displacement: A function `d(R_a, R_b)` that computes the displacement
between pairs of points.
box_size: Either a float specifying the size of the box or an array of
shape [spatial_dim] specifying the box size in each spatial dimension.
r_cutoff: A scalar specifying the neighborhood radius.
dr_threshold: A scalar specifying the maximum distance particles can move
before rebuilding the neighbor list.
capacity_multiplier: A floating point scalar specifying the fractional
increase in maximum neighborhood occupancy we allocate compared with the
maximum in the example positions.
cell_size: An optional scalar specifying the size of cells in the cell list
used in an intermediate step.
disable_cell_list: An optional boolean. If set to True then the neighbor
list is constructed using only distances. This can be useful for
debugging but should generally be left as False.
mask_self: An optional boolean. Determines whether points can consider
themselves to be their own neighbors.
**static_kwargs: kwargs that get threaded through the calculation of
example positions.
Returns:
A pair. The first element is a NeighborList containing the current neighbor
list. The second element contains a function
`neighbor_list_fn(R, neighbor_list=None)` that will update the neighbor
list. If neighbor_list is None then the function will construct a new
neighbor list whose capacity is inferred from R. If neighbor_list is given
then it will update the neighbor list (with fixed capacity) if any particle
has moved more than dr_threshold / 2. Note that only
`neighbor_list_fn(R, neighbor_list)` can be `jit` since it keeps array
shapes fixed.
"""
box_size = f32(box_size)
cutoff = r_cutoff + dr_threshold
cutoff_sq = cutoff**2
threshold_sq = (dr_threshold / f32(2))**2
metric_sq = _displacement_or_metric_to_metric_sq(displacement_or_metric)
if cell_size is None:
cell_size = cutoff
use_cell_list = np.all(cell_size < box_size / 3.) and not disable_cell_list
@jit
def candidate_fn(R, **kwargs):
return np.broadcast_to(
np.reshape(np.arange(R.shape[0]), (1, R.shape[0])),
(R.shape[0], R.shape[0]))
@jit
def cell_list_candidate_fn(cl, R, **kwargs):
N, dim = R.shape
R = cl.position_buffer
idx = cl.id_buffer
cell_idx = [idx]
for dindex in _neighboring_cells(dim):
if onp.all(dindex == 0):
continue
cell_idx += [_shift_array(idx, dindex)]
cell_idx = np.concatenate(cell_idx, axis=-2)
cell_idx = cell_idx[..., np.newaxis, :, :]
cell_idx = np.broadcast_to(cell_idx,
idx.shape[:-1] + cell_idx.shape[-2:])
def copy_values_from_cell(value, cell_value, cell_id):
scatter_indices = np.reshape(cell_id, (-1, ))
cell_value = np.reshape(cell_value, (-1, ) + cell_value.shape[-2:])
return ops.index_update(value, scatter_indices, cell_value)
# NOTE(schsam): Currently, this makes a verlet list that is larger than
# needed since the idx buffer inherets its size from the cell-list. In
# three-dimensions this seems to translate into an occupancy of ~70%. We
# can make this more efficient by shrinking the verlet list at the cost of
# another sort. However, this seems possibly less efficient than just
# computing everything.
neighbor_idx = np.zeros((N + 1, ) + cell_idx.shape[-2:], np.int32)
neighbor_idx = copy_values_from_cell(neighbor_idx, cell_idx, idx)
return neighbor_idx[:-1, :, 0]
@jit
def prune_neighbor_list(R, idx, **kwargs):
d = partial(metric_sq, **kwargs)
d = vmap(vmap(d, (None, 0)))
N = R.shape[0]
neigh_R = R[idx]
dR = d(R, neigh_R)
mask = np.logical_and(dR < cutoff_sq, idx < N)
out_idx = N * np.ones(idx.shape, np.int32)
cumsum = np.cumsum(mask, axis=1)
index = np.where(mask, cumsum - 1, idx.shape[1] - 1)
p_index = np.arange(idx.shape[0])[:, None]
out_idx = ops.index_update(out_idx, ops.index[p_index, index], idx)
max_occupancy = np.max(cumsum[:, -1])
return out_idx, max_occupancy
@jit
def mask_self_fn(idx):
self_mask = idx == np.reshape(np.arange(idx.shape[0]),
(idx.shape[0], 1))
return np.where(self_mask, idx.shape[0], idx)
def neighbor_list_fn(R: Array,
neighbor_list: NeighborList = None,
extra_capacity: int = 0,
**kwargs) -> NeighborList:
nbrs = neighbor_list
def neighbor_fn(R_and_overflow, max_occupancy=None):
R, overflow = R_and_overflow
if cell_list_fn is not None:
cl = cell_list_fn(R)
idx = cell_list_candidate_fn(cl, R, **kwargs)
else:
idx = candidate_fn(R, **kwargs)
idx, occupancy = prune_neighbor_list(R, idx, **kwargs)
if max_occupancy is None:
max_occupancy = int(occupancy * capacity_multiplier +
extra_capacity)
padding = max_occupancy - occupancy
N = R.shape[0]
if max_occupancy > occupancy:
idx = np.concatenate(
[idx, N * np.ones((N, padding), dtype=idx.dtype)],
axis=1)
idx = idx[:, :max_occupancy]
return NeighborList(
mask_self_fn(idx) if mask_self else idx, R,
np.logical_or(overflow, (max_occupancy < occupancy)),
max_occupancy, cell_list_fn) # pytype: disable=wrong-arg-count
if nbrs is None:
cell_list_fn = (cell_list(box_size, cell_size, R,
capacity_multiplier)
if use_cell_list else None)
return neighbor_fn((R, False))
else:
cell_list_fn = nbrs.cell_list_fn
neighbor_fn = partial(neighbor_fn,
max_occupancy=nbrs.max_occupancy)
d = partial(metric_sq, **kwargs)
d = vmap(d)
return lax.cond(np.any(d(R, nbrs.reference_position) > threshold_sq),
(R, nbrs.did_buffer_overflow), neighbor_fn, nbrs,
lambda x: x)
return neighbor_list_fn
def testEigvalsInf(self): # https://github.com/google/jax/issues/2661 x = np.array([[np.inf]], np.float64) self.assertTrue(np.all(np.isnan(np.linalg.eigvals(x))))
import numpy as np
from pysr import pysr, sympy2jax
from jax import numpy as jnp
from jax import random
from jax import grad
import sympy
print("Test JAX 1 - test export")
x, y, z = sympy.symbols('x y z')
cosx = 1.0 * sympy.cos(x) + y
key = random.PRNGKey(0)
X = random.normal(key, (1000, 2))
true = 1.0 * jnp.cos(X[:, 0]) + X[:, 1]
f, params = sympy2jax(cosx, [x, y, z])
assert jnp.all(jnp.isclose(f(X, params), true)).item()
def test_resample():
x = random.normal(key=random.PRNGKey(0), shape=(50,))
logits = -jnp.ones(50)
samples = {'x':x}
assert jnp.all(resample(random.PRNGKey(0), samples, logits)['x'] == resample(random.PRNGKey(0), x, logits))
def test_msqrt():
for i in range(10):
A = random.normal(random.PRNGKey(i),shape=(30,30))
A = A @ A.T
L = msqrt(A)
assert jnp.all(jnp.isclose(A, L @ L.T))
def test_random_ortho_normal_matrix():
H = random_ortho_matrix(random.PRNGKey(0), 3)
assert jnp.all(jnp.isclose(H @ H.conj().T, jnp.eye(3), atol=1e-7))
def bilinear_sampler(imgs, coords, mask_value):
"""Construct a new image by bilinear sampling from the input image.
Points falling outside the source image boundary have value of mask_value.
Args:
imgs: source image to be sampled from [b, h, w, c]
coords: coordinates of source pixels to sample from [b, h, w, 2].
height_t/width_t correspond to the dimensions of the output
image (don't need to be the same as height_s/width_s).
The two channels correspond to x and y coordinates respectively.
mask_value: value of points outside of image. -1 for edge sampling.
Returns:
A new sampled image [height_t, width_t, channels]
"""
coords_x, coords_y = jnp.split(coords, 2, axis=2)
inp_size = imgs.shape
out_size = list(coords.shape)
out_size[2] = imgs.shape[2]
coords_x = jnp.array(coords_x, dtype='float32')
coords_y = jnp.array(coords_y, dtype='float32')
y_max = jnp.array(jnp.shape(imgs)[0] - 1, dtype='float32')
x_max = jnp.array(jnp.shape(imgs)[1] - 1, dtype='float32')
zero = jnp.zeros([1], dtype='float32')
eps = jnp.array([0.5], dtype='float32')
coords_x_clipped = jnp.clip(coords_x, zero, x_max - eps)
coords_y_clipped = jnp.clip(coords_y, zero, y_max - eps)
x0 = jnp.floor(coords_x_clipped)
x1 = x0 + 1
y0 = jnp.floor(coords_y_clipped)
y1 = y0 + 1
x0_safe = jnp.clip(x0, zero, x_max)
y0_safe = jnp.clip(y0, zero, y_max)
x1_safe = jnp.clip(x1, zero, x_max)
y1_safe = jnp.clip(y1, zero, y_max)
# bilinear interp weights, with points outside the grid having weight 0
# wt_x0 = (x1 - coords_x) * jnp.equal(x0, x0_safe).astype('float32')
# wt_x1 = (coords_x - x0) * jnp.equal(x1, x1_safe).astype('float32')
# wt_y0 = (y1 - coords_y) * jnp.equal(y0, y0_safe).astype('float32')
# wt_y1 = (coords_y - y0) * jnp.equal(y1, y1_safe).astype('float32')
wt_x0 = x1_safe - coords_x # 1
wt_x1 = coords_x - x0_safe # 0
wt_y0 = y1_safe - coords_y # 1
wt_y1 = coords_y - y0_safe # 0
# indices in the flat image to sample from
dim2 = jnp.array(inp_size[1], dtype='float32')
base_y0 = y0_safe * dim2
base_y1 = y1_safe * dim2
idx00 = jnp.reshape(x0_safe + base_y0, [-1])
idx01 = x0_safe + base_y1
idx10 = x1_safe + base_y0
idx11 = x1_safe + base_y1
# sample from imgs
imgs_flat = jnp.reshape(imgs, [-1, inp_size[2]])
imgs_flat = imgs_flat.astype('float32')
im00 = jnp.reshape(
jnp.take(imgs_flat, idx00.astype('int32'), axis=0), out_size)
im01 = jnp.reshape(
jnp.take(imgs_flat, idx01.astype('int32'), axis=0), out_size)
im10 = jnp.reshape(
jnp.take(imgs_flat, idx10.astype('int32'), axis=0), out_size)
im11 = jnp.reshape(
jnp.take(imgs_flat, idx11.astype('int32'), axis=0), out_size)
w00 = wt_x0 * wt_y0
w01 = wt_x0 * wt_y1
w10 = wt_x1 * wt_y0
w11 = wt_x1 * wt_y1
output = jnp.clip(jnp.round(w00 * im00 + w01 * im01 + w10 * im10 +
w11 * im11), 0, 255)
return jnp.where(jnp.all(mask_value >= 0),
jnp.where(
compute_mask(coords_x, coords_y, x_max, y_max),
output,
jnp.ones_like(output) *
jnp.reshape(jnp.array(mask_value), [1, 1, -1])
),
output)
def test_mean_var(jax_dist, sp_dist, params):
n = 20000 if jax_dist in [dist.LKJ, dist.LKJCholesky] else 200000
d_jax = jax_dist(*params)
k = random.PRNGKey(0)
samples = d_jax.sample(k, sample_shape=(n, ))
# check with suitable scipy implementation if available
if sp_dist and not _is_batched_multivariate(d_jax):
d_sp = sp_dist(*params)
try:
sp_mean = d_sp.mean()
except TypeError: # mvn does not have .mean() method
sp_mean = d_sp.mean
# for multivariate distns try .cov first
if d_jax.event_shape:
try:
sp_var = np.diag(d_sp.cov())
except TypeError: # mvn does not have .cov() method
sp_var = np.diag(d_sp.cov)
except AttributeError:
sp_var = d_sp.var()
else:
sp_var = d_sp.var()
assert_allclose(d_jax.mean, sp_mean, rtol=0.01, atol=1e-7)
assert_allclose(d_jax.variance, sp_var, rtol=0.01, atol=1e-7)
if np.all(np.isfinite(sp_mean)):
assert_allclose(np.mean(samples, 0),
d_jax.mean,
rtol=0.05,
atol=1e-2)
if np.all(np.isfinite(sp_var)):
assert_allclose(np.std(samples, 0),
np.sqrt(d_jax.variance),
rtol=0.05,
atol=1e-2)
elif jax_dist in [dist.LKJ, dist.LKJCholesky]:
if jax_dist is dist.LKJCholesky:
corr_samples = np.matmul(samples, np.swapaxes(samples, -2, -1))
else:
corr_samples = samples
dimension, concentration, _ = params
# marginal of off-diagonal entries
marginal = dist.Beta(concentration + 0.5 * (dimension - 2),
concentration + 0.5 * (dimension - 2))
# scale statistics due to linear mapping
marginal_mean = 2 * marginal.mean - 1
marginal_std = 2 * np.sqrt(marginal.variance)
expected_mean = np.broadcast_to(
np.reshape(marginal_mean,
np.shape(marginal_mean) + (1, 1)),
np.shape(marginal_mean) + d_jax.event_shape)
expected_std = np.broadcast_to(
np.reshape(marginal_std,
np.shape(marginal_std) + (1, 1)),
np.shape(marginal_std) + d_jax.event_shape)
# diagonal elements of correlation matrices are 1
expected_mean = expected_mean * (
1 - np.identity(dimension)) + np.identity(dimension)
expected_std = expected_std * (1 - np.identity(dimension))
assert_allclose(np.mean(corr_samples, axis=0),
expected_mean,
atol=0.01)
assert_allclose(np.std(corr_samples, axis=0), expected_std, atol=0.01)
else:
if np.all(np.isfinite(d_jax.mean)):
assert_allclose(np.mean(samples, 0),
d_jax.mean,
rtol=0.05,
atol=1e-2)
if np.all(np.isfinite(d_jax.variance)):
assert_allclose(np.std(samples, 0),
np.sqrt(d_jax.variance),
rtol=0.05,
atol=1e-2)
def _validate_sample(self, value):
mask = super(ImproperUniform, self)._validate_sample(value)
batch_dim = jnp.ndim(value) - len(self.event_shape)
if batch_dim < jnp.ndim(mask):
mask = jnp.all(jnp.reshape(mask, jnp.shape(mask)[:batch_dim] + (-1,)), -1)
return mask
def _validate_sample(self, x):
if not np.all(self.support(x)):
raise ValueError('Invalid values provided to log prob method. '
'The value argument must be within the support.')
def testScaleDerivativeIsNegative(self):
# Assert that d_loss / d_scale < 0.
_, _, _, alpha, _, _, _, d_scale = self._precompute_lossfun_inputs()
mask = jnp.isfinite(alpha)
self.assertTrue(
jnp.all(d_scale[mask] < (300. * jnp.finfo(jnp.float32).eps)))
def initialize_model(rng_key,
model,
init_strategy=init_to_uniform,
dynamic_args=False,
model_args=(),
model_kwargs=None):
"""
(EXPERIMENTAL INTERFACE) Helper function that calls :func:`~numpyro.infer.util.get_potential_fn`
and :func:`~numpyro.infer.util.find_valid_initial_params` under the hood
to return a tuple of (`init_params_info`, `potential_fn`, `postprocess_fn`, `model_trace`).
:param jax.random.PRNGKey rng_key: random number generator seed to
sample from the prior. The returned `init_params` will have the
batch shape ``rng_key.shape[:-1]``.
:param model: Python callable containing Pyro primitives.
:param callable init_strategy: a per-site initialization function.
See :ref:`init_strategy` section for available functions.
:param bool dynamic_args: if `True`, the `potential_fn` and
`constraints_fn` are themselves dependent on model arguments.
When provided a `*model_args, **model_kwargs`, they return
`potential_fn` and `constraints_fn` callables, respectively.
:param tuple model_args: args provided to the model.
:param dict model_kwargs: kwargs provided to the model.
:return: a namedtupe `ModelInfo` which contains the fields
(`param_info`, `potential_fn`, `postprocess_fn`, `model_trace`), where
`param_info` is a namedtuple `ParamInfo` containing values from the prior
used to initiate MCMC, their corresponding potential energy, and their gradients;
`postprocess_fn` is a callable that uses inverse transforms
to convert unconstrained HMC samples to constrained values that
lie within the site's support, in addition to returning values
at `deterministic` sites in the model.
"""
model_kwargs = {} if model_kwargs is None else model_kwargs
substituted_model = substitute(seed(
model, rng_key if jnp.ndim(rng_key) == 1 else rng_key[0]),
substitute_fn=init_strategy)
inv_transforms, replay_model, model_trace = _get_model_transforms(
substituted_model, model_args, model_kwargs)
constrained_values = {
k: v['value']
for k, v in model_trace.items() if v['type'] == 'sample'
and not v['is_observed'] and not v['fn'].is_discrete
}
potential_fn, postprocess_fn = get_potential_fn(model,
inv_transforms,
replay_model=replay_model,
dynamic_args=dynamic_args,
model_args=model_args,
model_kwargs=model_kwargs)
init_strategy = init_strategy if isinstance(init_strategy,
partial) else init_strategy()
if init_strategy.func is init_to_value:
init_values = init_strategy.keywords.get("values")
unconstrained_values = transform_fn(inv_transforms,
init_values,
invert=True)
init_strategy = _init_to_unconstrained_value(
values=unconstrained_values)
prototype_params = transform_fn(inv_transforms,
constrained_values,
invert=True)
(init_params, pe, grad), is_valid = find_valid_initial_params(
rng_key,
model,
init_strategy=init_strategy,
model_args=model_args,
model_kwargs=model_kwargs,
prototype_params=prototype_params)
if not_jax_tracer(is_valid):
if device_get(~jnp.all(is_valid)):
raise RuntimeError(
"Cannot find valid initial parameters. Please check your model again."
)
return ModelInfo(ParamInfo(init_params, pe, grad), potential_fn,
postprocess_fn, model_trace)
def prod(self, value, axis=None):
if not isinstance(value, jnp.ndarray):
value = jnp.array(value)
if value.dtype == bool:
return jnp.all(value, axis=axis)
return jnp.prod(value, axis=axis)
def optimize(self, p0, num_iters, metric, step_size, tolerance, verbose,
return_model):
'''Workhorse of optimization.
p0: dict
A dictionary of the initial model parameters to be optimized.
num_iters: int
Maximum number of iteration.
metric: str
Method of model evaluation. Can be
`mse`, `corrcoeff`, `r2`
step_size: float or jax scheduler
Learning rate.
tolerance: int
Tolerance for early stop. If the training cost doesn't change more than 1e-5
in the last (tolerance) steps, or the dev cost monotonically increase, stop.
verbose: int
Print progress. If verbose=0, no progress will be print.
return_model: str
Return the 'best' model on dev set metrics or the 'last' model.
'''
@jit
def step(i, opt_state):
p = get_params(opt_state)
l, g = value_and_grad(self.cost)(p)
return l, opt_update(i, g, opt_state)
opt_init, opt_update, get_params = optimizers.adam(step_size=step_size)
opt_state = opt_init(p0)
cost_train = [0] * num_iters
cost_dev = [0] * num_iters
metric_train = [0] * num_iters
metric_dev = [0] * num_iters
params_list = [0] * num_iters
if verbose:
if 'dev' not in self.y:
if metric is None:
print('{0}\t{1:>10}\t{2:>10}'.format(
'Iters', 'Time (s)', 'Cost (train)'))
else:
print('{0}\t{1:>10}\t{2:>10}\t{3:>10}'.format(
'Iters', 'Time (s)', 'Cost (train)',
f'{metric} (train)'))
else:
if metric is None:
print('{0}\t{1:>10}\t{2:>10}\t{3:>10}'.format(
'Iters', 'Time (s)', 'Cost (train)', 'Cost (dev)'))
else:
print('{0}\t{1:>10}\t{2:>10}\t{3:>10}\t{4:>10}\t{5:>10}'.
format('Iters', 'Time (s)', 'Cost (train)',
'Cost (dev)', f'{metric} (train)',
f'{metric} (dev)'))
time_start = time.time()
for i in range(num_iters):
cost_train[i], opt_state = step(i, opt_state)
params_list[i] = get_params(opt_state)
y_pred_train = self.forwardpass(p=params_list[i], kind='train')
metric_train[i] = self._score(self.y['train'], y_pred_train,
metric)
if 'dev' in self.y:
y_pred_dev = self.forwardpass(p=params_list[i], kind='dev')
cost_dev[i] = self.cost(p=params_list[i],
kind='dev',
precomputed=y_pred_dev,
penalize=False)
metric_dev[i] = self._score(self.y['dev'], y_pred_dev, metric)
time_elapsed = time.time() - time_start
if verbose:
if i % int(verbose) == 0:
if 'dev' not in self.y:
if metric is None:
print('{0:>5}\t{1:>10.3f}\t{2:>10.3f}'.format(
i, time_elapsed, cost_train[i]))
else:
print('{0:>5}\t{1:>10.3f}\t{2:>10.3f}\t{3:>10.3f}'.
format(i, time_elapsed, cost_train[i],
metric_train[i]))
else:
if metric is None:
print('{0:>5}\t{1:>10.3f}\t{2:>10.3f}\t{3:>10.3f}'.
format(i, time_elapsed, cost_train[i],
cost_dev[i]))
else:
print(
'{0:>5}\t{1:>10.3f}\t{2:>10.3f}\t{3:>10.3f}\t{4:>10.3f}\t{5:>10.3f}'
.format(i, time_elapsed, cost_train[i],
cost_dev[i], metric_train[i],
metric_dev[i]))
if tolerance and i > 300: # tolerance = 0: no early stop.
total_time_elapsed = time.time() - time_start
cost_train_slice = np.array(cost_train[i - tolerance:i])
cost_dev_slice = np.array(cost_dev[i - tolerance:i])
if 'dev' in self.y and np.all(
cost_dev_slice[1:] - cost_dev_slice[:-1] > 0):
if verbose:
print(
'Stop at {0} steps: cost (dev) has been monotonically increasing for {1} steps.'
.format(i, tolerance))
print('Total time elapsed: {0:.3f}s.\n'.format(
total_time_elapsed))
stop = 'dev_stop'
break
if np.all(cost_train_slice[:-1] - cost_train_slice[1:] < 1e-5):
if verbose:
print(
'Stop at {0} steps: cost (train) has been changing less than 1e-5 for {1} steps.'
.format(i, tolerance))
print('Total time elapsed: {0:.3f}s.\n'.format(
total_time_elapsed))
stop = 'train_stop'
break
else:
total_time_elapsed = time.time() - time_start
stop = 'maxiter_stop'
if verbose:
print('Stop: reached {0} steps.'.format(num_iters))
print('Total time elapsed: {0:.3f}s.\n'.format(
total_time_elapsed))
if return_model == 'best_dev_cost':
best = np.argmin(np.asarray(cost_dev[:i + 1]))
elif return_model == 'best_train_cost':
best = np.argmin(np.asarray(cost_train[:i + 1]))
elif return_model == 'best_dev_metric':
if metric in ['mse', 'gcv']:
best = np.argmin(np.asarray(metric_dev[:i + 1]))
else:
best = np.argmax(np.asarray(metric_dev[:i + 1]))
elif return_model == 'best_train_metric':
if metric in ['mse', 'gcv']:
best = np.argmin(np.asarray(metric_train[:i + 1]))
else:
best = np.argmax(np.asarray(metric_train[:i + 1]))
elif return_model == 'last':
if stop == 'dev_stop':
best = i - tolerance
else:
best = i
else:
print(
'Provided `return_model` is not supported. Fell back to `best_dev_cost`'
)
best = np.argmin(np.asarray(cost_dev[:i + 1]))
params = params_list[best]
metric_dev_opt = metric_dev[best]
self.cost_train = np.hstack(cost_train[:i + 1])
self.cost_dev = np.hstack(cost_dev[:i + 1])
self.metric_train = np.hstack(metric_train[:i + 1])
self.metric_dev = np.hstack(metric_dev[:i + 1])
self.metric_dev_opt = metric_dev_opt
self.total_time_elapsed = total_time_elapsed
self.all_params = params_list[:i +
1] # not sure if this will occupy a lot of RAM.
self.y_pred['opt'].update({'train': y_pred_train})
if 'dev' in self.y:
self.y_pred['opt'].update({'dev': y_pred_dev})
return params
def _check_synced(pytree): mins = jax.lax.pmin(pytree, axis_name='batch') equals = jax.tree_multimap(jnp.array_equal, pytree, mins) return jnp.all(jnp.asarray(jax.tree_leaves(equals)))
def cond_fn(*args):
""" check if all are done or reached max number of iterations """
i, _, done, _, _ = args[0]
return jnp.bitwise_and(i < 100, jnp.logical_not(jnp.all(done)))
def body(carry, x):
checkify.check(jnp.all(x > 0), "should be positive")
return carry, x
def evaluate_batch(params, data):
logits = model.apply(params, data.predicates)
correct = jnp.all(data.targets == jnp.argmax(logits, axis=-1), axis=-1)
ce_loss = jnp.sum(cross_entropy(data.targets, logits), axis=-1)
return correct, ce_loss
def same(list1, list2):
allclose = functools.partial(lnp.allclose, atol=1e-3, rtol=1e-3)
elements_close = list(map(allclose, list1, list2))
return lnp.all(lnp.array(elements_close))
def interaction(q, d_qtm_nk1, d_qtm_nk2):
q_norm = jnp.linalg.norm(q @ bvec)
flag = jnp.all(d_qtm_nk1==d_qtm_nk2)
res = jnp.where(q_norm == 0., 0., jnp.where(flag, Uvalue * qM / jnp.sqrt(q_norm ** 2 + Kappa ** 2), Jvalue))
return res/num_k1**2
def body_fn(state):
i, key, _, _ = state
key, subkey = random.split(key)
if radius is None or prototype_params is None:
# XXX: we don't want to apply enum to draw latent samples
model_ = model
if enum:
from numpyro.contrib.funsor import enum as enum_handler
if isinstance(model, substitute) and isinstance(
model.fn, enum_handler):
model_ = substitute(model.fn.fn, data=model.data)
elif isinstance(model, enum_handler):
model_ = model.fn
# Wrap model in a `substitute` handler to initialize from `init_loc_fn`.
seeded_model = substitute(seed(model_, subkey),
substitute_fn=init_strategy)
model_trace = trace(seeded_model).get_trace(
*model_args, **model_kwargs)
constrained_values, inv_transforms = {}, {}
for k, v in model_trace.items():
if (v["type"] == "sample" and not v["is_observed"]
and not v["fn"].support.is_discrete):
constrained_values[k] = v["value"]
with helpful_support_errors(v):
inv_transforms[k] = biject_to(v["fn"].support)
params = transform_fn(
inv_transforms,
{k: v
for k, v in constrained_values.items()},
invert=True,
)
else: # this branch doesn't require tracing the model
params = {}
for k, v in prototype_params.items():
if k in init_values:
params[k] = init_values[k]
else:
params[k] = random.uniform(subkey,
jnp.shape(v),
minval=-radius,
maxval=radius)
key, subkey = random.split(key)
potential_fn = partial(potential_energy,
model,
model_args,
model_kwargs,
enum=enum)
if validate_grad:
if forward_mode_differentiation:
pe = potential_fn(params)
z_grad = jacfwd(potential_fn)(params)
else:
pe, z_grad = value_and_grad(potential_fn)(params)
z_grad_flat = ravel_pytree(z_grad)[0]
is_valid = jnp.isfinite(pe) & jnp.all(jnp.isfinite(z_grad_flat))
else:
pe = potential_fn(params)
is_valid = jnp.isfinite(pe)
z_grad = None
return i + 1, key, (params, pe, z_grad), is_valid
ReturnType = named_tuple_factory(name, get)
if isinstance(out, types.GeneratorType):
return (ReturnType(*tuple(output[g] for g in get))
for output in out)
else:
return ReturnType(*tuple(out[g] for g in get))
return canonicalize_output(fn_out)
return getter_fn
return getter_decorator
@nt_tree_fn(nargs=2, reduce=lambda x: np.all(np.array(x)))
def x1_is_x2(x1: np.ndarray,
x2: Optional[np.ndarray] = None,
eps: float = 1e-12) -> Union[bool, np.ndarray]:
if not isinstance(x1, (onp.ndarray, np.ndarray)):
raise TypeError('`x1` must be an ndarray. A {} is found.'.format(
type(x1)))
if x2 is None:
return True
if x1 is x2:
return True
if x1.shape != x2.shape:
return False
