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Implement BB full with gamma via numerically solving for nbeta #99

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166 changes: 148 additions & 18 deletions rabbit/fitter.py
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Original file line number Diff line number Diff line change
Expand Up @@ -81,15 +81,6 @@ def __init__(
else:
self.binByBinStatType = options.binByBinStatType

if (
self.binByBinStat
and self.binByBinStatMode == "full"
and not self.binByBinStatType.startswith("normal")
):
raise Exception(
'bin-by-bin stat only for option "--binByBinStatMode full" with "--binByBinStatType normal"'
)

if (
options.covarianceFit
and self.binByBinStat
Expand Down Expand Up @@ -231,9 +222,14 @@ def __init__(
self.sumw = self.indata.sumw

if self.binByBinStatType in ["gamma", "normal-multiplicative"]:
self.kstat = self.sumw**2 / self.varbeta
self.betamask = (self.varbeta == 0.0) | (self.kstat == 0.0)
self.kstat = tf.where(self.betamask, 1.0, self.kstat)
self.betamask = (self.varbeta == 0.0) | (self.sumw == 0.0)
self.kstat = tf.where(self.betamask, 1.0, self.sumw**2 / self.varbeta)

if self.binByBinStatType == "gamma" and self.binByBinStatMode == "full":
self.nbeta = tf.Variable(
tf.ones_like(self.nobs), trainable=True, name="nbeta"
)

elif self.binByBinStatType == "normal-additive":
# precompute decomposition of composite matrix to speed up
# calculation of profiled beta values
Expand Down Expand Up @@ -1405,13 +1401,74 @@ def _compute_yields_with_beta(self, profile=True, compute_norm=False, full=True)
if self.chisqFit:
if self.binByBinStatType == "gamma":
kstat = self.kstat[: self.indata.nbins]
betamask = self.betamask[: self.indata.nbins]

abeta = nexp_profile**2
bbeta = kstat * self.varnobs - nexp_profile * self.nobs
cbeta = -kstat * self.varnobs * beta0
beta = solve_quad_eq(abeta, bbeta, cbeta)
if self.binByBinStatMode == "lite":
abeta = nexp_profile**2
bbeta = kstat * self.varnobs - nexp_profile * self.nobs
cbeta = -kstat * self.varnobs * beta0
beta = solve_quad_eq(abeta, bbeta, cbeta)
elif self.binByBinStatMode == "full":
norm_profile = norm[: self.indata.nbins]

# solving nbeta numerically using newtons method (does not work with forward differentiation i.e. use --globalImpacts with --globalImpactsDisableJVP)
def fnll_nbeta(x):
beta = (
kstat
* beta0
/ (
kstat
+ ((x - self.nobs) / self.varnobs)[..., None]
* norm_profile
)
)
beta = tf.where(betamask, beta0, beta)
new_nexp = tf.reduce_sum(beta * norm_profile, axis=-1)
ln = 0.5 * (new_nexp - self.nobs) ** 2 / self.varnobs
lbeta = tf.reduce_sum(
kstat * (beta - beta0)
- kstat
* beta0
* (tf.math.log(beta) - tf.math.log(beta0)),
axis=-1,
)
return ln + lbeta

def body(i, edm):
with tf.GradientTape() as t2:
with tf.GradientTape() as t1:
nll = fnll_nbeta(nexp_profile * self.nbeta)
grad = t1.gradient(nll, self.nbeta)
hess = t2.gradient(grad, self.nbeta)

eps = 1e-8
safe_hess = tf.where(hess > 0, hess, tf.ones_like(hess))
step = grad / (safe_hess + eps)

self.nbeta.assign_sub(step)

return i + 1, tf.reduce_max(0.5 * grad * step)

def cond(i, edm):
return tf.logical_and(i < 50, edm > 1e-10)

i0 = tf.constant(0)
edm0 = tf.constant(tf.float64.max)
tf.while_loop(cond, body, loop_vars=(i0, edm0))

beta = (
kstat
* beta0
/ (
kstat
+ (
(nexp_profile * self.nbeta - self.nobs)
/ self.varnobs
)[..., None]
* norm_profile
)
)

betamask = self.betamask[: self.indata.nbins]
beta = tf.where(betamask, beta0, beta)
elif self.binByBinStatType == "normal-multiplicative":
kstat = self.kstat[: self.indata.nbins]
Expand Down Expand Up @@ -1560,7 +1617,72 @@ def _compute_yields_with_beta(self, profile=True, compute_norm=False, full=True)
kstat = self.kstat[: self.indata.nbins]
betamask = self.betamask[: self.indata.nbins]

beta = (self.nobs + kstat * beta0) / (nexp_profile + kstat)
if self.binByBinStatMode == "lite":
beta = (self.nobs + kstat * beta0) / (nexp_profile + kstat)
elif self.binByBinStatMode == "full":
norm_profile = norm[: self.indata.nbins]

# solving nbeta numerically using newtons method (does not work with forward differentiation i.e. use --globalImpacts with --globalImpactsDisableJVP)
def fnll_nbeta(x):
beta = (
kstat
* beta0
/ (
norm_profile
+ kstat
- (self.nobs / x)[..., None] * norm_profile
)
)
beta = tf.where(betamask, beta0, beta)
new_nexp = tf.reduce_sum(beta * norm_profile, axis=-1)
ln = (
new_nexp
- self.nobs
- self.nobs
* (tf.math.log(new_nexp) - tf.math.log(self.nobs))
)
lbeta = tf.reduce_sum(
kstat * (beta - beta0)
- kstat
* beta0
* (tf.math.log(beta) - tf.math.log(beta0)),
axis=-1,
)
return ln + lbeta

def body(i, edm):
with tf.GradientTape() as t2:
with tf.GradientTape() as t1:
nll = fnll_nbeta(nexp_profile * self.nbeta)
grad = t1.gradient(nll, self.nbeta)
hess = t2.gradient(grad, self.nbeta)

eps = 1e-8
safe_hess = tf.where(hess > 0, hess, tf.ones_like(hess))
step = grad / (safe_hess + eps)
self.nbeta.assign_sub(step)
return i + 1, tf.reduce_max(0.5 * grad * step)

def cond(i, edm):
return tf.logical_and(i < 50, edm > 1e-10)

i0 = tf.constant(0)
edm0 = tf.constant(tf.float64.max)
tf.while_loop(cond, body, loop_vars=(i0, edm0))

beta = (
kstat
* beta0
/ (
norm_profile
- (self.nobs / (nexp_profile * self.nbeta))[
..., None
]
* norm_profile
+ kstat
)
)

beta = tf.where(betamask, beta0, beta)
elif self.binByBinStatType == "normal-multiplicative":
kstat = self.kstat[: self.indata.nbins]
Expand Down Expand Up @@ -2063,6 +2185,14 @@ def loss_val_grad_hess_beta(self, profile=True):
grad = t1.gradient(val, self.ubeta)
hess = t2.jacobian(grad, self.ubeta)

grad = tf.reshape(grad, [-1])
hess = tf.reshape(hess, [grad.shape[0], grad.shape[0]])

betamask = ~tf.reshape(self.betamask, [-1])
grad = grad[betamask]
hess = tf.boolean_mask(hess, betamask, axis=0)
hess = tf.boolean_mask(hess, betamask, axis=1)

return val, grad, hess

def minimize(self):
Expand Down