def _scipy_objective_and_grad(
x: np.ndarray, mll: MarginalLogLikelihood, property_dict: Dict[str, TorchAttr]
) -> Tuple[float, np.ndarray]:
r"""Get objective and gradient in format that scipy expects.
Args:
x: The (flattened) input parameters.
mll: The MarginalLogLikelihood module to evaluate.
property_dict: The property dictionary required to "unflatten" the input
parameter vector, as generated by `module_to_array`.
Returns:
2-element tuple containing
- The objective value.
- The gradient of the objective.
"""
mll = set_params_with_array(mll, x, property_dict)
train_inputs, train_targets = mll.model.train_inputs, mll.model.train_targets
mll.zero_grad()
output = mll.model(*train_inputs)
args = [output, train_targets] + _get_extra_mll_args(mll)
loss = -mll(*args).sum()
loss.backward()
param_dict = OrderedDict(mll.named_parameters())
grad = []
for p_name in property_dict:
t = param_dict[p_name].grad
if t is None:
# this deals with parameters that do not affect the loss
grad.append(np.zeros(property_dict[p_name].shape.numel()))
else:
grad.append(t.detach().view(-1).cpu().double().clone().numpy())
mll.zero_grad()
return loss.item(), np.concatenate(grad)
def _scipy_objective_and_grad(
x: np.ndarray, mll: MarginalLogLikelihood,
property_dict: Dict[str, TorchAttr]) -> Tuple[float, np.ndarray]:
r"""Get objective and gradient in format that scipy expects.
Args:
x: The (flattened) input parameters.
mll: The MarginalLogLikelihood module to evaluate.
property_dict: The property dictionary required to "unflatten" the input
parameter vector, as generated by `module_to_array`.
Returns:
2-element tuple containing
- The objective value.
- The gradient of the objective.
"""
mll = set_params_with_array(mll, x, property_dict)
train_inputs, train_targets = mll.model.train_inputs, mll.model.train_targets
mll.zero_grad()
output = mll.model(*train_inputs)
args = [output, train_targets] + _get_extra_mll_args(mll)
loss = -mll(*args).sum()
loss.backward()
param_dict = OrderedDict(mll.named_parameters())
grad = []
for p_name in property_dict:
t = param_dict[p_name].grad
if t is None:
# this deals with parameters that do not affect the loss
grad.append(np.zeros(property_dict[p_name].shape.numel()))
else:
grad.append(t.detach().view(-1).cpu().double().clone().numpy())
mll.zero_grad()
return loss.item(), np.concatenate(grad)
def fit_gpytorch_torch(
mll: MarginalLogLikelihood,
bounds: Optional[ParameterBounds] = None,
optimizer_cls: Optimizer = Adam,
options: Optional[Dict[str, Any]] = None,
track_iterations: bool = True,
approx_mll: bool = True,
) -> Tuple[MarginalLogLikelihood, Dict[str, Union[float, List[OptimizationIteration]]]]:
r"""Fit a gpytorch model by maximizing MLL with a torch optimizer.
The model and likelihood in mll must already be in train mode.
Note: this method requires that the model has `train_inputs` and `train_targets`.
Args:
mll: MarginalLogLikelihood to be maximized.
bounds: A ParameterBounds dictionary mapping parameter names to tuples
of lower and upper bounds. Bounds specified here take precedence
over bounds on the same parameters specified in the constraints
registered with the module.
optimizer_cls: Torch optimizer to use. Must not require a closure.
options: options for model fitting. Relevant options will be passed to
the `optimizer_cls`. Additionally, options can include: "disp"
to specify whether to display model fitting diagnostics and "maxiter"
to specify the maximum number of iterations.
track_iterations: Track the function values and wall time for each
iteration.
approx_mll: If True, use gpytorch's approximate MLL computation (
according to the gpytorch defaults based on the training at size).
Unlike for the deterministic algorithms used in fit_gpytorch_scipy,
this is not an issue for stochastic optimizers.
Returns:
2-element tuple containing
- mll with parameters optimized in-place.
- Dictionary with the following key/values:
"fopt": Best mll value.
"wall_time": Wall time of fitting.
"iterations": List of OptimizationIteration objects with information on each
iteration. If track_iterations is False, will be empty.
Example:
>>> gp = SingleTaskGP(train_X, train_Y)
>>> mll = ExactMarginalLogLikelihood(gp.likelihood, gp)
>>> mll.train()
>>> fit_gpytorch_torch(mll)
>>> mll.eval()
"""
optim_options = {"maxiter": 100, "disp": True, "lr": 0.05}
optim_options.update(options or {})
exclude = optim_options.pop("exclude", None)
if exclude is not None:
mll_params = [
t for p_name, t in mll.named_parameters() if p_name not in exclude
]
else:
mll_params = list(mll.parameters())
optimizer = optimizer_cls(
params=[{"params": mll_params}],
**_filter_kwargs(optimizer_cls, **optim_options),
)
# get bounds specified in model (if any)
bounds_: ParameterBounds = {}
if hasattr(mll, "named_parameters_and_constraints"):
for param_name, _, constraint in mll.named_parameters_and_constraints():
if constraint is not None and not constraint.enforced:
bounds_[param_name] = constraint.lower_bound, constraint.upper_bound
# update with user-supplied bounds (overwrites if already exists)
if bounds is not None:
bounds_.update(bounds)
iterations = []
t1 = time.time()
param_trajectory: Dict[str, List[Tensor]] = {
name: [] for name, param in mll.named_parameters()
}
loss_trajectory: List[float] = []
i = 0
converged = False
convergence_criterion = ConvergenceCriterion(
**_filter_kwargs(ConvergenceCriterion, **optim_options)
)
train_inputs, train_targets = mll.model.train_inputs, mll.model.train_targets
while not converged:
optimizer.zero_grad()
with gpt_settings.fast_computations(log_prob=approx_mll):
output = mll.model(*train_inputs)
# we sum here to support batch mode
args = [output, train_targets] + _get_extra_mll_args(mll)
loss = -mll(*args).sum()
loss.backward()
loss_trajectory.append(loss.item())
for name, param in mll.named_parameters():
param_trajectory[name].append(param.detach().clone())
if optim_options["disp"] and (
(i + 1) % 10 == 0 or i == (optim_options["maxiter"] - 1)
):
print(f"Iter {i + 1}/{optim_options['maxiter']}: {loss.item()}")
if track_iterations:
iterations.append(OptimizationIteration(i, loss.item(), time.time() - t1))
optimizer.step()
# project onto bounds:
if bounds_:
for pname, param in mll.named_parameters():
if pname in bounds_:
param.data = param.data.clamp(*bounds_[pname])
i += 1
converged = convergence_criterion.evaluate(fvals=loss.detach())
info_dict = {
"fopt": loss_trajectory[-1],
"wall_time": time.time() - t1,
"iterations": iterations,
}
return mll, info_dict
def fit_gpytorch_torch(
mll: MarginalLogLikelihood,
bounds: Optional[ParameterBounds] = None,
optimizer_cls: Optimizer = Adam,
options: Optional[Dict[str, Any]] = None,
track_iterations: bool = True,
) -> Tuple[MarginalLogLikelihood, List[OptimizationIteration]]:
r"""Fit a gpytorch model by maximizing MLL with a torch optimizer.
The model and likelihood in mll must already be in train mode.
Note: this method requires that the model has `train_inputs` and `train_targets`.
Args:
mll: MarginalLogLikelihood to be maximized.
bounds: A ParameterBounds dictionary mapping parameter names to tuples
of lower and upper bounds. Bounds specified here take precedence
over bounds on the same parameters specified in the constraints
registered with the module.
optimizer_cls: Torch optimizer to use. Must not require a closure.
options: options for model fitting. Relevant options will be passed to
the `optimizer_cls`. Additionally, options can include: "disp"
to specify whether to display model fitting diagnostics and "maxiter"
to specify the maximum number of iterations.
track_iterations: Track the function values and wall time for each
iteration.
Returns:
2-element tuple containing
- mll with parameters optimized in-place.
- List of OptimizationIteration objects with information on each
iteration. If track_iterations is False, this will be an empty list.
Example:
>>> gp = SingleTaskGP(train_X, train_Y)
>>> mll = ExactMarginalLogLikelihood(gp.likelihood, gp)
>>> mll.train()
>>> fit_gpytorch_torch(mll)
>>> mll.eval()
"""
optim_options = {"maxiter": 100, "disp": True, "lr": 0.05}
optim_options.update(options or {})
optimizer = optimizer_cls(
params=[{"params": mll.parameters()}],
**_filter_kwargs(optimizer_cls, **optim_options),
)
# get bounds specified in model (if any)
bounds_: ParameterBounds = {}
if hasattr(mll, "named_parameters_and_constraints"):
for param_name, _, constraint in mll.named_parameters_and_constraints():
if constraint is not None and not constraint.enforced:
bounds_[param_name] = constraint.lower_bound, constraint.upper_bound
# update with user-supplied bounds (overwrites if already exists)
if bounds is not None:
bounds_.update(bounds)
iterations = []
t1 = time.time()
param_trajectory: Dict[str, List[Tensor]] = {
name: [] for name, param in mll.named_parameters()
}
loss_trajectory: List[float] = []
i = 0
converged = False
train_inputs, train_targets = mll.model.train_inputs, mll.model.train_targets
while not converged:
optimizer.zero_grad()
output = mll.model(*train_inputs)
# we sum here to support batch mode
args = [output, train_targets] + _get_extra_mll_args(mll)
loss = -mll(*args).sum()
loss.backward()
loss_trajectory.append(loss.item())
for name, param in mll.named_parameters():
param_trajectory[name].append(param.detach().clone())
if optim_options["disp"] and (
(i + 1) % 10 == 0 or i == (optim_options["maxiter"] - 1)
):
print(f"Iter {i + 1}/{optim_options['maxiter']}: {loss.item()}")
if track_iterations:
iterations.append(OptimizationIteration(i, loss.item(), time.time() - t1))
optimizer.step()
# project onto bounds:
if bounds_:
for pname, param in mll.named_parameters():
if pname in bounds_:
param.data = param.data.clamp(*bounds_[pname])
i += 1
converged = check_convergence(
loss_trajectory=loss_trajectory,
param_trajectory=param_trajectory,
options={"maxiter": optim_options["maxiter"]},
)
return mll, iterations
def fit_gpytorch_torch(
mll: MarginalLogLikelihood,
bounds: Optional[ParameterBounds] = None,
optimizer_cls: Optimizer = Adam,
options: Optional[Dict[str, Any]] = None,
track_iterations: bool = True,
) -> Tuple[MarginalLogLikelihood, List[OptimizationIteration]]:
r"""Fit a gpytorch model by maximizing MLL with a torch optimizer.
The model and likelihood in mll must already be in train mode.
Note: this method requires that the model has `train_inputs` and `train_targets`.
Args:
mll: MarginalLogLikelihood to be maximized.
bounds: A ParameterBounds dictionary mapping parameter names to tuples
of lower and upper bounds. Bounds specified here take precedence
over bounds on the same parameters specified in the constraints
registered with the module.
optimizer_cls: Torch optimizer to use. Must not require a closure.
options: options for model fitting. Relevant options will be passed to
the `optimizer_cls`. Additionally, options can include: "disp"
to specify whether to display model fitting diagnostics and "maxiter"
to specify the maximum number of iterations.
track_iterations: Track the function values and wall time for each
iteration.
Returns:
2-element tuple containing
- mll with parameters optimized in-place.
- List of OptimizationIteration objects with information on each
iteration. If track_iterations is False, this will be an empty list.
Example:
>>> gp = SingleTaskGP(train_X, train_Y)
>>> mll = ExactMarginalLogLikelihood(gp.likelihood, gp)
>>> mll.train()
>>> fit_gpytorch_torch(mll)
>>> mll.eval()
"""
optim_options = {"maxiter": 100, "disp": True, "lr": 0.05}
optim_options.update(options or {})
optimizer = optimizer_cls(
params=[{
"params": mll.parameters()
}],
**_filter_kwargs(optimizer_cls, **optim_options),
)
# get bounds specified in model (if any)
bounds_: ParameterBounds = {}
if hasattr(mll, "named_parameters_and_constraints"):
for param_name, _, constraint in mll.named_parameters_and_constraints(
):
if constraint is not None and not constraint.enforced:
bounds_[
param_name] = constraint.lower_bound, constraint.upper_bound
# update with user-supplied bounds (overwrites if already exists)
if bounds is not None:
bounds_.update(bounds)
iterations = []
t1 = time.time()
param_trajectory: Dict[str, List[Tensor]] = {
name: []
for name, param in mll.named_parameters()
}
loss_trajectory: List[float] = []
i = 0
converged = False
train_inputs, train_targets = mll.model.train_inputs, mll.model.train_targets
while not converged:
optimizer.zero_grad()
output = mll.model(*train_inputs)
# we sum here to support batch mode
args = [output, train_targets] + _get_extra_mll_args(mll)
loss = -mll(*args).sum()
loss.backward()
loss_trajectory.append(loss.item())
for name, param in mll.named_parameters():
param_trajectory[name].append(param.detach().clone())
if optim_options["disp"] and ((i + 1) % 10 == 0
or i == (optim_options["maxiter"] - 1)):
print(f"Iter {i + 1}/{optim_options['maxiter']}: {loss.item()}")
if track_iterations:
iterations.append(
OptimizationIteration(i, loss.item(),
time.time() - t1))
optimizer.step()
# project onto bounds:
if bounds_:
for pname, param in mll.named_parameters():
if pname in bounds_:
param.data = param.data.clamp(*bounds_[pname])
i += 1
converged = check_convergence(
loss_trajectory=loss_trajectory,
param_trajectory=param_trajectory,
options={"maxiter": optim_options["maxiter"]},
)
return mll, iterations
def fit_gpytorch_manifold(
mll: MarginalLogLikelihood,
bounds: Optional[ParameterBounds] = None,
solver: Solver = pyman_solvers.ConjugateGradient(maxiter=500),
nb_init_candidates: int = 200,
last_x_as_candidate_prob: float = 0.9,
options: Optional[Dict[str, Any]] = None,
track_iterations: bool = True,
approx_mll: bool = False,
module_to_array_func: TModToArray = module_to_list_of_array,
module_from_array_func: TArrayToMod = set_params_with_list_of_array,
) -> Tuple[MarginalLogLikelihood, Dict[str, Union[
float, List[OptimizationIteration]]]]:
"""
This function fits a gpytorch model by maximizing MLL with a pymanopt optimizer.
The model and likelihood in mll must already be in train mode.
This method requires that the model has `train_inputs` and `train_targets`.
Parameters
----------
:param mll: MarginalLogLikelihood to be maximized.
Optional parameters
-------------------
:param nb_init_candidates: number of random initial candidates for the GP parameters
:param last_x_as_candidate_prob: probability that the last set of parameter is among the initial candidates
:param bounds: A dictionary mapping parameter names to tuples of lower and upper bounds.
:param solver: Pymanopt solver.
:param options: Dictionary of solver options, passed along to scipy.minimize.
:param track_iterations: Track the function values and wall time for each iteration.
:param approx_mll: If True, use gpytorch's approximate MLL computation. This is disabled by default since the
stochasticity is an issue for determistic optimizers). Enabling this is only recommended when working with
large training data sets (n>2000).
Returns
-------
:return: 2-element tuple containing
- MarginalLogLikelihood with parameters optimized in-place.
- Dictionary with the following key/values:
"fopt": Best mll value.
"wall_time": Wall time of fitting.
"iterations": List of OptimizationIteration objects with information on each iteration.
If track_iterations is False, will be empty.
Example:
gp = SingleTaskGP(train_X, train_Y)
mll = ExactMarginalLogLikelihood(gp.likelihood, gp)
mll.train()
fit_gpytorch_scipy(mll)
mll.eval()
"""
options = options or {}
# Current parameters
x0, property_dict, bounds = module_to_array_func(module=mll,
bounds=bounds,
exclude=options.pop(
"exclude", None))
x0 = [x0i.astype(np.float64) for x0i in x0]
if bounds is not None:
warnings.warn(
'Bounds handling not supported yet in fit_gpytorch_manifold')
# bounds = Bounds(lb=bounds[0], ub=bounds[1], keep_feasible=True)
t1 = time.time()
# Define cost function
def cost(x):
param_dict = OrderedDict(mll.named_parameters())
idx = 0
for p_name, attrs in property_dict.items():
# Construct the new tensor
if len(attrs.shape) == 0: # deal with scalar tensors
# new_data = torch.tensor(x[0], dtype=attrs.dtype, device=attrs.device)
new_data = torch.tensor(x[idx][0],
dtype=attrs.dtype,
device=attrs.device)
else:
# new_data = torch.tensor(x, dtype=attrs.dtype, device=attrs.device).view(*attrs.shape)
new_data = torch.tensor(x[idx],
dtype=attrs.dtype,
device=attrs.device).view(*attrs.shape)
param_dict[p_name].data = new_data
idx += 1
# mllx = set_params_with_array(mll, x, property_dict)
train_inputs, train_targets = mll.model.train_inputs, mll.model.train_targets
mll.zero_grad()
output = mll.model(*train_inputs)
args = [output, train_targets] + _get_extra_mll_args(mll)
loss = -mll(*args).sum()
return loss
def egrad(x):
loss = cost(x)
loss.backward()
param_dict = OrderedDict(mll.named_parameters())
grad = []
for p_name in property_dict:
t = param_dict[p_name].grad
if t is None:
# this deals with parameters that do not affect the loss
if len(property_dict[p_name].shape
) > 1 and property_dict[p_name].shape[0] > 1:
# if the variable is a matrix, keep its shape
grad.append(np.zeros(property_dict[p_name].shape))
else:
grad.append(np.zeros(property_dict[p_name].shape))
else:
if t.ndim > 1 and t.shape[
0] > 1: # if the variable is a matrix, keep its shape
grad.append(t.detach().cpu().double().clone().numpy())
else: # Vector case
grad.append(
t.detach().view(-1).cpu().double().clone().numpy())
return grad
# Define the manifold (product of manifolds)
manifolds_list = []
for p_name, t in mll.named_parameters():
try:
# If a manifold is given add it
manifolds_list.append(attrgetter(p_name + "_manifold")(mll))
except AttributeError:
# Otherwise, default: Euclidean
manifolds_list.append(
Euclidean(int(np.prod(property_dict[p_name].shape))))
# Product of manifolds
manifold = Product(manifolds_list)
# Instanciate the problem on the manifold
if track_iterations:
verbosity = 2
else:
verbosity = 0
problem = Problem(manifold=manifold,
cost=cost,
egrad=egrad,
verbosity=verbosity,
arg=torch.Tensor()) #, precon=precon)
# For cases where the Hessian is hard/long to compute, we approximate it with finite differences of the gradient.
# Typical cases: the Hessian can be hard to compute due to the 2nd derivative of the eigenvalue decomposition,
# e.g. in the SPD affine-invariant distance.
problem._hess = types.MethodType(get_hessianfd, problem)
# Choose initial parameters
# Do not always consider x0, to encourage variations of the parameters.
if np.random.rand() < last_x_as_candidate_prob:
x0_candidates = [x0]
x0_candidates += [
manifold.rand() for i in range(nb_init_candidates - 1)
]
else:
x0_candidates = []
x0_candidates += [manifold.rand() for i in range(nb_init_candidates)]
for i in range(int(3 * nb_init_candidates / 4)):
x0_candidates[i][0:4] = x0[0:4] #TODO remove hard-coding
y0_candidates = [cost(x0_candidates[i]) for i in range(nb_init_candidates)]
y_init, x_init_idx = torch.Tensor(y0_candidates).min(0)
x_init = x0_candidates[x_init_idx]
with gpt_settings.fast_computations(log_prob=approx_mll):
# Logverbosity of the solver to 1
solver._logverbosity = 1
# Solve
opt_x, opt_log = solver.solve(problem, x=x_init)
# Construct info dict
info_dict = {
"fopt": float(cost(opt_x).detach().numpy()),
"wall_time": time.time() - t1,
"opt_log": opt_log,
}
# if not res.success: # TODO update
# try:
# # Some res.message are bytes
# msg = res.message.decode("ascii")
# except AttributeError:
# # Others are str
# msg = res.message
# warnings.warn(
# f"Fitting failed with the optimizer reporting '{msg}'", OptimizationWarning
# )
# Set to optimum
mll = module_from_array_func(mll, opt_x, property_dict)
return mll, info_dict