model

This module provides methods to calculate NLL(Negative Log-Likelihood) as well as its derivatives.

class BaseModel(signal, resolution_size=1)

Bases: object

This class implements methods to calculate NLL as well as its derivatives for an amplitude model. It may include data for both signal and background.

Parameters

signal – Signal Model

get_params(trainable_only=False)

It has interface to Amplitude.get_params().

grad_hessp_batch(p, data, mcdata, weight, mc_weight)

self.nll_grad() is replaced by this one???

\[- \frac{\partial \ln L}{\partial \theta_k } = -\sum_{x_i \in data } w_i \frac{\partial}{\partial \theta_k} \ln f(x_i;\theta_k) + (\sum w_j ) \left( \frac{ \partial }{\partial \theta_k} \sum_{x_i \in mc} f(x_i;\theta_k) \right) \frac{1}{ \sum_{x_i \in mc} f(x_i;\theta_k) }\]

Parameters

• data –

• mcdata –

• weight –

• mc_weight –

Returns

nll(data, mcdata)

Negative log-Likelihood

nll_grad(data, mcdata, batch=65000)

nll_grad_batch(data, mcdata, weight, mc_weight)

self.nll_grad() is replaced by this one???

\[- \frac{\partial \ln L}{\partial \theta_k } = -\sum_{x_i \in data } w_i \frac{\partial}{\partial \theta_k} \ln f(x_i;\theta_k) + (\sum w_j ) \left( \frac{ \partial }{\partial \theta_k} \sum_{x_i \in mc} f(x_i;\theta_k) \right) \frac{1}{ \sum_{x_i \in mc} f(x_i;\theta_k) }\]

Parameters

• data –

• mcdata –

• weight –

• mc_weight –

Returns

nll_grad_hessian(data, mcdata, batch=25000)

The parameters are the same with self.nll(), but it will return Hessian as well.

Return NLL

Real number. The value of NLL.

Return gradients

List of real numbers. The gradients for each variable.

Return Hessian

2-D Array of real numbers. The Hessian matrix of the variables.

set_params(var)

It has interface to Amplitude.set_params().

sum_log_integral_grad_batch(mcdata, ndata)

sum_nll_grad_bacth(data)

property trainable_variables

class CombineFCN(model=None, data=None, mcdata=None, bg=None, fcns=None, batch=65000, gauss_constr={})

Bases: object

This class implements methods to calculate the NLL as well as its derivatives for a general function.

Parameters

• model – List of model object.

• data – List of data array.

• mcdata – list of MCdata array.

• bg – list of Background array.

• batch – The length of array to calculate as a vector at a time. How to fold the data array may depend on the GPU computability.

get_grad(x={})

Parameters

x – List. Values of variables.

Return gradients

List of real numbers. The gradients for each variable.

get_grad_hessp(x, p, batch)

Parameters

x – List. Values of variables.

Return nll

Real number. The value of NLL.

Return gradients

List of real numbers. The gradients for each variable.

get_nll(x={})

Parameters

x – List. Values of variables.

Return nll

Real number. The value of NLL.

get_nll_grad(x={})

Parameters

x – List. Values of variables.

Return nll

Real number. The value of NLL.

Return gradients

List of real numbers. The gradients for each variable.

get_nll_grad_hessian(x={}, batch=None)

Parameters

x – List. Values of variables.

Return nll

Real number. The value of NLL.

Return gradients

List of real numbers. The gradients for each variable.

Return hessian

2-D Array of real numbers. The Hessian matrix of the variables.

get_params(trainable_only=False)

grad(x={})

grad_hessp(x, p, batch=None)

nll_grad(x={})

nll_grad_hessian(x={}, batch=None)

class ConstrainModel(amp, w_bkg=1.0, constrain={})

Bases: Model

negative log likelihood model with constrains

get_constrain_grad()

constrain: Gauss(mean,sigma)

by add a term \(\frac{d}{d\theta_i}\frac{(\theta_i-\bar{\theta_i})^2}{2\sigma^2} = \frac{\theta_i-\bar{\theta_i}}{\sigma^2}\)

get_constrain_hessian()

the constrained parameter’s 2nd differentiation

get_constrain_term()

constrain: Gauss(mean,sigma)

by add a term \(\frac{(\theta_i-\bar{\theta_i})^2}{2\sigma^2}\)

nll(data, mcdata, weight=1.0, bg=None, batch=None)

calculate negative log-likelihood

\[-\ln L = -\sum_{x_i \in data } w_i \ln f(x_i;\theta_i) + (\sum w_i ) \ln \sum_{x_i \in mc } f(x_i;\theta_i) + cons\]

nll_gradient(data, mcdata, weight=1.0, batch=None, bg=None)

calculate negative log-likelihood with gradient

\[\frac{\partial }{\partial \theta_i }(-\ln L) = -\sum_{x_i \in data } w_i \frac{\partial }{\partial \theta_i } \ln f(x_i;\theta_i) + \frac{\sum w_i }{\sum_{x_i \in mc }f(x_i;\theta_i)} \sum_{x_i \in mc } \frac{\partial }{\partial \theta_i } f(x_i;\theta_i) + cons\]

class FCN(model, data, mcdata, bg=None, batch=65000, inmc=None, gauss_constr={})

Bases: object

This class implements methods to calculate the NLL as well as its derivatives for a general function.

Parameters

• model – Model object.

• data – Data array.

• mcdata – MCdata array.

• bg – Background array.

• batch – The length of array to calculate as a vector at a time. How to fold the data array may depend on the GPU computability.

get_grad(x={})

Parameters

x – List. Values of variables.

Return gradients

List of real numbers. The gradients for each variable.

get_grad_hessp(x, p, batch)

get_nll(x={})

Parameters

x – List. Values of variables.

Return nll

Real number. The value of NLL.

get_nll_grad(x={})

Parameters

x – List. Values of variables.

Return nll

Real number. The value of NLL.

Return gradients

List of real numbers. The gradients for each variable.

get_nll_grad_hessian(x={}, batch=None)

Parameters

x – List. Values of variables.

Return nll

Real number. The value of NLL.

Return gradients

List of real numbers. The gradients for each variable.

Return hessian

2-D Array of real numbers. The Hessian matrix of the variables.

get_params(trainable_only=False)

grad(x={})

grad_hessp(x, p, batch=None)

nll_grad(x={})

nll_grad_hessian(x={}, batch=None)

class GaussianConstr(vm, constraint={})

Bases: object

get_constrain_grad()

constraint: Gauss(mean,sigma)

by add a term \(\frac{d}{d\theta_i}\frac{(\theta_i-\bar{\theta_i})^2}{2\sigma^2} = \frac{\theta_i-\bar{\theta_i}}{\sigma^2}\)

get_constrain_hessian()

the constrained parameter’s 2nd differentiation

get_constrain_term()

constraint: Gauss(mean,sigma)

by add a term \(\frac{(\theta_i-\bar{\theta_i})^2}{2\sigma^2}\)

update(constraint={})

class MixLogLikehoodFCN(model, data, mcdata, bg=None, batch=65000, gauss_constr={})

Bases: CombineFCN

This class implements methods to calculate the NLL as well as its derivatives for a general function.

Parameters

• model – List of model object.

• data – List of data array.

• mcdata – list of MCdata array.

• bg – list of Background array.

• batch – The length of array to calculate as a vector at a time. How to fold the data array may depend on the GPU computability.

get_nll_grad(x={})

Parameters

x – List. Values of variables.

Return nll

Real number. The value of NLL.

Return gradients

List of real numbers. The gradients for each variable.

class Model(amp, w_bkg=1.0, resolution_size=1)

Bases: object

This class implements methods to calculate NLL as well as its derivatives for an amplitude model. It may include data for both signal and background.

Parameters

• amp – AllAmplitude object. The amplitude model.

• w_bkg – Real number. The weight of background.

get_params(trainable_only=False)

It has interface to Amplitude.get_params().

get_weight_data(data, weight=None, bg=None, alpha=True)

Blend data and background data together multiplied by their weights.

Parameters

• data – Data array

• weight – Weight for data

• bg – Data array for background

• alpha – Boolean. If it’s true, weight will be multiplied by a factor \(\alpha=\)???

Returns

Data, weight. Their length both equals len(data)+len(bg).

grad_hessp_batch(p, data, mcdata, weight, mc_weight)

self.nll_grad() is replaced by this one???

\[- \frac{\partial \ln L}{\partial \theta_k } = -\sum_{x_i \in data } w_i \frac{\partial}{\partial \theta_k} \ln f(x_i;\theta_k) + (\sum w_j ) \left( \frac{ \partial }{\partial \theta_k} \sum_{x_i \in mc} f(x_i;\theta_k) \right) \frac{1}{ \sum_{x_i \in mc} f(x_i;\theta_k) }\]

Parameters

• data –

• mcdata –

• weight –

• mc_weight –

Returns

mix_data_bakcground(data, bg)

nll(data, mcdata, weight: Tensor = 1.0, batch=None, bg=None, mc_weight=1.0)

Calculate NLL.

\[-\ln L = -\sum_{x_i \in data } w_i \ln f(x_i;\theta_k) + (\sum w_j ) \ln \sum_{x_i \in mc } f(x_i;\theta_k)\]

Parameters

• data – Data array

• mcdata – MCdata array

• weight – Weight of data???

• batch – The length of array to calculate as a vector at a time. How to fold the data array may depend on the GPU computability.

• bg – Background data array. It can be set to None if there is no such thing.

Returns

Real number. The value of NLL.

nll_grad(data, mcdata, weight=1.0, batch=65000, bg=None, mc_weight=1.0)

Calculate NLL and its gradients.

\[- \frac{\partial \ln L}{\partial \theta_k } = -\sum_{x_i \in data } w_i \frac{\partial}{\partial \theta_k} \ln f(x_i;\theta_k) + (\sum w_j ) \left( \frac{ \partial }{\partial \theta_k} \sum_{x_i \in mc} f(x_i;\theta_k) \right) \frac{1}{ \sum_{x_i \in mc} f(x_i;\theta_k) }\]

The parameters are the same with self.nll(), but it will return gradients as well.

Return NLL

Real number. The value of NLL.

Return gradients

List of real numbers. The gradients for each variable.

nll_grad_batch(data, mcdata, weight, mc_weight)

self.nll_grad() is replaced by this one???

\[- \frac{\partial \ln L}{\partial \theta_k } = -\sum_{x_i \in data } w_i \frac{\partial}{\partial \theta_k} \ln f(x_i;\theta_k) + (\sum w_j ) \left( \frac{ \partial }{\partial \theta_k} \sum_{x_i \in mc} f(x_i;\theta_k) \right) \frac{1}{ \sum_{x_i \in mc} f(x_i;\theta_k) }\]

Parameters

• data –

• mcdata –

• weight –

• mc_weight –

Returns

nll_grad_hessian(data, mcdata, weight=1.0, batch=24000, bg=None, mc_weight=1.0)

The parameters are the same with self.nll(), but it will return Hessian as well.

Return NLL

Real number. The value of NLL.

Return gradients

List of real numbers. The gradients for each variable.

Return Hessian

2-D Array of real numbers. The Hessian matrix of the variables.

set_params(var)

It has interface to Amplitude.set_params().

sum_log_integral_grad_batch(mcdata, ndata)

sum_nll_grad_bacth(data)

class Model_new(amp, w_bkg=1.0, w_inmc=0, float_wmc=False)

Bases: Model

This class implements methods to calculate NLL as well as its derivatives for an amplitude model. It may include data for both signal and background.

Parameters

• amp – AllAmplitude object. The amplitude model.

• w_bkg – Real number. The weight of background.

get_weight_data(data, weight=1.0, bg=None, inmc=None, alpha=True)

Blend data and background data together multiplied by their weights.

Parameters

• data – Data array

• weight – Weight for data

• bg – Data array for background

• alpha – Boolean. If it’s true, weight will be multiplied by a factor \(\alpha=\)???

Returns

Data, weight. Their length both equals len(data)+len(bg).

nll(data, mcdata, weight: Tensor = 1.0, batch=None, bg=None)

Calculate NLL.

\[-\ln L = -\sum_{x_i \in data } w_i \ln f(x_i;\theta_k) + (\sum w_j ) \ln \sum_{x_i \in mc } f(x_i;\theta_k)\]

Parameters

• data – Data array

• mcdata – MCdata array

• weight – Weight of data???

• batch – The length of array to calculate as a vector at a time. How to fold the data array may depend on the GPU computability.

• bg – Background data array. It can be set to None if there is no such thing.

Returns

Real number. The value of NLL.

nll_grad_batch(data, mcdata, weight, mc_weight)

self.nll_grad_new

nll_grad_hessian(data, mcdata, weight, mc_weight)

The parameters are the same with self.nll(), but it will return Hessian as well.

Return NLL

Real number. The value of NLL.

Return gradients

List of real numbers. The gradients for each variable.

Return Hessian

2-D Array of real numbers. The Hessian matrix of the variables.

clip_log(x, _epsilon=1e-06)

clip log to allowed large value

get_shape(x)

sum_grad_hessp(f, p, data, var, weight=1.0, trans=<function identity>, resolution_size=1, args=(), kwargs=None)

The parameters are the same with sum_gradient(), but this function will return hessian as well, which is the matrix of the second-order derivative.

Returns

Real number NLL, list gradient, 2-D list hessian

sum_gradient(f, data, var, weight=1.0, trans=<function identity>, resolution_size=1, args=(), kwargs=None)

NLL is the sum of trans(f(data)):math:*`weight; gradient is the derivatives for each variable in ``var`.

Parameters

• f – Function. The amplitude PDF.

• data – Data array

• var – List of strings. Names of the trainable variables in the PDF.

• weight – Weight factor for each data point. It’s either a real number or an array of the same shape with data.

• trans – Function. Transformation of data before multiplied by weight.

• kwargs – Further arguments for f.

Returns

Real number NLL, list gradient

sum_gradient_new(amp, data, mcdata, weight, mcweight, var, trans=<function log>, w_flatmc=<function <lambda>>, args=(), kwargs=None)

NLL is the sum of trans(f(data)):math:*`weight; gradient is the derivatives for each variable in ``var`.

Parameters

• f – Function. The amplitude PDF.

• data – Data array

• var – List of strings. Names of the trainable variables in the PDF.

• weight – Weight factor for each data point. It’s either a real number or an array of the same shape with data.

• trans – Function. Transformation of data before multiplied by weight.

• kwargs – Further arguments for f.

Returns

Real number NLL, list gradient

sum_hessian(f, data, var, weight=1.0, trans=<function identity>, resolution_size=1, args=(), kwargs=None)

The parameters are the same with sum_gradient(), but this function will return hessian as well, which is the matrix of the second-order derivative.

Returns

Real number NLL, list gradient, 2-D list hessian

sum_hessian_new(amp, data, mcdata, weight, mcweight, var, trans=<function log>, w_flatmc=<function <lambda>>, args=(), kwargs=None)

The parameters are the same with sum_gradient(), but this function will return hessian as well, which is the matrix of the second-order derivative.

Returns

Real number NLL, list gradient, 2-D list hessian