def get_internal_first_derivative(
func, params, constraints=None, func_kwargs=None, numdiff_options=None
):
"""Get the first_derivative of func with respect to internal parameters.
If there are no constraints, we simply call the first_derivative function.
Args:
func (callable): Function to take the derivative of.
params (pandas.DataFrame): Data frame with external parameters. See
:ref:`params`.
constraints (list): Constraints that define how to convert between internal
and external parameters.
func_kwargs (dict): Additional keyword arguments for func.
numdiff_options (dict): Additional options for first_derivative.
Returns:
dict: See ``first_derivative`` for details. The only difference is that the
the "derivative" entry is always a numpy array instead of a DataFrame
"""
numdiff_options = {} if numdiff_options is None else numdiff_options
func_kwargs = {} if func_kwargs is None else func_kwargs
_func = functools.partial(func, **func_kwargs)
if constraints is None:
out = first_derivative(
func=_func,
params=params,
**numdiff_options,
)
out["has_transforming_constraints"] = False
else:
lower_bounds, upper_bounds = get_internal_bounds(params, constraints)
_internal_func = numpy_interface(
func=_func, params=params, constraints=constraints
)
_to_internal, _ = get_reparametrize_functions(params, constraints)
_x = _to_internal(params)
out = first_derivative(
_internal_func,
_x,
lower_bounds=lower_bounds,
upper_bounds=upper_bounds,
**numdiff_options,
)
if isinstance(out["derivative"], (pd.DataFrame, pd.Series)):
out["derivative"] = out["derivative"].to_numpy()
return out
def _compute_testable_estimagic_and_jax_derivatives(func,
params,
func_jax=None):
"""
Computes first and second derivative using estimagic and jax. Then converts leaves
of jax output to numpy so that we can use numpy.testing. For higher dimensional
output we need to define two function, one with numpy array output and one with
jax.numpy array output.
"""
func_jax = func if func_jax is None else func_jax
estimagic_jac = first_derivative(func, params)["derivative"]
jax_jac = jax.jacobian(func_jax)(params)
estimagic_hess = second_derivative(func, params)["derivative"]
jax_hess = jax.hessian(func_jax)(params)
out = {
"jac": {
"estimagic": estimagic_jac,
"jax": jax_jac
},
"hess": {
"estimagic": estimagic_hess,
"jax": jax_hess
},
}
return out
def test_first_derivative_scalar(method):
def f(x):
return x ** 2
calculated = first_derivative(f, 3.0, n_cores=1)
expected = 6.0
assert calculated == expected
def test_first_derivative_scalar_with_return_func_value(method):
def f(x):
return x ** 2
calculated = first_derivative(f, 3.0, return_func_value=True, n_cores=1)
expected = (6.0, 9.0)
assert calculated == expected
def statsmodels_fixture():
"""These fixtures are taken from the statsmodels test battery and adapted towards
a random test."""
fix = {}
num_obs = 100
num_params = 3
max_range = 10
x = np.linspace(0, max_range, num_obs)
x = sm.add_constant(np.column_stack((x, x**2)), prepend=False)
beta = np.random.rand(num_params) * max_range
y = np.dot(x, beta) + np.random.normal(size=num_obs)
results = sm.OLS(y, x).fit()
fix["stats_cov"] = results.cov_HC0
params_df = pd.DataFrame({"value": results.params})
moment_cond = np.zeros((num_obs, num_params))
moment_jac = np.zeros((num_obs, num_params, num_params))
for i in range(num_obs):
moment_cond[i, :] = calc_moment_condition(params_df, x[i, :], y[i])
moment_jac[i, :, :] = first_derivative(calc_moment_condition,
params_df,
func_kwargs={
"x_t": x[i, :],
"y_t": y[i]
})
fix["mom_cond"] = moment_cond
fix["mom_cond_jacob"] = moment_jac
fix["weighting_matrix"] = np.eye(num_params)
return fix
def flexible_sos_ls_derivative(params):
deriv_dict = first_derivative(
flexible_sos_ls,
params,
key="root_contributions",
)
return deriv_dict["derivative"]
def test_first_derivative_jacobian_works_at_defaults(binary_choice_inputs):
fix = binary_choice_inputs
func = partial(logit_loglikeobs, y=fix["y"], x=fix["x"])
calculated = first_derivative(func=func,
params=fix["params_np"],
n_cores=1)
expected = logit_loglikeobs_jacobian(fix["params_np"], fix["y"], fix["x"])
aaae(calculated["derivative"], expected, decimal=6)
def test_probability_to_internal_jacobian(dim, seed):
external = get_external_probability(dim)
func = partial(kt.probability_to_internal, **{"constr": None})
numerical_deriv = first_derivative(func, external)
deriv = kt.probability_to_internal_jacobian(external, None)
aaae(deriv, numerical_deriv, decimal=3)
def test_sdcorr_from_internal_jacobian(dim, seed):
internal = get_internal_cholesky(dim)
func = partial(kt.sdcorr_from_internal, **{"constr": None})
numerical_deriv = first_derivative(func, internal)
deriv = kt.sdcorr_from_internal_jacobian(internal, None)
aaae(deriv, numerical_deriv, decimal=3)
def test_covariance_to_internal_jacobian(dim, seed):
external = get_external_covariance(dim)
func = partial(kt.covariance_to_internal, **{"constr": None})
numerical_deriv = first_derivative(func, external)
deriv = kt.covariance_to_internal_jacobian(external, None)
aaae(deriv, numerical_deriv["derivative"], decimal=3)
def calculate_scaling_factor_and_offset(
params,
constraints,
criterion,
method="start_values",
clipping_value=0.1,
magnitude=1,
numdiff_options=None,
processed_params=None,
processed_constraints=None,
):
numdiff_options = {} if numdiff_options is None else numdiff_options
to_internal, from_internal = get_reparametrize_functions(
params=params,
constraints=constraints,
processed_params=processed_params,
processed_constraints=processed_constraints,
)
x = to_internal(params["value"].to_numpy())
if method in ("bounds", "gradient"):
lower_bounds, upper_bounds = get_internal_bounds(
params, constraints, processed_params=processed_params)
if method == "start_values":
raw_factor = np.clip(np.abs(x), clipping_value, np.inf)
scaling_offset = None
elif method == "bounds":
raw_factor = upper_bounds - lower_bounds
scaling_offset = lower_bounds
elif method == "gradient":
default_numdiff_options = {
"scaling_factor": 100,
"lower_bounds": lower_bounds,
"upper_bounds": upper_bounds,
"error_handling": "raise",
}
numdiff_options = {**default_numdiff_options, **numdiff_options}
def func(x):
p = params.copy(deep=True)
p["value"] = from_internal(x)
crit = criterion(p)
if isinstance(crit, dict):
crit = crit["value"]
return crit
gradient = first_derivative(func, x, **numdiff_options)["derivative"]
raw_factor = np.clip(np.abs(gradient), clipping_value, np.inf)
scaling_offset = None
scaling_factor = raw_factor / magnitude
return scaling_factor, scaling_offset
def jac(params, func_kwargs):
derivative_dict = first_derivative(
func=simulate_aggregated_moments,
params=params,
func_kwargs=func_kwargs,
)
g = derivative_dict["derivative"]
return g.to_numpy()
def test_first_derivative_jacobian_richardson(example_function_jacobian_fixtures):
f = example_function_jacobian_fixtures["func"]
fprime = example_function_jacobian_fixtures["func_prime"]
true_fprime = fprime(np.ones(3))
scipy_fprime = approx_derivative(f, np.ones(3))
our_fprime = first_derivative(f, np.ones(3), n_steps=3, method="central", n_cores=1)
aaae(scipy_fprime, our_fprime)
aaae(true_fprime, our_fprime)
def test_derivative_plot(func_and_params, n_steps):
func, params = func_and_params
derivative = first_derivative(
func,
params,
n_steps=n_steps,
return_func_value=True,
return_info=True,
)
fig = derivative_plot(derivative)
fig.clf()
def test_derivative_plot(func_and_params, n_steps, grid):
func, params = func_and_params
derivative = first_derivative(
func,
params,
n_steps=n_steps,
return_func_value=True,
return_info=True,
)
derivative_plot(derivative, combine_plots_in_grid=grid)
def test_first_derivative_scalar_with_return_func_value(method):
def f(x):
return x**2
calculated = first_derivative(f,
3.0,
return_func_value=True,
return_info=False,
n_cores=1)
expected = {"derivative": 6.0, "func_value": 9.0}
assert calculated == expected
def test_first_derivative_gradient(binary_choice_inputs, method):
fix = binary_choice_inputs
func = partial(logit_loglike, y=fix["y"], x=fix["x"])
calculated = first_derivative(
func=func,
method=method,
params=fix["params_np"],
n_steps=1,
f0=func(fix["params_np"]),
n_cores=1,
)
expected = logit_loglike_gradient(fix["params_np"], fix["y"], fix["x"])
aaae(calculated, expected, decimal=4)
def test_penalty_derivatives(func, deriv):
np.random.seed(1234)
x = np.random.uniform(size=5)
x0 = np.random.uniform(size=5)
slope = 0.3
constant = 3
dim_out = 8
calculated = deriv(x, constant, slope, x0, dim_out)
partialed = functools.partial(func,
constant=constant,
slope=slope,
x0=x0,
dim_out=dim_out)
expected = first_derivative(partialed, x)
aaae(calculated, expected["derivative"])
def test_first_derivative_jacobian(binary_choice_inputs, method):
fix = binary_choice_inputs
func = partial(logit_loglikeobs, y=fix["y"], x=fix["x"])
calculated = first_derivative(
func=func,
method=method,
params=fix["params_np"],
n_steps=1,
base_steps=None,
lower_bounds=np.full(fix["params_np"].shape, -np.inf),
upper_bounds=np.full(fix["params_np"].shape, np.inf),
min_steps=1e-8,
step_ratio=2.0,
f0=func(fix["params_np"]),
n_cores=1,
)
expected = logit_loglikeobs_jacobian(fix["params_np"], fix["y"], fix["x"])
aaae(calculated, expected, decimal=6)
def estimate_ml(
loglike,
params,
optimize_options,
*,
lower_bounds=None,
upper_bounds=None,
constraints=None,
logging=False,
log_options=None,
loglike_kwargs=None,
numdiff_options=None,
jacobian=None,
jacobian_kwargs=None,
hessian=None,
hessian_kwargs=None,
design_info=None,
):
"""Do a maximum likelihood (ml) estimation.
This is a high level interface of our lower level functions for maximization,
numerical differentiation and inference. It does the full workflow for maximum
likelihood estimation with just one function call.
While we have good defaults, you can still configure each aspect of each step
via the optional arguments of this function. If you find it easier to do the
maximization separately, you can do so and just provide the optimal parameters as
``params`` and set ``optimize_options=False``
Args:
loglike (callable): Likelihood function that takes a params (and potentially
other keyword arguments) and returns a dictionary that has at least the
entries "value" (a scalar float) and "contributions" (a 1d numpy array or
pytree) with the log likelihood contribution per individual.
params (pytree): A pytree containing the estimated or start parameters of the
likelihood model. If the supplied parameters are estimated parameters, set
optimize_options to False. Pytrees can be a numpy array, a pandas Series, a
DataFrame with "value" column, a float and any kind of (nested) dictionary
or list containing these elements. See :ref:`params` for examples.
optimize_options (dict, str or False): Keyword arguments that govern the
numerical optimization. Valid entries are all arguments of
:func:`~estimagic.optimization.optimize.minimize` except for those that are
passed explicilty to ``estimate_ml``. If you pass False as optimize_options
you signal that ``params`` are already the optimal parameters and no
numerical optimization is needed. If you pass a str as optimize_options it
is used as the ``algorithm`` option.
lower_bounds (pytree): A pytree with the same structure as params with lower
bounds for the parameters. Can be ``-np.inf`` for parameters with no lower
bound.
upper_bounds (pytree): As lower_bounds. Can be ``np.inf`` for parameters with
no upper bound.
constraints (list, dict): List with constraint dictionaries or single dict.
See :ref:`constraints`.
logging (pathlib.Path, str or False): Path to sqlite3 file (which typically has
the file extension ``.db``. If the file does not exist, it will be created.
The dashboard can only be used when logging is used.
log_options (dict): Additional keyword arguments to configure the logging.
- "fast_logging": A boolean that determines if "unsafe" settings are used
to speed up write processes to the database. This should only be used for
very short running criterion functions where the main purpose of the log
is a real-time dashboard and it would not be catastrophic to get a
corrupted database in case of a sudden system shutdown. If one evaluation
of the criterion function (and gradient if applicable) takes more than
100 ms, the logging overhead is negligible.
- "if_table_exists": (str) One of "extend", "replace", "raise". What to
do if the tables we want to write to already exist. Default "extend".
- "if_database_exists": (str): One of "extend", "replace", "raise". What to
do if the database we want to write to already exists. Default "extend".
loglike_kwargs (dict): Additional keyword arguments for loglike.
numdiff_options (dict): Keyword arguments for the calculation of numerical
derivatives for the calculation of standard errors. See
:ref:`first_derivative` for details.
jacobian (callable or None): A function that takes ``params`` and potentially
other keyword arguments and returns the jacobian of loglike["contributions"]
with respect to the params. Note that you only need to pass a Jacobian
function if you have a closed form Jacobian. If you pass None, a numerical
Jacobian will be calculated.
jacobian_kwargs (dict): Additional keyword arguments for the Jacobian function.
hessian (callable or None or False): A function that takes ``params`` and
potentially other keyword arguments and returns the Hessian of
loglike["value"] with respect to the params. If you pass None, a numerical
Hessian will be calculated. If you pass ``False``, you signal that no
Hessian should be calculated. Thus, no result that requires the Hessian will
be calculated.
hessian_kwargs (dict): Additional keyword arguments for the Hessian function.
design_info (pandas.DataFrame): DataFrame with one row per observation that
contains some or all of the variables "psu" (primary sampling unit),
"strata" and "fpc" (finite population corrector). See
:ref:`robust_likelihood_inference` for details.
Returns:
LikelihoodResult: A LikelihoodResult object.
"""
# ==================================================================================
# Check and process inputs
# ==================================================================================
is_optimized = optimize_options is False
if not is_optimized:
if isinstance(optimize_options, str):
optimize_options = {"algorithm": optimize_options}
check_optimization_options(
optimize_options,
usage="estimate_ml",
algorithm_mandatory=True,
)
jac_case = get_derivative_case(jacobian)
hess_case = get_derivative_case(hessian)
check_numdiff_options(numdiff_options, "estimate_ml")
numdiff_options = {} if numdiff_options in (None,
False) else numdiff_options
loglike_kwargs = {} if loglike_kwargs is None else loglike_kwargs
constraints = [] if constraints is None else constraints
jacobian_kwargs = {} if jacobian_kwargs is None else jacobian_kwargs
hessian_kwargs = {} if hessian_kwargs is None else hessian_kwargs
# ==================================================================================
# Calculate estimates via maximization (if necessary)
# ==================================================================================
if is_optimized:
estimates = params
opt_res = None
else:
opt_res = maximize(
criterion=loglike,
criterion_kwargs=loglike_kwargs,
params=params,
lower_bounds=lower_bounds,
upper_bounds=upper_bounds,
constraints=constraints,
logging=logging,
log_options=log_options,
**optimize_options,
)
estimates = opt_res.params
# ==================================================================================
# Do first function evaluations at estimated parameters
# ==================================================================================
try:
loglike_eval = loglike(estimates, **loglike_kwargs)
except (KeyboardInterrupt, SystemExit):
raise
except Exception as e:
msg = "Error while evaluating loglike at estimated params."
raise InvalidFunctionError(msg) from e
if callable(jacobian):
try:
jacobian_eval = jacobian(estimates, **jacobian_kwargs)
except (KeyboardInterrupt, SystemExit):
raise
except Exception as e:
msg = "Error while evaluating closed form jacobian at estimated params."
raise InvalidFunctionError(msg) from e
else:
jacobian_eval = None
if callable(hessian):
try:
hessian_eval = hessian(estimates, **hessian_kwargs)
except (KeyboardInterrupt, SystemExit):
raise
except Exception as e:
msg = "Error while evaluating closed form hessian at estimated params."
raise InvalidFunctionError(msg) from e
else:
hessian_eval = None
# ==================================================================================
# Get the converter for params and function outputs
# ==================================================================================
converter, internal_estimates = get_converter(
params=estimates,
constraints=constraints,
lower_bounds=lower_bounds,
upper_bounds=upper_bounds,
func_eval=loglike_eval,
primary_key="contributions",
scaling=False,
scaling_options=None,
derivative_eval=jacobian_eval,
)
# ==================================================================================
# Calculate internal jacobian
# ==================================================================================
if jac_case == "closed-form":
int_jac = converter.derivative_to_internal(jacobian_eval,
internal_estimates.values)
elif jac_case == "numerical":
def func(x):
p = converter.params_from_internal(x)
loglike_eval = loglike(p, **loglike_kwargs)["contributions"]
out = converter.func_to_internal(loglike_eval)
return out
jac_res = first_derivative(
func=func,
params=internal_estimates.values,
lower_bounds=internal_estimates.lower_bounds,
upper_bounds=internal_estimates.upper_bounds,
**numdiff_options,
)
int_jac = jac_res["derivative"]
else:
int_jac = None
if constraints in [None, []
] and jacobian_eval is None and int_jac is not None:
loglike_contribs = loglike_eval
if isinstance(loglike_contribs,
dict) and "contributions" in loglike_contribs:
loglike_contribs = loglike_contribs["contributions"]
jacobian_eval = matrix_to_block_tree(
int_jac,
outer_tree=loglike_contribs,
inner_tree=estimates,
)
if jacobian_eval is None:
_no_jac_reason = (
"no closed form jacobian was provided and there are constraints")
else:
_no_jac_reason = None
# ==================================================================================
# Calculate internal Hessian
# ==================================================================================
if hess_case == "skip":
int_hess = None
elif hess_case == "numerical":
def func(x):
p = converter.params_from_internal(x)
loglike_eval = loglike(p, **loglike_kwargs)["value"]
out = converter.func_to_internal(loglike_eval)
return out
hess_res = second_derivative(
func=func,
params=internal_estimates.values,
lower_bounds=internal_estimates.lower_bounds,
upper_bounds=internal_estimates.upper_bounds,
**numdiff_options,
)
int_hess = hess_res["derivative"]
elif hess_case == "closed-form" and constraints:
raise NotImplementedError(
"Closed-form Hessians are not yet compatible with constraints.")
elif hess_case == "closed-form":
int_hess = block_tree_to_matrix(
hessian_eval,
outer_tree=params,
inner_tree=params,
)
else:
raise ValueError()
if constraints in [None, []
] and hessian_eval is None and int_hess is not None:
hessian_eval = matrix_to_block_tree(
int_hess,
outer_tree=params,
inner_tree=params,
)
if hessian_eval is None:
if hess_case == "skip":
_no_hess_reason = "the hessian calculation was explicitly skipped."
else:
_no_hess_reason = (
"no closed form hessian was provided and there are constraints"
)
else:
_no_hess_reason = None
# ==================================================================================
# create a LikelihoodResult object
# ==================================================================================
free_estimates = calculate_free_estimates(estimates, internal_estimates)
res = LikelihoodResult(
_params=estimates,
_converter=converter,
_optimize_result=opt_res,
_jacobian=jacobian_eval,
_no_jacobian_reason=_no_jac_reason,
_hessian=hessian_eval,
_no_hessian_reason=_no_hess_reason,
_internal_jacobian=int_jac,
_internal_hessian=int_hess,
_design_info=design_info,
_internal_estimates=internal_estimates,
_free_estimates=free_estimates,
_has_constraints=constraints not in [None, []],
)
return res
def estimate_msm(
simulate_moments,
empirical_moments,
moments_cov,
params,
optimize_options,
*,
lower_bounds=None,
upper_bounds=None,
constraints=None,
logging=False,
log_options=None,
simulate_moments_kwargs=None,
weights="diagonal",
numdiff_options=None,
jacobian=None,
jacobian_kwargs=None,
):
"""Do a method of simulated moments or indirect inference estimation.
This is a high level interface for our lower level functions for minimization,
numerical differentiation, inference and sensitivity analysis. It does the full
workflow for MSM or indirect inference estimation with just one function call.
While we have good defaults, you can still configure each aspect of each steps
vial the optional arguments of this functions. If you find it easier to do the
minimization separately, you can do so and just provide the optimal parameters as
``params`` and set ``optimize_options=False``.
Args:
simulate_moments (callable): Function that takes params and potentially other
keyword arguments and returns a pytree with simulated moments. If the
function returns a dict containing the key ``"simulated_moments"`` we only
use the value corresponding to that key. Other entries are stored in the
log database if you use logging.
empirical_moments (pandas.Series): A pytree with the same structure as the
result of ``simulate_moments``.
moments_cov (pandas.DataFrame): A block-pytree containing the covariance
matrix of the empirical moments. This is typically calculated with
our ``get_moments_cov`` function.
params (pytree): A pytree containing the estimated or start parameters of the
model. If the supplied parameters are estimated parameters, set
optimize_options to False. Pytrees can be a numpy array, a pandas Series, a
DataFrame with "value" column, a float and any kind of (nested) dictionary
or list containing these elements. See :ref:`params` for examples.
optimize_options (dict, str or False): Keyword arguments that govern the
numerical optimization. Valid entries are all arguments of
:func:`~estimagic.optimization.optimize.minimize` except for those that can
be passed explicitly to ``estimate_msm``. If you pass False as
``optimize_options`` you signal that ``params`` are already
the optimal parameters and no numerical optimization is needed. If you pass
a str as optimize_options it is used as the ``algorithm`` option.
lower_bounds (pytree): A pytree with the same structure as params with lower
bounds for the parameters. Can be ``-np.inf`` for parameters with no lower
bound.
upper_bounds (pytree): As lower_bounds. Can be ``np.inf`` for parameters with
no upper bound.
simulate_moments_kwargs (dict): Additional keyword arguments for
``simulate_moments``.
weights (str): One of "diagonal" (default), "identity" or "optimal".
Note that "optimal" refers to the asymptotically optimal weighting matrix
and is often not a good choice due to large finite sample bias.
constraints (list, dict): List with constraint dictionaries or single dict.
See :ref:`constraints`.
logging (pathlib.Path, str or False): Path to sqlite3 file (which typically has
the file extension ``.db``. If the file does not exist, it will be created.
The dashboard can only be used when logging is used.
log_options (dict): Additional keyword arguments to configure the logging.
- "fast_logging" (bool):
A boolean that determines if "unsafe" settings are used to speed up
write processes to the database. This should only be used for very short
running criterion functions where the main purpose of the log is a
real-time dashboard and it would not be catastrophic to get a corrupted
database in case of a sudden system shutdown. If one evaluation of the
criterion function (and gradient if applicable) takes more than 100 ms,
the logging overhead is negligible.
- "if_table_exists" (str):
One of "extend", "replace", "raise". What to do if the tables we want to
write to already exist. Default "extend".
- "if_database_exists" (str):
One of "extend", "replace", "raise". What to do if the database we want
to write to already exists. Default "extend".
numdiff_options (dict): Keyword arguments for the calculation of numerical
derivatives for the calculation of standard errors. See
:ref:`first_derivative` for details. Note that by default we increase the
step_size by a factor of 2 compared to the rule of thumb for optimal
step sizes. This is because many msm criterion functions are slightly noisy.
jacobian (callable): A function that take ``params`` and
potentially other keyword arguments and returns the jacobian of
simulate_moments with respect to the params.
jacobian_kwargs (dict): Additional keyword arguments for the jacobian function.
Returns:
dict: The estimated parameters, standard errors and sensitivity measures
and covariance matrix of the parameters.
"""
# ==================================================================================
# Check and process inputs
# ==================================================================================
if weights not in ["diagonal", "optimal"]:
raise NotImplementedError(
"Custom weighting matrices are not yet implemented.")
is_optimized = optimize_options is False
if not is_optimized:
if isinstance(optimize_options, str):
optimize_options = {"algorithm": optimize_options}
check_optimization_options(
optimize_options,
usage="estimate_msm",
algorithm_mandatory=True,
)
jac_case = get_derivative_case(jacobian)
check_numdiff_options(numdiff_options, "estimate_msm")
numdiff_options = {} if numdiff_options in (
None, False) else numdiff_options.copy()
if "scaling_factor" not in numdiff_options:
numdiff_options["scaling_factor"] = 2
weights, internal_weights = get_weighting_matrix(
moments_cov=moments_cov,
method=weights,
empirical_moments=empirical_moments,
return_type="pytree_and_array",
)
internal_moments_cov = block_tree_to_matrix(
moments_cov,
outer_tree=empirical_moments,
inner_tree=empirical_moments,
)
constraints = [] if constraints is None else constraints
jacobian_kwargs = {} if jacobian_kwargs is None else jacobian_kwargs
simulate_moments_kwargs = ({} if simulate_moments_kwargs is None else
simulate_moments_kwargs)
# ==================================================================================
# Calculate estimates via minimization (if necessary)
# ==================================================================================
if is_optimized:
estimates = params
opt_res = None
else:
funcs = get_msm_optimization_functions(
simulate_moments=simulate_moments,
empirical_moments=empirical_moments,
weights=weights,
simulate_moments_kwargs=simulate_moments_kwargs,
# Always pass None because we do not support closed form jacobians during
# optimization yet. Otherwise we would get a NotImplementedError
jacobian=None,
jacobian_kwargs=jacobian_kwargs,
)
opt_res = minimize(
lower_bounds=lower_bounds,
upper_bounds=upper_bounds,
constraints=constraints,
logging=logging,
log_options=log_options,
params=params,
**funcs, # contains the criterion func and possibly more
**optimize_options,
)
estimates = opt_res.params
# ==================================================================================
# do first function evaluations
# ==================================================================================
try:
sim_mom_eval = simulate_moments(estimates, **simulate_moments_kwargs)
except (KeyboardInterrupt, SystemExit):
raise
except Exception as e:
msg = "Error while evaluating simulate_moments at estimated params."
raise InvalidFunctionError(msg) from e
if callable(jacobian):
try:
jacobian_eval = jacobian(estimates, **jacobian_kwargs)
except (KeyboardInterrupt, SystemExit):
raise
except Exception as e:
msg = "Error while evaluating derivative at estimated params."
raise InvalidFunctionError(msg) from e
else:
jacobian_eval = None
# ==================================================================================
# get converter for params and function outputs
# ==================================================================================
def helper(params):
raw = simulate_moments(params, **simulate_moments_kwargs)
if isinstance(raw, dict) and "simulated_moments" in raw:
out = {"contributions": raw["simulated_moments"]}
else:
out = {"contributions": raw}
return out
if isinstance(sim_mom_eval, dict) and "simulated_moments" in sim_mom_eval:
func_eval = {"contributions": sim_mom_eval["simulated_moments"]}
else:
func_eval = {"contributions": sim_mom_eval}
converter, internal_estimates = get_converter(
params=estimates,
constraints=constraints,
lower_bounds=lower_bounds,
upper_bounds=upper_bounds,
func_eval=func_eval,
primary_key="contributions",
scaling=False,
scaling_options=None,
derivative_eval=jacobian_eval,
)
# ==================================================================================
# Calculate internal jacobian
# ==================================================================================
if jac_case == "closed-form":
x = converter.params_to_internal(estimates)
int_jac = converter.derivative_to_internal(jacobian_eval, x)
else:
def func(x):
p = converter.params_from_internal(x)
sim_mom_eval = helper(p)
out = converter.func_to_internal(sim_mom_eval)
return out
int_jac = first_derivative(
func=func,
params=internal_estimates.values,
lower_bounds=internal_estimates.lower_bounds,
upper_bounds=internal_estimates.upper_bounds,
**numdiff_options,
)["derivative"]
# ==================================================================================
# Calculate external jac (if no constraints and not closed form )
# ==================================================================================
if constraints in [None, []
] and jacobian_eval is None and int_jac is not None:
jacobian_eval = matrix_to_block_tree(
int_jac,
outer_tree=empirical_moments,
inner_tree=estimates,
)
if jacobian_eval is None:
_no_jac_reason = (
"no closed form jacobian was provided and there are constraints")
else:
_no_jac_reason = None
# ==================================================================================
# Create MomentsResult
# ==================================================================================
free_estimates = calculate_free_estimates(estimates, internal_estimates)
res = MomentsResult(
_params=estimates,
_weights=weights,
_converter=converter,
_internal_weights=internal_weights,
_internal_moments_cov=internal_moments_cov,
_internal_jacobian=int_jac,
_jacobian=jacobian_eval,
_no_jacobian_reason=_no_jac_reason,
_empirical_moments=empirical_moments,
_internal_estimates=internal_estimates,
_free_estimates=free_estimates,
_has_constraints=constraints not in [None, []],
)
return res
internal_p = params[f"internal_value{number}"][keep].to_numpy()
fixed_val = pp["_internal_fixed_value"].to_numpy()
pre_repl = pp["_pre_replacements"].to_numpy()
post_repl = pp["_post_replacements"].to_numpy()
func = partial(
reparametrize_from_internal,
**{
"fixed_values": fixed_val,
"pre_replacements": pre_repl,
"processed_constraints": pc,
"post_replacements": post_repl,
},
)
numerical_jacobian = first_derivative(func, internal_p)
# calling convert_external_derivative with identity matrix as external derivative
# is just a trick to get out the jacobian of reparametrize_from_internal
jacobian = convert_external_derivative_to_internal(
external_derivative=np.eye(len(fixed_val)),
internal_values=internal_p,
fixed_values=fixed_val,
pre_replacements=pre_repl,
processed_constraints=pc,
post_replacements=post_repl,
)
aaae(jacobian, numerical_jacobian)
processed_constraints, processed_params = process_constraints(
constraints, params)
internal_params = reparametrize_to_internal(
external=params["value"].to_numpy(),
internal_free=processed_params["_internal_free"],
processed_constraints=processed_constraints,
)
if cov_type == "jacobian":
numdiff_options = numdiff_options.copy()
numdiff_options["key"] = "contributions"
internal_jac = first_derivative(
internal_loglike,
internal_params,
**numdiff_options,
)
internal_cov = cov_jacobian(internal_jac)
else:
raise NotImplementedError(
"Hessian calculation is not yet implemented.")
# transform internal covariance matrix
free_cov = transform_covariance(
params=params,
internal_cov=internal_cov,
constraints=constraints,
n_samples=n_samples,
bounds_handling=bounds_handling,
)
_, pp = process_constraints(constraints, params)
n_free = int(pp._internal_free.sum())
scaling_factor = np.ones(n_free) * 2 # np.arange(n_free) + 1
scaling_offset = np.arange(n_free) - 1
params_to_internal, params_from_internal = get_reparametrize_functions(
params=params,
constraints=constraints,
scaling_factor=scaling_factor,
scaling_offset=scaling_offset,
)
internal_p = params_to_internal(params["value"].to_numpy())
numerical_jacobian = first_derivative(params_from_internal, internal_p)
derivative_to_internal = get_derivative_conversion_function(
params=params,
constraints=constraints,
scaling_factor=scaling_factor,
scaling_offset=scaling_offset,
)
# calling convert_external_derivative with identity matrix as external derivative
# is just a trick to get out the jacobian of reparametrize_from_internal
jacobian = derivative_to_internal(
external_derivative=np.eye(len(params)),
internal_values=internal_p,
)
def internal_criterion_and_derivative_template(
x,
*,
task,
direction,
criterion,
params,
reparametrize_from_internal,
convert_derivative,
algorithm_info,
derivative,
criterion_and_derivative,
numdiff_options,
logging,
db_kwargs,
error_handling,
error_penalty,
first_criterion_evaluation,
cache,
cache_size,
fixed_log_data,
):
"""Template for the internal criterion and derivative function.
The internal criterion and derivative function only has the arguments x and task
and algorithm_info. The other arguments will be partialed in by estimagic at some
point. Algorithm_info and possibly even task will be partialed in by the algorithm.
That is the reason why this function is called a template.
Args:
x (np.ndarray): 1d numpy array with internal parameters.
task (str): One of "criterion", "derivative" and "criterion_and_derivative".
direction (str): One of "maximize" or "minimize"
criterion (callable): (partialed) user provided criterion function that takes a
parameter dataframe as only argument and returns a scalar, an array like
object or a dictionary. See :ref:`criterion`.
params (pd.DataFrame): see :ref:`params`
reparametrize_from_internal (callable): Function that takes x and returns a
numpy array with the values of the external parameters.
convert_derivative (callable): Function that takes the derivative of criterion
at the external version of x and x and returns the derivative
of the internal criterion.
algorithm_info (dict): Dict with the following entries:
"primary_criterion_entry": One of "value", "contributions" and
"root_contributions" or "dict".
"parallelizes": Bool that indicates if the algorithm calls the internal
criterion function in parallel. If so, caching is disabled.
"needs_scaling": bool
"name": string
derivative (callable, optional): (partialed) user provided function that
calculates the first derivative of criterion. For most algorithm, this is
the gradient of the scalar output (or "value" entry of the dict). However
some algorithms (e.g. bhhh) require the jacobian of the "contributions"
entry of the dict. You will get an error if you provide the wrong type of
derivative.
criterion_and_derivative (callable): Function that returns criterion
and derivative as a tuple. This can be used to exploit synergies in the
evaluation of both functions. The fist element of the tuple has to be
exactly the same as the output of criterion. The second has to be exactly
the same as the output of derivative.
numdiff_options (dict): Keyword arguments for the calculation of numerical
derivatives. See :ref:`first_derivative` for details. Note that the default
method is changed to "forward" for speed reasons.
logging (bool): Wether logging is used.
db_kwargs (dict): Dictionary with entries "database", "path" and "fast_logging".
error_handling (str): Either "raise" or "continue". Note that "continue" does
not absolutely guarantee that no error is raised but we try to handle as
many errors as possible in that case without aborting the optimization.
error_penalty (dict): Dict with the entries "constant" (float) and "slope"
(float). If the criterion or derivative raise an error and error_handling is
"continue", return ``constant + slope * norm(params - start_params)`` where
``norm`` is the euclidean distance as criterion value and adjust the
derivative accordingly. This is meant to guide the optimizer back into a
valid region of parameter space (in direction of the start parameters).
Note that the constant has to be high enough to ensure that the penalty is
actually a bad function value. The default constant is 2 times the criterion
value at the start parameters. The default slope is 0.1.
first_criterion_evaluation (dict): Dictionary with entries "internal_params",
"external_params", "output".
cache (dict): Dictionary used as cache for criterion and derivative evaluations.
cache_size (int): Number of evaluations that are kept in cache. Default 10.
fixed_log_data (dict): Dictionary with fixed data to be saved in the database.
Has the entries "stage" (str) and "substage" (int).
Returns:
float, np.ndarray or tuple: If task=="criterion" it returns the output of
criterion which can be a float or 1d numpy array. If task=="derivative" it
returns the first derivative of criterion, which is a numpy array.
If task=="criterion_and_derivative" it returns both as a tuple.
"""
if algorithm_info["primary_criterion_entry"] == "root_contributions":
if direction == "maximize":
msg = (
"Optimizers that exploit a least squares structure like {} can only be "
"used for minimization.")
raise ValueError(msg.format(algorithm_info["name"]))
x_hash = hash_array(x)
cache_entry = cache.get(x_hash, {})
to_dos = _determine_to_dos(task, cache_entry, derivative,
criterion_and_derivative)
caught_exceptions = []
new_criterion, new_derivative, new_external_derivative = None, None, None
current_params = params.copy()
external_x = reparametrize_from_internal(x)
current_params["value"] = external_x
if to_dos == []:
pass
elif "numerical_criterion_and_derivative" in to_dos:
def func(x):
external_x = reparametrize_from_internal(x)
p = params.copy()
p["value"] = external_x
return criterion(p)
options = numdiff_options.copy()
options["key"] = algorithm_info["primary_criterion_entry"]
options["f0"] = cache_entry.get("criterion", None)
options["return_func_value"] = True
try:
derivative_dict = first_derivative(func, x, **options)
new_derivative = {
algorithm_info["primary_criterion_entry"]:
derivative_dict["derivative"]
}
new_criterion = derivative_dict["func_value"]
except (KeyboardInterrupt, SystemExit):
raise
except Exception as e:
caught_exceptions.append(get_traceback())
if "criterion" in cache_entry:
raise Exception(DERIVATIVE_ERROR_MESSAGE) from e
elif "criterion_and_derivative" in to_dos:
try:
new_criterion, new_external_derivative = criterion_and_derivative(
current_params)
except (KeyboardInterrupt, SystemExit):
raise
except Exception as e:
caught_exceptions.append(get_traceback())
if "criterion" in cache_entry:
raise Exception(DERIVATIVE_ERROR_MESSAGE) from e
else:
if "criterion" in to_dos:
try:
new_criterion = criterion(current_params)
except (KeyboardInterrupt, SystemExit):
raise
except Exception as e:
caught_exceptions.append(get_traceback())
if "derivative" in cache_entry:
raise Exception(CRITERION_ERROR_MESSAGE) from e
if "derivative" in to_dos:
try:
new_external_derivative = derivative(current_params)
except (KeyboardInterrupt, SystemExit):
raise
except Exception as e:
caught_exceptions.append(get_traceback())
if "criterion" in cache_entry:
raise Exception(DERIVATIVE_ERROR_MESSAGE) from e
if new_derivative is None and new_external_derivative is not None:
if not isinstance(new_external_derivative, dict):
new_external_derivative = {
algorithm_info["primary_criterion_entry"]:
new_external_derivative
}
new_derivative = {
k: convert_derivative(v, internal_values=x)
for k, v in new_external_derivative.items()
}
if caught_exceptions:
if error_handling == "continue":
new_criterion, new_derivative = _penalty_and_derivative(
x, first_criterion_evaluation, error_penalty, algorithm_info)
warnings.warn("\n\n".join(caught_exceptions))
else:
raise Exception("\n\n".join(caught_exceptions))
if not algorithm_info["parallelizes"] and cache_size >= 1:
_cache_new_evaluations(new_criterion, new_derivative, x_hash, cache,
cache_size)
new_criterion = _check_and_harmonize_criterion_output(
cache_entry.get("criterion", new_criterion), algorithm_info)
new_derivative = _check_and_harmonize_derivative(
cache_entry.get("derivative", new_derivative), algorithm_info)
if (new_criterion is not None or new_derivative is not None) and logging:
_log_new_evaluations(
new_criterion=new_criterion,
new_derivative=new_derivative,
external_x=external_x,
caught_exceptions=caught_exceptions,
db_kwargs=db_kwargs,
fixed_log_data=fixed_log_data,
)
res = _get_output_for_optimizer(new_criterion, new_derivative, task,
algorithm_info, direction)
return res
def jacobian(p):
return first_derivative(
constraint_func,
p,
**options,
)["derivative"]
def internal_criterion_and_derivative_template(
x,
*,
task,
direction,
criterion,
converter,
algo_info,
derivative,
criterion_and_derivative,
numdiff_options,
logging,
db_kwargs,
error_handling,
error_penalty_func,
fixed_log_data,
history_container=None,
return_history_entry=False,
):
"""Template for the internal criterion and derivative function.
This function forms the basis of all functions that define the optimization problem
and are passed to the internal optimizers in estimagic. I.e. the criterion,
derivative and criterion_and_derivative functions.
Most of the arguments of this function will be partialled in before the functions
are passed to internal optimizers.
That is the reason why this function is called a template.
Args:
x (np.ndarray): 1d numpy array with internal parameters.
task (str): One of "criterion", "derivative" and "criterion_and_derivative".
direction (str): One of "maximize" or "minimize"
criterion (callable): (partialed) user provided criterion function that takes a
parameter dataframe as only argument and returns a scalar, an array like
object or a dictionary. See :ref:`criterion`.
params (pd.DataFrame): see :ref:`params`
converter (Converter): NamedTuple with methods to convert between internal
and external derivatives, parameters and criterion outputs.
algo_info (AlgoInfo): NamedTuple with attributes
- primary_criterion_entry
- name
- parallelizes
- needs_scaling
- is_available
derivative (callable, optional): (partialed) user provided function that
calculates the first derivative of criterion. For most algorithm, this is
the gradient of the scalar output (or "value" entry of the dict). However
some algorithms (e.g. bhhh) require the jacobian of the "contributions"
entry of the dict. You will get an error if you provide the wrong type of
derivative.
criterion_and_derivative (callable): Function that returns criterion
and derivative as a tuple. This can be used to exploit synergies in the
evaluation of both functions. The fist element of the tuple has to be
exactly the same as the output of criterion. The second has to be exactly
the same as the output of derivative.
numdiff_options (dict): Keyword arguments for the calculation of numerical
derivatives. See :ref:`first_derivative` for details. Note that the default
method is changed to "forward" for speed reasons.
logging (bool): Whether logging is used.
db_kwargs (dict): Dictionary with entries "database", "path" and "fast_logging".
error_handling (str): Either "raise" or "continue". Note that "continue" does
not absolutely guarantee that no error is raised but we try to handle as
many errors as possible in that case without aborting the optimization.
error_penalty_func (callable): Function that takes ``x`` and ``task`` and
returns a penalized criterion function, its derivative or both (depending)
on task.
fixed_log_data (dict): Dictionary with fixed data to be saved in the database.
Has the entries "stage" (str) and "substage" (int).
history_container (list or None): List to which parameter, criterion and
derivative histories are appended. Should be set to None if an algorithm
parallelizes over criterion or derivative evaluations.
return_history_entry (bool): Whether the history container should be returned.
Returns:
float, np.ndarray or tuple: If task=="criterion" it returns the output of
criterion which can be a float or 1d numpy array. If task=="derivative" it
returns the first derivative of criterion, which is a numpy array.
If task=="criterion_and_derivative" it returns both as a tuple.
"""
now = time.perf_counter()
to_dos = _determine_to_dos(task, derivative, criterion_and_derivative)
caught_exceptions = []
new_criterion, new_external_criterion = None, None
new_derivative, new_external_derivative = None, None
current_params, external_x = converter.params_from_internal(
x,
return_type="tree_and_flat",
)
if to_dos == []:
pass
elif "numerical_criterion_and_derivative" in to_dos:
def func(x):
p = converter.params_from_internal(x, "tree")
crit_full = criterion(p)
crit_relevant = converter.func_to_internal(crit_full)
out = {"full": crit_full, "relevant": crit_relevant}
return out
options = numdiff_options.copy()
options["key"] = "relevant"
options["return_func_value"] = True
try:
derivative_dict = first_derivative(func, x, **options)
new_derivative = derivative_dict["derivative"]
new_criterion = derivative_dict["func_value"]["relevant"]
new_external_criterion = derivative_dict["func_value"]["full"]
except (KeyboardInterrupt, SystemExit):
raise
except Exception as e:
tb = get_traceback()
caught_exceptions.append(tb)
if error_handling == "raise":
msg = (
"An error occurred when evaluating criterion to calculate a "
"numerical derivative during optimization.")
raise UserFunctionRuntimeError(msg) from e
else:
msg = (
"The following exception was caught when evaluating criterion to "
f"calculate a numerical derivative during optimization:\n\n{tb}"
)
warnings.warn(msg)
elif "criterion_and_derivative" in to_dos:
try:
new_external_criterion, new_external_derivative = criterion_and_derivative(
current_params)
except (KeyboardInterrupt, SystemExit):
raise
except Exception as e:
tb = get_traceback()
caught_exceptions.append(tb)
if error_handling == "raise":
msg = (
"An error ocurred when evaluating criterion_and_derivative "
"during optimization.")
raise UserFunctionRuntimeError(msg) from e
else:
msg = (
"The following exception was caught when evaluating "
f"criterion_and_derivative during optimization:\n\n{tb}")
warnings.warn(msg)
else:
if "criterion" in to_dos:
try:
new_external_criterion = criterion(current_params)
except (KeyboardInterrupt, SystemExit):
raise
except Exception as e:
tb = get_traceback()
caught_exceptions.append(tb)
if error_handling == "raise":
msg = ("An error ocurred when evaluating criterion during "
"optimization.")
raise UserFunctionRuntimeError(msg) from e
else:
msg = (
"The following exception was caught when evaluating "
f"criterion during optimization:\n\n{tb}")
warnings.warn(msg)
if "derivative" in to_dos:
try:
new_external_derivative = derivative(current_params)
except (KeyboardInterrupt, SystemExit):
raise
except Exception as e:
tb = get_traceback()
caught_exceptions.append(tb)
if error_handling == "raise":
msg = (
"An error ocurred when evaluating derivative during "
"optimization")
raise UserFunctionRuntimeError(msg) from e
else:
msg = (
"The following exception was caught when evaluating "
f"derivative during optimization:\n\n{tb}")
warnings.warn(msg)
if new_external_criterion is not None and new_criterion is None:
new_criterion = converter.func_to_internal(new_external_criterion)
if new_external_derivative is not None and new_derivative is None:
new_derivative = converter.derivative_to_internal(
new_external_derivative, x)
if caught_exceptions:
new_criterion, new_derivative = error_penalty_func(
x, task="criterion_and_derivative")
if new_criterion is not None:
scalar_critval = aggregate_func_output_to_value(
f_eval=new_criterion,
primary_key=algo_info.primary_criterion_entry,
)
else:
scalar_critval = None
if (new_criterion is not None or new_derivative is not None) and logging:
_log_new_evaluations(
new_criterion=new_external_criterion,
new_derivative=new_derivative,
external_x=external_x,
caught_exceptions=caught_exceptions,
db_kwargs=db_kwargs,
fixed_log_data=fixed_log_data,
scalar_value=scalar_critval,
now=now,
)
res = _get_output_for_optimizer(
new_criterion=new_criterion,
new_derivative=new_derivative,
task=task,
direction=direction,
)
if new_criterion is not None:
hist_entry = {
"params": current_params,
"criterion": scalar_critval,
"runtime": now,
}
else:
hist_entry = None
if history_container is not None and new_criterion is not None:
history_container.append(hist_entry)
if return_history_entry:
res = (res, hist_entry)
return res
