Source code for pyomo.contrib.parmest.parmest

#  ___________________________________________________________________________
#
#  Pyomo: Python Optimization Modeling Objects
#  Copyright 2017 National Technology and Engineering Solutions of Sandia, LLC
#  Under the terms of Contract DE-NA0003525 with National Technology and
#  Engineering Solutions of Sandia, LLC, the U.S. Government retains certain
#  rights in this software.
#  This software is distributed under the 3-clause BSD License.
#  ___________________________________________________________________________
#### Using mpi-sppy instead of PySP; May 2020
#### Adding option for "local" EF starting Sept 2020
#### Wrapping mpi-sppy functionality and local option Jan 2021, Feb 2021

# False implies always use the EF that is local to parmest
use_mpisppy = True  # Use it if we can but use local if not.
if use_mpisppy:
    try:
        import mpisppy.utils.sputils as sputils
    except:
        use_mpisppy = False  # we can't use it
if use_mpisppy:
    # These things should be outside the try block.
    sputils.disable_tictoc_output()
    import mpisppy.opt.ef as st
    import mpisppy.scenario_tree as scenario_tree
else:
    import pyomo.contrib.parmest.create_ef as local_ef
    import pyomo.contrib.parmest.scenario_tree as scenario_tree

import re
import importlib as im
import logging
import types
import json
from itertools import combinations

from pyomo.common.dependencies import (
    attempt_import,
    numpy as np, numpy_available,
    pandas as pd, pandas_available,
    scipy, scipy_available,
)

import pyomo.environ as pyo

from pyomo.opt import SolverFactory
from pyomo.environ import Block, ComponentUID

import pyomo.contrib.parmest.mpi_utils as mpiu
import pyomo.contrib.parmest.ipopt_solver_wrapper as ipopt_solver_wrapper
import pyomo.contrib.parmest.graphics as graphics

parmest_available = numpy_available & pandas_available & scipy_available

inverse_reduced_hessian, inverse_reduced_hessian_available = attempt_import(
    'pyomo.contrib.interior_point.inverse_reduced_hessian')

logger = logging.getLogger(__name__)

[docs]def ef_nonants(ef): # Wrapper to call someone's ef_nonants # (the function being called is very short, but it might be changed) if use_mpisppy: return sputils.ef_nonants(ef) else: return local_ef.ef_nonants(ef)
def _experiment_instance_creation_callback(scenario_name, node_names=None, cb_data=None): """ This is going to be called by mpi-sppy or the local EF and it will call into the user's model's callback. Parameters: ----------- scenario_name: `str` Scenario name should end with a number node_names: `None` ( Not used here ) cb_data : dict with ["callback"], ["BootList"], ["theta_names"], ["cb_data"], etc. "cb_data" is passed through to user's callback function that is the "callback" value. "BootList" is None or bootstrap experiment number list. (called cb_data by mpisppy) Returns: -------- instance: `ConcreteModel` instantiated scenario Note: ---- There is flexibility both in how the function is passed and its signature. """ assert(cb_data is not None) outer_cb_data = cb_data scen_num_str = re.compile(r'(\d+)$').search(scenario_name).group(1) scen_num = int(scen_num_str) basename = scenario_name[:-len(scen_num_str)] # to reconstruct name CallbackFunction = outer_cb_data["callback"] if callable(CallbackFunction): callback = CallbackFunction else: cb_name = CallbackFunction if "CallbackModule" not in outer_cb_data: raise RuntimeError(\ "Internal Error: need CallbackModule in parmest callback") else: modname = outer_cb_data["CallbackModule"] if isinstance(modname, str): cb_module = im.import_module(modname, package=None) elif isinstance(modname, types.ModuleType): cb_module = modname else: print("Internal Error: bad CallbackModule") raise try: callback = getattr(cb_module, cb_name) except: print("Error getting function="+cb_name+" from module="+str(modname)) raise if "BootList" in outer_cb_data: bootlist = outer_cb_data["BootList"] #print("debug in callback: using bootlist=",str(bootlist)) # assuming bootlist itself is zero based exp_num = bootlist[scen_num] else: exp_num = scen_num scen_name = basename + str(exp_num) cb_data = outer_cb_data["cb_data"] # cb_data might be None. # at least three signatures are supported. The first is preferred try: instance = callback(experiment_number = exp_num, cb_data = cb_data) except TypeError: raise RuntimeError("Only one callback signature is supported: " "callback(experiment_number, cb_data) ") """ try: instance = callback(scenario_tree_model, scen_name, node_names) except TypeError: # deprecated signature? try: instance = callback(scen_name, node_names) except: print("Failed to create instance using callback; TypeError+") raise except: print("Failed to create instance using callback.") raise """ if hasattr(instance, "_mpisppy_node_list"): raise RuntimeError (f"scenario for experiment {exp_num} has _mpisppy_node_list") nonant_list = [instance.find_component(vstr) for vstr in\ outer_cb_data["theta_names"]] instance._mpisppy_node_list = [scenario_tree.ScenarioNode( name="ROOT", cond_prob=1.0, stage=1, cost_expression=instance.FirstStageCost, scen_name_list=None, # Deprecated? nonant_list=nonant_list, scen_model=instance)] if "ThetaVals" in outer_cb_data: thetavals = outer_cb_data["ThetaVals"] # dlw august 2018: see mea code for more general theta for vstr in thetavals: object = instance.find_component(vstr) if thetavals[vstr] is not None: #print("Fixing",vstr,"at",str(thetavals[vstr])) object.fix(thetavals[vstr]) else: #print("Freeing",vstr) object.fixed = False return instance #============================================= def _treemaker(scenlist): """ Makes a scenario tree (avoids dependence on daps) Parameters ---------- scenlist (list of `int`): experiment (i.e. scenario) numbers Returns ------- a `ConcreteModel` that is the scenario tree """ num_scenarios = len(scenlist) m = scenariotree.tree_structure_model.CreateAbstractScenarioTreeModel() m = m.create_instance() m.Stages.add('Stage1') m.Stages.add('Stage2') m.Nodes.add('RootNode') for i in scenlist: m.Nodes.add('LeafNode_Experiment'+str(i)) m.Scenarios.add('Experiment'+str(i)) m.NodeStage['RootNode'] = 'Stage1' m.ConditionalProbability['RootNode'] = 1.0 for node in m.Nodes: if node != 'RootNode': m.NodeStage[node] = 'Stage2' m.Children['RootNode'].add(node) m.Children[node].clear() m.ConditionalProbability[node] = 1.0/num_scenarios m.ScenarioLeafNode[node.replace('LeafNode_','')] = node return m
[docs]def group_data(data, groupby_column_name, use_mean=None): """ Group data by scenario Parameters ---------- data: DataFrame Data groupby_column_name: strings Name of data column which contains scenario numbers use_mean: list of column names or None, optional Name of data columns which should be reduced to a single value per scenario by taking the mean Returns ---------- grouped_data: list of dictionaries Grouped data """ grouped_data = [] for exp_num, group in data.groupby(data[groupby_column_name]): d = {} for col in group.columns: if col in use_mean: d[col] = group[col].mean() else: d[col] = list(group[col]) grouped_data.append(d) return grouped_data
class _SecondStageCostExpr(object): """ Class to pass objective expression into the Pyomo model """ def __init__(self, ssc_function, data): self._ssc_function = ssc_function self._data = data def __call__(self, model): return self._ssc_function(model, self._data)
[docs]class Estimator(object): """ Parameter estimation class Parameters ---------- model_function: function Function that generates an instance of the Pyomo model using 'data' as the input argument data: pandas DataFrame, list of dictionaries, or list of json file names Data that is used to build an instance of the Pyomo model and build the objective function theta_names: list of strings List of Var names to estimate obj_function: function, optional Function used to formulate parameter estimation objective, generally sum of squared error between measurements and model variables. If no function is specified, the model is used "as is" and should be defined with a "FirstStageCost" and "SecondStageCost" expression that are used to build an objective. tee: bool, optional Indicates that ef solver output should be teed diagnostic_mode: bool, optional If True, print diagnostics from the solver solver_options: dict, optional Provides options to the solver (also the name of an attribute) """ def __init__(self, model_function, data, theta_names, obj_function=None, tee=False, diagnostic_mode=False, solver_options=None): self.model_function = model_function self.callback_data = data if len(theta_names) == 0: self.theta_names = ['parmest_dummy_var'] else: self.theta_names = theta_names self.obj_function = obj_function self.tee = tee self.diagnostic_mode = diagnostic_mode self.solver_options = solver_options self._second_stage_cost_exp = "SecondStageCost" self._numbers_list = list(range(len(data))) def _create_parmest_model(self, data): """ Modify the Pyomo model for parameter estimation """ from pyomo.core import Objective model = self.model_function(data) if (len(self.theta_names) == 1) and (self.theta_names[0] == 'parmest_dummy_var'): model.parmest_dummy_var = pyo.Var(initialize = 1.0) for i, theta in enumerate(self.theta_names): # First, leverage the parser in ComponentUID to locate the # component. If that fails, fall back on the original # (insecure) use of 'eval' var_cuid = ComponentUID(theta) var_validate = var_cuid.find_component_on(model) if var_validate is None: logger.warning( "theta_name[%s] (%s) was not found on the model", (i, theta)) else: try: # If the component that was found is not a variable, # this will generate an exception (and the warning # in the 'except') var_validate.fixed = False # We want to standardize on the CUID string # representation self.theta_names[i] = repr(var_cuid) except: logger.warning(theta + ' is not a variable') if self.obj_function: for obj in model.component_objects(Objective): obj.deactivate() def FirstStageCost_rule(model): return 0 model.FirstStageCost = pyo.Expression(rule=FirstStageCost_rule) model.SecondStageCost = pyo.Expression(rule=_SecondStageCostExpr(self.obj_function, data)) def TotalCost_rule(model): return model.FirstStageCost + model.SecondStageCost model.Total_Cost_Objective = pyo.Objective(rule=TotalCost_rule, sense=pyo.minimize) self.parmest_model = model return model def _instance_creation_callback(self, experiment_number=None, cb_data=None): # DataFrame if isinstance(cb_data, pd.DataFrame): # Keep single experiments in a Dataframe (not a Series) exp_data = cb_data.loc[experiment_number,:].to_frame().transpose() # List of dictionaries OR list of json file names elif isinstance(cb_data, list): exp_data = cb_data[experiment_number] if isinstance(exp_data, dict): pass if isinstance(exp_data, str): try: with open(exp_data,'r') as infile: exp_data = json.load(infile) except: raise RuntimeError(f'Could not read {exp_data} as json') else: raise RuntimeError(f'Unexpected data format for cb_data={cb_data}') model = self._create_parmest_model(exp_data) return model def _Q_opt(self, ThetaVals=None, solver="ef_ipopt", return_values=[], bootlist=None, calc_cov=False): """ Set up all thetas as first stage Vars, return resulting theta values as well as the objective function value. """ if (solver == "k_aug"): raise RuntimeError("k_aug no longer supported.") # (Bootstrap scenarios will use indirection through the bootlist) if bootlist is None: scen_names = ["Scenario{}".format(i) for i in self._numbers_list] else: scen_names = ["Scenario{}".format(i)\ for i in range(len(self._numbers_list))] # tree_model.CallbackModule = None outer_cb_data = dict() outer_cb_data["callback"] = self._instance_creation_callback if ThetaVals is not None: outer_cb_data["ThetaVals"] = ThetaVals if bootlist is not None: outer_cb_data["BootList"] = bootlist outer_cb_data["cb_data"] = self.callback_data # None is OK outer_cb_data["theta_names"] = self.theta_names options = {"solver": "ipopt"} scenario_creator_options = {"cb_data": outer_cb_data} if use_mpisppy: ef = sputils.create_EF(scen_names, _experiment_instance_creation_callback, EF_name = "_Q_opt", suppress_warnings=True, scenario_creator_kwargs=scenario_creator_options) else: ef = local_ef.create_EF(scen_names, _experiment_instance_creation_callback, EF_name = "_Q_opt", suppress_warnings=True, scenario_creator_kwargs=scenario_creator_options) self.ef_instance = ef # Solve the extensive form with ipopt if solver == "ef_ipopt": if not calc_cov: # Do not calculate the reduced hessian solver = SolverFactory('ipopt') if self.solver_options is not None: for key in self.solver_options: solver.options[key] = self.solver_options[key] solve_result = solver.solve(ef, tee = self.tee) # The import error will be raised when we attempt to use # inv_reduced_hessian_barrier below. # #elif not asl_available: # raise ImportError("parmest requires ASL to calculate the " # "covariance matrix with solver 'ipopt'") else: # parmest makes the fitted parameters stage 1 variables ind_vars = [] for ndname, Var, solval in ef_nonants(ef): ind_vars.append(Var) # calculate the reduced hessian solve_result, inv_red_hes = \ inverse_reduced_hessian.inv_reduced_hessian_barrier( self.ef_instance, independent_variables= ind_vars, solver_options=self.solver_options, tee=self.tee) if self.diagnostic_mode: print(' Solver termination condition = ', str(solve_result.solver.termination_condition)) # assume all first stage are thetas... thetavals = {} for ndname, Var, solval in ef_nonants(ef): # process the name # the scenarios are blocks, so strip the scenario name vname = Var.name[Var.name.find(".")+1:] thetavals[vname] = solval objval = pyo.value(ef.EF_Obj) if calc_cov: # Calculate the covariance matrix # Extract number of data points considered n = len(self.callback_data) # Extract number of fitted parameters l = len(thetavals) # Assumption: Objective value is sum of squared errors sse = objval '''Calculate covariance assuming experimental observation errors are independent and follow a Gaussian distribution with constant variance. The formula used in parmest was verified against equations (7-5-15) and (7-5-16) in "Nonlinear Parameter Estimation", Y. Bard, 1974. This formula is also applicable if the objective is scaled by a constant; the constant cancels out. (was scaled by 1/n because it computes an expected value.) ''' cov = 2 * sse / (n - l) * inv_red_hes cov = pd.DataFrame(cov, index=thetavals.keys(), columns=thetavals.keys()) if len(return_values) > 0: var_values = [] for exp_i in self.ef_instance.component_objects(Block, descend_into=False): vals = {} for var in return_values: exp_i_var = exp_i.find_component(str(var)) if exp_i_var is None: # we might have a block such as _mpisppy_data continue temp = [pyo.value(_) for _ in exp_i_var.values()] if len(temp) == 1: vals[var] = temp[0] else: vals[var] = temp if len(vals) > 0: var_values.append(vals) var_values = pd.DataFrame(var_values) if calc_cov: return objval, thetavals, var_values, cov else: return objval, thetavals, var_values if calc_cov: return objval, thetavals, cov else: return objval, thetavals else: raise RuntimeError("Unknown solver in Q_Opt="+solver) def _Q_at_theta(self, thetavals): """ Return the objective function value with fixed theta values. Parameters ---------- thetavals: dict A dictionary of theta values. Returns ------- objectiveval: float The objective function value. thetavals: dict A dictionary of all values for theta that were input. solvertermination: Pyomo TerminationCondition Tries to return the "worst" solver status across the scenarios. pyo.TerminationCondition.optimal is the best and pyo.TerminationCondition.infeasible is the worst. """ dummy_cb = {"callback": self._instance_creation_callback, "ThetaVals": thetavals, "theta_names": self.theta_names, "cb_data": self.callback_data} optimizer = pyo.SolverFactory('ipopt') if self.diagnostic_mode: print(' Compute objective at theta = ',str(thetavals)) # start block of code to deal with models with no constraints # (ipopt will crash or complain on such problems without special care) instance = _experiment_instance_creation_callback("FOO1", None, dummy_cb) try: # deal with special problems so Ipopt will not crash first = next(instance.component_objects(pyo.Constraint, active=True)) except: sillylittle = True else: sillylittle = False # end block of code to deal with models with no constraints WorstStatus = pyo.TerminationCondition.optimal totobj = 0 for snum in self._numbers_list: sname = "scenario_NODE"+str(snum) instance = _experiment_instance_creation_callback(sname, None, dummy_cb) if not sillylittle: if self.diagnostic_mode: print(' Experiment = ',snum) print(' First solve with with special diagnostics wrapper') status_obj, solved, iters, time, regu \ = ipopt_solver_wrapper.ipopt_solve_with_stats(instance, optimizer, max_iter=500, max_cpu_time=120) print(" status_obj, solved, iters, time, regularization_stat = ", str(status_obj), str(solved), str(iters), str(time), str(regu)) results = optimizer.solve(instance) if self.diagnostic_mode: print('standard solve solver termination condition=', str(results.solver.termination_condition)) if results.solver.termination_condition \ != pyo.TerminationCondition.optimal : # DLW: Aug2018: not distinguishing "middlish" conditions if WorstStatus != pyo.TerminationCondition.infeasible: WorstStatus = results.solver.termination_condition objobject = getattr(instance, self._second_stage_cost_exp) objval = pyo.value(objobject) totobj += objval retval = totobj / len(self._numbers_list) # -1?? return retval, thetavals, WorstStatus def _get_sample_list(self, samplesize, num_samples, replacement=True): samplelist = list() if num_samples is None: # This could get very large for i, l in enumerate(combinations(self._numbers_list, samplesize)): samplelist.append((i, np.sort(l))) else: for i in range(num_samples): attempts = 0 unique_samples = 0 # check for duplicates in each sample duplicate = False # check for duplicates between samples while (unique_samples <= len(self.theta_names)) and (not duplicate): sample = np.random.choice(self._numbers_list, samplesize, replace=replacement) sample = np.sort(sample).tolist() unique_samples = len(np.unique(sample)) if sample in samplelist: duplicate = True attempts += 1 if attempts > num_samples: # arbitrary timeout limit raise RuntimeError("""Internal error: timeout constructing a sample, the dim of theta may be too close to the samplesize""") samplelist.append((i, sample)) return samplelist
[docs] def theta_est(self, solver="ef_ipopt", return_values=[], bootlist=None, calc_cov=False): """ Parameter estimation using all scenarios in the data Parameters ---------- solver: string, optional "ef_ipopt" or "k_aug". Default is "ef_ipopt". return_values: list, optional List of Variable names used to return values from the model bootlist: list, optional List of bootstrap sample numbers, used internally when calling theta_est_bootstrap calc_cov: boolean, optional If True, calculate and return the covariance matrix (only for "ef_ipopt" solver) Returns ------- objectiveval: float The objective function value thetavals: dict A dictionary of all values for theta variable values: pd.DataFrame Variable values for each variable name in return_values (only for solver='ef_ipopt') Hessian: dict A dictionary of dictionaries for the Hessian (only for solver='k_aug') cov: pd.DataFrame Covariance matrix of the fitted parameters (only for solver='ef_ipopt') """ assert isinstance(solver, str) assert isinstance(return_values, list) assert isinstance(bootlist, (type(None), list)) return self._Q_opt(solver=solver, return_values=return_values, bootlist=bootlist, calc_cov=calc_cov)
[docs] def theta_est_bootstrap(self, bootstrap_samples, samplesize=None, replacement=True, seed=None, return_samples=False): """ Parameter estimation using bootstrap resampling of the data Parameters ---------- bootstrap_samples: int Number of bootstrap samples to draw from the data samplesize: int or None, optional Size of each bootstrap sample. If samplesize=None, samplesize will be set to the number of samples in the data replacement: bool, optional Sample with or without replacement seed: int or None, optional Random seed return_samples: bool, optional Return a list of sample numbers used in each bootstrap estimation Returns ------- bootstrap_theta: DataFrame Theta values for each sample and (if return_samples = True) the sample numbers used in each estimation """ assert isinstance(bootstrap_samples, int) assert isinstance(samplesize, (type(None), int)) assert isinstance(replacement, bool) assert isinstance(seed, (type(None), int)) assert isinstance(return_samples, bool) if samplesize is None: samplesize = len(self._numbers_list) if seed is not None: np.random.seed(seed) global_list = self._get_sample_list(samplesize, bootstrap_samples, replacement) task_mgr = mpiu.ParallelTaskManager(bootstrap_samples) local_list = task_mgr.global_to_local_data(global_list) # Reset numbers_list self._numbers_list = list(range(samplesize)) bootstrap_theta = list() for idx, sample in local_list: objval, thetavals = self.theta_est(bootlist=list(sample)) thetavals['samples'] = sample bootstrap_theta.append(thetavals) # Reset numbers_list (back to original) self._numbers_list = list(range(len(self.callback_data))) global_bootstrap_theta = task_mgr.allgather_global_data(bootstrap_theta) bootstrap_theta = pd.DataFrame(global_bootstrap_theta) if not return_samples: del bootstrap_theta['samples'] return bootstrap_theta
[docs] def theta_est_leaveNout(self, lNo, lNo_samples=None, seed=None, return_samples=False): """ Parameter estimation where N data points are left out of each sample Parameters ---------- lNo: int Number of data points to leave out for parameter estimation lNo_samples: int Number of leave-N-out samples. If lNo_samples=None, the maximum number of combinations will be used seed: int or None, optional Random seed return_samples: bool, optional Return a list of sample numbers that were left out Returns ------- lNo_theta: DataFrame Theta values for each sample and (if return_samples = True) the sample numbers left out of each estimation """ assert isinstance(lNo, int) assert isinstance(lNo_samples, (type(None), int)) assert isinstance(seed, (type(None), int)) assert isinstance(return_samples, bool) samplesize = len(self._numbers_list)-lNo if seed is not None: np.random.seed(seed) global_list = self._get_sample_list(samplesize, lNo_samples, replacement=False) task_mgr = mpiu.ParallelTaskManager(len(global_list)) local_list = task_mgr.global_to_local_data(global_list) # Reset numbers_list self._numbers_list = list(range(samplesize)) lNo_theta = list() for idx, sample in local_list: objval, thetavals = self.theta_est(bootlist=list(sample)) lNo_s = list(set(range(len(self.callback_data))) - set(sample)) thetavals['lNo'] = np.sort(lNo_s) lNo_theta.append(thetavals) # Reset numbers_list (back to original) self._numbers_list = list(range(len(self.callback_data))) global_bootstrap_theta = task_mgr.allgather_global_data(lNo_theta) lNo_theta = pd.DataFrame(global_bootstrap_theta) if not return_samples: del lNo_theta['lNo'] return lNo_theta
[docs] def leaveNout_bootstrap_test(self, lNo, lNo_samples, bootstrap_samples, distribution, alphas, seed=None): """ Leave-N-out bootstrap test to compare theta values where N data points are left out to a bootstrap analysis using the remaining data, results indicate if theta is within a confidence region determined by the bootstrap analysis Parameters ---------- lNo: int Number of data points to leave out for parameter estimation lNo_samples: int Leave-N-out sample size. If lNo_samples=None, the maximum number of combinations will be used bootstrap_samples: int: Bootstrap sample size distribution: string Statistical distribution used to define a confidence region, options = 'MVN' for multivariate_normal, 'KDE' for gaussian_kde, and 'Rect' for rectangular. alphas: list List of alpha values used to determine if theta values are inside or outside the region. seed: int or None, optional Random seed Returns ---------- List of tuples with one entry per lNo_sample: * The first item in each tuple is the list of N samples that are left out. * The second item in each tuple is a DataFrame of theta estimated using the N samples. * The third item in each tuple is a DataFrame containing results from the bootstrap analysis using the remaining samples. For each DataFrame a column is added for each value of alpha which indicates if the theta estimate is in (True) or out (False) of the alpha region for a given distribution (based on the bootstrap results) """ assert isinstance(lNo, int) assert isinstance(lNo_samples, (type(None), int)) assert isinstance(bootstrap_samples, int) assert distribution in ['Rect', 'MVN', 'KDE'] assert isinstance(alphas, list) assert isinstance(seed, (type(None), int)) if seed is not None: np.random.seed(seed) data = self.callback_data.copy() global_list = self._get_sample_list(lNo, lNo_samples, replacement=False) results = [] for idx, sample in global_list: # Reset callback_data and numbers_list self.callback_data = data.loc[sample,:] self._numbers_list = self.callback_data.index obj, theta = self.theta_est() # Reset callback_data and numbers_list self.callback_data = data.drop(index=sample) self._numbers_list = self.callback_data.index bootstrap_theta = self.theta_est_bootstrap(bootstrap_samples) training, test = self.confidence_region_test(bootstrap_theta, distribution=distribution, alphas=alphas, test_theta_values=theta) results.append((sample, test, training)) # Reset callback_data and numbers_list (back to original) self.callback_data = data self._numbers_list = self.callback_data.index return results
[docs] def objective_at_theta(self, theta_values): """ Objective value for each theta Parameters ---------- theta_values: DataFrame, columns=theta_names Values of theta used to compute the objective Returns ------- obj_at_theta: DataFrame Objective value for each theta (infeasible solutions are omitted). """ assert isinstance(theta_values, pd.DataFrame) # for parallel code we need to use lists and dicts in the loop theta_names = theta_values.columns all_thetas = theta_values.to_dict('records') task_mgr = mpiu.ParallelTaskManager(len(all_thetas)) local_thetas = task_mgr.global_to_local_data(all_thetas) # walk over the mesh, return objective function all_obj = list() for Theta in local_thetas: obj, thetvals, worststatus = self._Q_at_theta(Theta) if worststatus != pyo.TerminationCondition.infeasible: all_obj.append(list(Theta.values()) + [obj]) # DLW, Aug2018: should we also store the worst solver status? global_all_obj = task_mgr.allgather_global_data(all_obj) dfcols = list(theta_names) + ['obj'] obj_at_theta = pd.DataFrame(data=global_all_obj, columns=dfcols) return obj_at_theta
[docs] def likelihood_ratio_test(self, obj_at_theta, obj_value, alphas, return_thresholds=False): r""" Likelihood ratio test to identify theta values within a confidence region using the :math:`\chi^2` distribution Parameters ---------- obj_at_theta: DataFrame, columns = theta_names + 'obj' Objective values for each theta value (returned by objective_at_theta) obj_value: int or float Objective value from parameter estimation using all data alphas: list List of alpha values to use in the chi2 test return_thresholds: bool, optional Return the threshold value for each alpha Returns ------- LR: DataFrame Objective values for each theta value along with True or False for each alpha thresholds: dictionary If return_threshold = True, the thresholds are also returned. """ assert isinstance(obj_at_theta, pd.DataFrame) assert isinstance(obj_value, (int, float)) assert isinstance(alphas, list) assert isinstance(return_thresholds, bool) LR = obj_at_theta.copy() S = len(self.callback_data) thresholds = {} for a in alphas: chi2_val = scipy.stats.chi2.ppf(a, 2) thresholds[a] = obj_value * ((chi2_val / (S - 2)) + 1) LR[a] = LR['obj'] < thresholds[a] if return_thresholds: return LR, thresholds else: return LR
[docs] def confidence_region_test(self, theta_values, distribution, alphas, test_theta_values=None): """ Confidence region test to determine if theta values are within a rectangular, multivariate normal, or Gaussian kernel density distribution for a range of alpha values Parameters ---------- theta_values: DataFrame, columns = theta_names Theta values used to generate a confidence region (generally returned by theta_est_bootstrap) distribution: string Statistical distribution used to define a confidence region, options = 'MVN' for multivariate_normal, 'KDE' for gaussian_kde, and 'Rect' for rectangular. alphas: list List of alpha values used to determine if theta values are inside or outside the region. test_theta_values: dictionary or DataFrame, keys/columns = theta_names, optional Additional theta values that are compared to the confidence region to determine if they are inside or outside. Returns ------- training_results: DataFrame Theta value used to generate the confidence region along with True (inside) or False (outside) for each alpha test_results: DataFrame If test_theta_values is not None, returns test theta value along with True (inside) or False (outside) for each alpha """ assert isinstance(theta_values, pd.DataFrame) assert distribution in ['Rect', 'MVN', 'KDE'] assert isinstance(alphas, list) assert isinstance(test_theta_values, (type(None), dict, pd.DataFrame)) if isinstance(test_theta_values, dict): test_theta_values = pd.Series(test_theta_values).to_frame().transpose() training_results = theta_values.copy() if test_theta_values is not None: test_result = test_theta_values.copy() for a in alphas: if distribution == 'Rect': lb, ub = graphics.fit_rect_dist(theta_values, a) training_results[a] = ((theta_values > lb).all(axis=1) & \ (theta_values < ub).all(axis=1)) if test_theta_values is not None: # use upper and lower bound from the training set test_result[a] = ((test_theta_values > lb).all(axis=1) & \ (test_theta_values < ub).all(axis=1)) elif distribution == 'MVN': dist = graphics.fit_mvn_dist(theta_values) Z = dist.pdf(theta_values) score = scipy.stats.scoreatpercentile(Z, (1-a)*100) training_results[a] = (Z >= score) if test_theta_values is not None: # use score from the training set Z = dist.pdf(test_theta_values) test_result[a] = (Z >= score) elif distribution == 'KDE': dist = graphics.fit_kde_dist(theta_values) Z = dist.pdf(theta_values.transpose()) score = scipy.stats.scoreatpercentile(Z, (1-a)*100) training_results[a] = (Z >= score) if test_theta_values is not None: # use score from the training set Z = dist.pdf(test_theta_values.transpose()) test_result[a] = (Z >= score) if test_theta_values is not None: return training_results, test_result else: return training_results