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kde_classes.py
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kde_classes.py
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# -*- coding: utf-8 -*-
import importlib
import itertools
import logging
import numpy as np
import os
from sklearn.model_selection import KFold
from scipy.interpolate import RegularGridInterpolator
from config import CFG
from dataset import load_and_prepare_data
# ROOT imports.
os.environ["ROOT_INCLUDE_PATH"] = os.pathsep + CFG['paths']['meerkat_root']
from ROOT import gSystem, gStyle, RooRealVar, std, Double
gSystem.Load(CFG['paths']['meerkat_lib'])
from ROOT import (
OneDimPhaseSpace,
CombinedPhaseSpace,
BinnedKernelDensity,
AdaptiveKernelDensity,
Logger
)
from root_numpy import array2tree
# Set Meerkat package log level to errors only.
Logger.setLogLevel(2)
class Model(object):
"""The Model class initializes and stores variables based on the provided
model module and given parameters. It is used for the KDE instance
generation.
"""
def __init__(self, model_module, mc=None, weighting=None, phi0=1.0,
gamma=2.0):
"""Creates a new model object.
Parameters
----------
model_module : str
Name of model file inside models directory.
mc : numpy record ndarray, optional
Monte-carlo data. If not provided the default `IC_mc` dataset from
configuration is used.
weighting : function | str | sequence of floats, optional
The function is called with `mc`, `phi0` and `gamma` arguments.
String is looked for in config `weighting_dict`. Sequence of weights
has to be the same length as the monte-carlo data. If no option is
given falls back to uniform weighting.
phi0: float, optional
Powerlaw normalization, default is 1.0.
gamma : float, optional
Powerlaw index, default is 2.0.
"""
super(Model, self).__init__()
self.logger = logging.getLogger('KDE.' + __name__ + '.Model')
model = importlib.import_module('models.{}'.format(model_module))
settings = model.settings
grid = model.grid
if mc is None:
if CFG['paths']['IC_mc'] is not None:
mc = load_and_prepare_data(CFG['paths']['IC_mc'])
else:
raise ValueError('No suitable Monte Carlo provided.')
self.values = [eval(settings[key]['values']) for key in settings]
self.vars = [key for key in settings]
self.bandwidth_vars = [key + '_bandwidth' for key in settings]
self.nbins = [settings[key]['nbins'] for key in settings]
self.bandwidths = [settings[key]['bandwidth'] for key in settings]
self.ranges = [eval(str(settings[key]['range']))
if settings[key]['range'] is not None
else [min(self.values[i]), max(self.values[i])]
for i, key in enumerate(settings)]
self.mc = mc
self.phi0 = phi0*1e-18 # Renormalize in units of 1e-18 1/GeV/cm^2/sr/s.
self.gamma = gamma
# Calculate KDE normalization.
range_norm = [1.0] + [bound[1] - bound[0] for bound in self.ranges]
self.kde_norm = reduce((lambda x, y : x/y), range_norm)
self.weighting_dict = CFG['weighting_dict']
self.weights = self._generate_weights(weighting)
if grid is None:
self.out_bins = [np.linspace(self.ranges[i][0], self.ranges[i][1],
self.nbins[i])
for i, key in enumerate(settings)]
else:
self.out_bins = [grid[key] for key in settings]
for i, key in enumerate(settings):
if len(self.out_bins[i]) != self.nbins[i]:
raise ValueError('Grid has different dimensions to nbins.')
self.coords = np.array(list(itertools.product(*self.out_bins)))
def _generate_weights(self, weighting):
"""Private method to generate weights by a given option.
Parameters
----------
weighting : function | str | sequence of floats, optional
The function is called with `mc`, `phi0` and `gamma` arguments.
String is looked for in config `weighting_dict`. Sequence of weights
has to be the same length as the monte-carlo data. If no option is
given falls back to uniform weighting.
Returns
-------
weights : numpy ndarray of floats
Generated weights with a given `weighting` option.
"""
if callable(weighting):
return weighting(self.mc, self.phi0, self.gamma)
elif isinstance(weighting, list):
if len(weighting) != len(self.mc):
raise ValueError('Weighting list length should be equal to the '
'MC length.')
return weighting
elif weighting in self.weighting_dict:
return self.weighting_dict[weighting](self.mc, self.phi0, self.gamma)
else:
self.logger.info('Using ones as weight.')
return np.ones(len(self.mc))
class KDE(object):
"""The KDE class provides methods for kernel density estimation and cross
validation.
"""
def __init__(self, model):
"""Creates a new KDE object.
Parameters
----------
model : Model
Instance of `Model` class.
"""
super(KDE, self).__init__()
self.logger = logging.getLogger('KDE.' + __name__ + '.KDE')
self.model = model
self.binned_kernel = None
self.adaptive_kernel = None
self.cv_result_dtype = np.dtype({
'names': ['bandwidth', 'LLH', 'Zeros'],
'formats': ['(' + str(len(self.model.vars)) + ',)f4', 'f4', 'f4']
})
self._generate_tree_and_space()
def _generate_tree_and_space(self, index=None):
"""Private method to generate a tree object of the given data with
weights and a combined phase space over data ranges.
Parameters
----------
index : numpy ndarray of floats | None
Indices for selection of the monte-carlo and weights data subset.
"""
self.tree = None
spaces = []
if index is None:
index = slice(len(self.model.values[0])) # Index the whole array.
for i, var in enumerate(self.model.vars):
spaces.append(OneDimPhaseSpace(var, *self.model.ranges[i]))
if self.tree is None:
value_array = np.array(self.model.values[i][index], dtype=[(var, np.float32)])
self.tree = array2tree(value_array)
else:
value_array = np.array(self.model.values[i][index], dtype=[(var, np.float32)])
array2tree(value_array, tree=self.tree)
array2tree(np.array(self.model.weights[index],
dtype=[("weight", np.float32)]), tree=self.tree)
if len(spaces) == 1:
self.space = spaces[0]
else:
self.space = CombinedPhaseSpace("PhspCombined", *spaces)
def generate_binned_kd(self, bandwidth, pdf_seed=None):
"""Wrapper method of `BinnedKernelDensity` constructor for N-dimensional
kernel PDF with binned interpolation from the sample of points in an
NTuple with weight.
Parameters
----------
bandwidth : list floats
List of kernel widths.
pdf_seed : KernelDensity | None
PDF seed for the approximation PDF.
Returns
-------
binned_kernel : BinnedKernelDensity
BinnedKernelDensity instance.
"""
if pdf_seed is None:
pdf_seed = 0
args = []
args.extend([
"BinnedKernelDensity",
self.space, # Phase space.
self.tree # Input NTuple.
])
args.extend(self.model.vars) # Variables to use.
args.append("weight") # Weights.
args.extend(self.model.nbins) # Numbers of bins.
args.extend(bandwidth) # Kernel widths.
args.extend([pdf_seed, # Approximation PDF (0 for flat approximation).
0]) # Sample size for MC convolution (0 for binned convolution)
self.binned_kernel = BinnedKernelDensity(*args)
return self.binned_kernel
def generate_adaptive_kd(self, bandwidth, pdf_seed=None):
"""Wrapper method of `AdaptiveKernelDensity` constructor for
N-dimensional adaptive kernel PDF from the sample of points in an NTuple
with weight.
Parameters
----------
bandwidth : list floats
List of kernel widths.
pdf_seed : KernelDensity | None
PDF seed for the width scaling and the approximation PDF.
Returns
-------
adaptive_kernel : AdaptiveKernelDensity
AdaptiveKernelDensity instance.
"""
# Generate pdf_seed if not provided.
if pdf_seed is None:
pdf_seed = self.generate_binned_kd(bandwidth)
args = []
args.extend([
"AdaptiveKernelDensity",
self.space, # Phase space.
self.tree # Input NTuple.
])
args.extend(self.model.vars) # Variables to use.
args.append("weight") # Weights.
args.extend(self.model.nbins) # Numbers of bins.
args.extend(bandwidth) # Kernel widths.
args.extend([pdf_seed, # PDF for kernel width scaling.
pdf_seed, # Approximation PDF (0 for flat approximation).
0]) # Sample size for MC convolution (0 for binned convolution)
self.adaptive_kernel = AdaptiveKernelDensity(*args)
return self.adaptive_kernel
def eval_point(self, kernel_density, coord):
"""Evaluates PDF value at a given coordinate of normalized
`KernelDensity` instance.
Parameters
----------
kernel_density : KernelDensity
Binned or adaptive `KernelDensity` instance.
coord : tuple of floats
Coordinates of a point at which the `kernel_density` is evaluated.
Returns
-------
value : float
Evaluated PDF value at a given coordinate of normalized
`kernel_density`.
"""
l = len(coord)
v = std.vector(Double)(l)
for i in range(l):
v[i] = coord[i]
return kernel_density.density(v)*self.model.kde_norm
def cross_validate_split(self, bandwidth, n_split, adaptive=False, pdf_seed=None):
"""Calculates average log likelihood value with given bandwidth on a
dataset using K-Folds cross-validator.
Parameters
----------
bandwidth : list floats
List of kernel widths.
n_split : int
Number of fold to cross validate.
adaptive : boolean
Chooses AdaptiveKernelDensity generator if True and
BinnedKernelDensity generator if False.
pdf_seed : KernelDensity | None
PDF seed for the width scaling and the approximation PDF.
Returns
-------
cv_result_split : numpy record ndarray
Cross validation array containing bandwidth, log likelihood and
zeros values.
"""
kfold = KFold(n_splits=CFG['project']['n_splits'],
random_state=CFG['project']['random_state'], shuffle=True)
training_index, validation_index = list(kfold.split(self.model.mc))[n_split]
self._generate_tree_and_space(training_index)
if adaptive:
kernel_density = self.generate_adaptive_kd(bandwidth, pdf_seed)
else:
kernel_density = self.generate_binned_kd(bandwidth, pdf_seed)
training_pdf_vals = self.get_pdf_values(kernel_density)
# Validation
rgi_pdf = RegularGridInterpolator(tuple(self.model.out_bins),
training_pdf_vals, method='linear', bounds_error=False,
fill_value=0)
mc_validation_values = []
for i, var in enumerate(self.model.vars):
mc_validation_values.append(
self.model.values[i][validation_index])
likelihood = rgi_pdf(zip(*mc_validation_values))
inds = likelihood > 0.
weights = self.model.weights[validation_index]
weights /= np.sum(weights)
llh = np.sum(np.log(likelihood[inds])*weights[inds])
zeros = len(likelihood) - len(inds)
result_tuple = tuple([tuple(bandwidth), llh, zeros])
cv_result_split = np.array([result_tuple], dtype=self.cv_result_dtype)
return cv_result_split
def cross_validate(self, bandwidth, adaptive=False, pdf_seed=None):
"""Calculates average log likelihood value with given bandwidth on a
dataset using K-Folds cross-validator.
Parameters
----------
bandwidth : list floats
List of kernel widths.
adaptive : boolean
Chooses AdaptiveKernelDensity generator if True and
BinnedKernelDensity generator if False.
pdf_seed : KernelDensity | None
PDF seed for the width scaling and the approximation PDF.
Returns
-------
cv_result : numpy record ndarray
Cross validation array containing bandwidth, log likelihood and
zeros values.
"""
result = np.array([], dtype=self.cv_result_dtype)
for n_split in range(CFG['project']['n_splits']):
cv_result_split = self.cross_validate_split(bandwidth, n_split,
adaptive=adaptive, pdf_seed=pdf_seed)
result = np.append(result, cv_result_split)
result_tuple = tuple([tuple(bandwidth), np.average(result['LLH']),
np.average(result['Zeros'])])
cv_result = np.array([result_tuple], dtype=self.cv_result_dtype)
return cv_result
def cross_validate_bandwidths(self, bandwidths=None, adaptive=False,
pdf_seed=None):
"""Calculates average log likelihood value with given bandwidth on a
dataset using K-Folds cross-validator for given `bandwidths` or
generated product of the model bandwidth ranges.
Parameters
----------
bandwidths : list of list floats | None
List of kernel widths.
adaptive : boolean
Chooses AdaptiveKernelDensity generator if True and
BinnedKernelDensity generator if False.
pdf_seed : KernelDensity | None
PDF seed for the width scaling and the approximation PDF.
Returns
-------
cv_results : numpy record ndarray
Cross validation array containing bandwidths, log likelihoods and
zeros values.
"""
cv_results = np.array([], dtype=self.cv_result_dtype)
if bandwidths is None:
bandwidths = self.model.bandwidths
for bandwidth in itertools.product(*bandwidths):
self.logger.info('Bandwidth: %s', bandwidth)
result = self.cross_validate(bandwidth, adaptive)
cv_results = np.append(cv_results, result)
return cv_results
def get_pdf_values(self, kernel_density):
"""Evaluates PDF values at all coordinates of normalized `KernelDensity`
instance.
Parameters
----------
kernel_density : KernelDensity
Binned or adaptive `KernelDensity` instance.
Returns
-------
pdf_values : numpy ndarray of floats
Evaluated PDF values.
"""
pdf_values = np.asarray([self.eval_point(kernel_density, coord)
for coord in self.model.coords])
pdf_values = pdf_values.reshape(self.model.nbins)
return pdf_values