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template_model.py
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template_model.py
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from __future__ import absolute_import
from __future__ import division
from __future__ import print_function
import numpy as np
import tensorflow as tf
from neyman.inferences import batch_hessian
from ast import literal_eval
import json
import itertools as it
import tensorflow_probability as tfp
from collections import OrderedDict
from fisher_matrix import FisherMatrix
ds = tfp.distributions
def int_quad_lin(alpha, c_nom, c_up, c_dw, multiple_pars=False):
"Three-point interpolation, quadratic inside and linear outside"
if multiple_pars:
tiling_shape = [1, 1, 1, tf.shape(c_nom)[0]]
expand_axis = 1
else:
tiling_shape = [1, 1, tf.shape(c_nom)[0]]
expand_axis = 0
# alpha dimensions are (1, n_par_types, n_par_inst)
# c_dw and c_up are (n_bins, n_par_types)
alpha_t = tf.tile(tf.expand_dims(alpha, axis=-1), tiling_shape)
# alpha_t dimensions are (1, n_par_types, n_par_inst, n_bins)
# if multiple_pars is True or (1, n_par_types, n_bins)
a = tf.expand_dims(0.5 * (c_up + c_dw) - c_nom,
axis=expand_axis, name="a")
b = tf.expand_dims(0.5 * (c_up - c_dw),
axis=expand_axis, name="b")
ones = tf.ones_like(alpha_t)
# (1, n_par_types, n_par_inst, n_bins) broadcast when multiple_pars
# (n_par_types, 1, n_bins) (if expand axis 1)
# (1, n_par_types, n_bins) broadcast when not multiple_pars
# (n_par_types,n_bins) (if expand axis 0)
switch = tf.where(alpha_t < 0.,
ones * tf.expand_dims(c_dw - c_nom, axis=expand_axis),
ones * tf.expand_dims(c_up - c_nom, axis=expand_axis))
abs_var = tf.where(tf.abs(alpha_t) > 1.,
(2 * b + tf.sign(alpha_t) * a) *
(alpha_t - tf.sign(alpha_t)) + switch,
a * tf.pow(alpha_t, 2) + b * alpha_t)
# abs_var is (1, n_par_types, n_par_inst, n_bins) or (1, n_par_types, n_bins)
return c_nom + tf.reduce_sum(abs_var, axis=1)
class TemplateModel(object):
def __init__(self, multiple_pars=False):
self.multiple_pars = multiple_pars
if multiple_pars:
shape_pars = (None,)
else:
shape_pars = ()
def default_ph_value(val):
if multiple_pars:
return [val, ]
else:
return val
self.r_dist_init = tf.placeholder_with_default(
2., shape=(), name="r_dist_init")
self.b_rate_init = tf.placeholder_with_default(
3., shape=(), name="b_rate_init")
self.r_dist_shift = tf.placeholder_with_default(
0.2, shape=(), name="r_dist_shift")
self.b_rate_shift = tf.placeholder_with_default(
0.5, shape=(), name="b_rate_shift")
self.r_dist = tf.placeholder_with_default(default_ph_value(2.),
shape=shape_pars,
name="r_dist")
self.b_rate = tf.placeholder_with_default(default_ph_value(3.),
shape=shape_pars,
name="b_rate")
# background templates
self.c_nom = tf.placeholder(dtype=tf.float32, shape=(None,), name="c_nom")
self.c_up = tf.placeholder(
dtype=tf.float32, shape=(None, None), name="c_up")
self.c_dw = tf.placeholder(
dtype=tf.float32, shape=(None, None), name="c_dw")
# signal template
self.sig_shape = tf.placeholder(
dtype=tf.float32, shape=(None,), name="sig_shape")
self.alpha_pars = [[(self.r_dist - self.r_dist_init) / self.r_dist_shift,
(self.b_rate - self.b_rate_init) / self.b_rate_shift]]
# bkg_shape shape is (n_par_inst, n_bins, 1) if multiple_pars
self.bkg_shape = int_quad_lin(self.alpha_pars,
self.c_nom, self.c_up, self.c_dw,
multiple_pars=multiple_pars)[0]
# expected amount of signal
self.s_exp = tf.placeholder_with_default(default_ph_value(50.),
shape=shape_pars, name="s_exp")
# expected amount of background
self.b_exp = tf.placeholder_with_default(default_ph_value(1000.),
shape=shape_pars, name="b_exp")
if multiple_pars:
sig_shape = tf.expand_dims(self.sig_shape, axis=0,
name="expanded_sig_shape")
s_exp = tf.expand_dims(self.s_exp, axis=-1, name="expanded_s_exp")
b_exp = tf.expand_dims(self.b_exp, axis=-1, name="expanded_b_exp")
else:
sig_shape = self.sig_shape
s_exp = self.s_exp
b_exp = self.b_exp
self.t_exp = tf.cast(s_exp * sig_shape +
b_exp * self.bkg_shape,
dtype=tf.float64, name="t_exp")
# placeholder for observed data
self.obs = tf.placeholder(dtype=tf.float64, shape=(None,), name="obs")
self.h_pois = ds.Poisson(self.t_exp)
self.h_nll = - \
tf.cast(tf.reduce_sum(self.h_pois.log_prob(self.obs), axis=-1),
dtype=tf.float32)
self.all_pars = OrderedDict([('s_exp', self.s_exp),
('r_dist', self.r_dist),
('b_rate', self.b_rate),
('b_exp', self.b_exp)])
pars = list(self.all_pars.values())
self.h_hess, self.h_grad = batch_hessian(self.h_nll, pars)
def templates_from_dict(self, templates,
r_dist=[2.0, 2.2, 1.8],
b_rate=[3.0, 3.5, 2.5]):
def normalise(arr):
arr = np.array(arr, dtype=np.float32)
return arr / arr.sum()
templates = {k: normalise(v) for k, v in templates.items()}
shift_phs = {self.r_dist_init: r_dist[0],
self.r_dist_shift: (r_dist[1] - r_dist[2]) / 2.,
self.b_rate_init: b_rate[0],
self.b_rate_shift: (b_rate[1] - b_rate[2]) / 2.}
c_nom = templates[('bkg', r_dist[0], b_rate[0])]
c_up = np.array([templates[('bkg', r_dist[1], b_rate[0])],
templates[('bkg', r_dist[0], b_rate[1])]])
c_dw = np.array([templates[('bkg', r_dist[2], b_rate[0])],
templates[('bkg', r_dist[0], b_rate[2])]])
sig_shape = templates[('sig',)]
# remove zeroes
zero_filter = np.all([(sig_shape != 0.), (c_nom != 0.)], axis=0)
templates = {k: v[zero_filter] for k, v in templates.items()
if not ('pars' in k[0])}
self.shape_phs = {self.c_nom: c_nom[zero_filter],
self.c_up: c_up[:, zero_filter],
self.c_dw: c_dw[:, zero_filter],
self.sig_shape: sig_shape[zero_filter],
**shift_phs}
return templates
def templates_from_json(self, json_path,
r_dist=[2.0, 2.2, 1.8],
b_rate=[3.0, 3.5, 2.5]):
with open(json_path) as f:
templates = json.load(f)
templates = {literal_eval(k): v for k, v in templates.items()}
templates = self.templates_from_dict(templates, r_dist=r_dist,
b_rate=b_rate)
return templates
def asimov_data(self, par_phs={}, sess=None):
if sess is None:
sess = tf.get_default_session()
asimov_data = sess.run(self.t_exp, {**par_phs, **self.shape_phs})
if self.multiple_pars:
asimov_data = asimov_data[0]
return asimov_data
def asimov_hess(self, par_phs={}, sess=None):
if sess is None:
sess = tf.get_default_session()
obs_phs = {self.obs: self.asimov_data(par_phs, sess=sess)}
h_hess = sess.run(self.h_hess, {**par_phs, **obs_phs, **self.shape_phs})
return FisherMatrix(h_hess, par_names=list(self.all_pars.keys()))
def hessian_and_gradient(self, pars, par_phs={}, obs_phs={}, sess=None):
if sess is None:
sess = tf.get_default_session()
pars = tuple(pars)
nll, hess, grad = sess.run([self.h_nll, self.h_hess, self.h_grad],
feed_dict={**par_phs, **obs_phs,
**self.shape_phs})
indices = [list(self.all_pars.keys()).index(par) for par in pars]
idx_subset = np.reshape(list(it.product(indices, indices)),
(len(pars), len(pars), -1)).T
sub_hess = hess[:, idx_subset[0], idx_subset[1]]
sub_grad = grad[:, indices]
return nll, sub_hess, sub_grad