from itertools import product
import logging

import numpy as np

from csrank.learner import Learner
import csrank.numpy_util as npu
import csrank.theano_util as ttu
from csrank.util import print_dictionary
from .discrete_choice import DiscreteObjectChooser
from .likelihoods import create_weight_dictionary
from .likelihoods import fit_pymc3_model
from .likelihoods import likelihood_dict
from .likelihoods import LogLikelihood

try:
import pymc3 as pm
from pymc3.variational.callbacks import CheckParametersConvergence
except ImportError:
from csrank.util import MissingExtraError

raise MissingExtraError("pymc3", "probabilistic")

try:
import theano
from theano import tensor as tt
except ImportError:
from csrank.util import MissingExtraError

raise MissingExtraError("theano", "probabilistic")

class MixedLogitModel(DiscreteObjectChooser, Learner):
def __init__(self, n_mixtures=4, loss_function="", regularization="l2", **kwargs):
"""
Create an instance of the Mixed Logit model for learning the discrete choice function. In this model we
assume weights of this model to be random due to which this model can learn different variations in choices
amongst the individuals. The utility score for each object in query set :math:Q is defined as
:math:U_r(x) = w_r \\cdot x, where :math:w_r is the k-th sample weight vector from the underlying distribution
The probability of choosing an object :math:x_i is defined by taking softmax over the
utility scores of the objects:

.. math::

P(x_i \\lvert Q) = \\frac{1}{R} \\sum_{r=1}^R \\frac{exp(U_r(x_i))}{\\sum_{x_j \\in Q} exp(U_r(x_j))}

The discrete choice for the given query set :math:Q is defined as:

.. math::

dc(Q) := \\operatorname{argmax}_{x_i \\in Q }  \\; P(x_i \\lvert Q)

Parameters
----------
n_mixtures: int (range : [2, inf])
The number of logit models (:math:R) which are used to estimate the choice probability
loss_function : string , {‘categorical_crossentropy’, ‘binary_crossentropy’, ’categorical_hinge’}
Loss function to be used for the discrete choice decision from the query set
regularization : string, {‘l1’, ‘l2’}, string
Regularizer function (L1 or L2) applied to the kernel weights matrix
random_state : int or object
Numpy random state
**kwargs
Keyword arguments for the algorithms

References
----------
[1] Kenneth E Train. „Discrete choice methods with simulation“. In: Cambridge university press, 2009. Chap Mixed Logit, pp. 153–172.

[2] Kenneth Train. Qualitative choice analysis. Cambridge, MA: MIT Press, 1986

[3] Daniel McFadden and Kenneth Train. „Mixed MNL models for discrete response“. In: Journal of applied Econometrics 15.5 (2000), pp. 447–470
"""
self.logger = logging.getLogger(MixedLogitModel.__name__)
self.loss_function = loss_function
known_regularization_functions = {"l1", "l2"}
if regularization not in known_regularization_functions:
raise ValueError(
f"Regularization function {regularization} is unknown. Must be one of {known_regularization_functions}"
)
self.regularization = regularization
self._config = None
self.n_mixtures = n_mixtures
self.model = None
self.trace = None
self.trace_vi = None
self.Xt = None
self.Yt = None
self.p = None

@property
def model_configuration(self):
"""
Constructs the dictionary containing the priors for the weight vectors for the model according to the
regularization function. The parameters are:
* **weights** : Distribution of the weigh vectors to evaluates the utility of the objects

For l1 regularization the priors are:

.. math::

\\text{mu}_w \\sim \\text{Normal}(\\text{mu}=0, \\text{sd}=5.0) \\\\
\\text{b}_w \\sim \\text{HalfCauchy}(\\beta=1.0) \\\\
\\text{weights} \\sim \\text{Laplace}(\\text{mu}=\\text{mu}_w, \\text{b}=\\text{b}_w)

For l2 regularization the priors are:

.. math::

\\text{mu}_w \\sim \\text{Normal}(\\text{mu}=0, \\text{sd}=5.0) \\\\
\\text{sd}_w \\sim \\text{HalfCauchy}(\\beta=1.0) \\\\
\\text{weights} \\sim \\text{Normal}(\\text{mu}=\\text{mu}_w, \\text{sd}=\\text{sd}_w)
"""
if self._config is None:
if self.regularization == "l2":
weight = pm.Normal
prior = "sd"
elif self.regularization == "l1":
weight = pm.Laplace
prior = "b"
self._config = {
"weights": [
weight,
{
"mu": (pm.Normal, {"mu": 0, "sd": 5}),
prior: (pm.HalfCauchy, {"beta": 1}),
},
]
}
self.logger.info(
"Creating model with config {}".format(print_dictionary(self._config))
)
return self._config

def construct_model(self, X, Y):
"""
Constructs the mixed logit model by applying priors on weight vectors **weights** as per
:meth:model_configuration. The probability of choosing the object :math:x_i from the query set
:math:Q = \\{x_1, \\ldots ,x_n\\} assuming we draw :math:R samples of the weight vectors is:

.. math::

P(x_i \\lvert Q) = \\frac{1}{R} \\sum_{r=1}^R \\frac{exp(U_r(x_i))}{\\sum_{x_j \\in Q} exp(U_r(x_j))}

Parameters
----------
X : numpy array
(n_instances, n_objects, n_features)
Feature vectors of the objects
Y : numpy array
(n_instances, n_objects)
Preferences in the form of discrete choices for given objects

Returns
-------
model : pymc3 Model :class:pm.Model
"""
self.loss_function_ = likelihood_dict.get(self.loss_function, None)
with pm.Model() as self.model:
self.Xt = theano.shared(X)
self.Yt = theano.shared(Y)
shapes = {"weights": (self.n_object_features_fit_, self.n_mixtures)}
weights_dict = create_weight_dictionary(self.model_configuration, shapes)
utility = tt.dot(self.Xt, weights_dict["weights"])
self.p = tt.mean(ttu.softmax(utility, axis=1), axis=2)
LogLikelihood(
"yl", loss_func=self.loss_function_, p=self.p, observed=self.Yt
)
self.logger.info("Model construction completed")

def fit(
self,
X,
Y,
sampler="variational",
tune=500,
draws=500,
vi_params={
"n": 20000,
"callbacks": [CheckParametersConvergence()],
},
**kwargs,
):
"""
Fit a mixed logit model on the provided set of queries X and choices Y of those objects. The provided
queries and corresponding preferences are of a fixed size (numpy arrays). For learning this network
the categorical cross entropy loss function for each object :math:x_i \\in Q is defined as:

.. math::

C_{i} =  -y(i)\\log(P_i) \\enspace,

where :math:y is ground-truth discrete choice vector of the objects in the given query set :math:Q.
The value :math:y(i) = 1 if object :math:x_i is chosen else :math:y(i) = 0.

Parameters
----------
X : numpy array (n_instances, n_objects, n_features)
Feature vectors of the objects
Y : numpy array (n_instances, n_objects)
Choices for given objects in the query
sampler : {‘variational’, ‘metropolis’, ‘nuts’}, string
The sampler used to estimate the posterior mean and mass matrix from the trace

* **variational** : Run inference methods to estimate posterior mean and diagonal mass matrix
* **metropolis** : Use the MAP as starting point and Metropolis-Hastings sampler
* **nuts** : Use the No-U-Turn sampler
vi_params : dict
The parameters for the **variational** inference method
draws : int
The number of samples to draw. Defaults to 500. The number of tuned samples are discarded by default
tune : int
Number of iterations to tune, defaults to 500. Ignored when using 'SMC'. Samplers adjust
the step sizes, scalings or similar during tuning. Tuning samples will be drawn in addition
to the number specified in the draws argument, and will be discarded unless
discard_tuned_samples is set to False.
**kwargs :
Keyword arguments for the fit function of :meth:pymc3.fitor :meth:pymc3.sample
"""
_n_instances, self.n_objects_fit_, self.n_object_features_fit_ = X.shape
self.construct_model(X, Y)
fit_pymc3_model(self, sampler, draws, tune, vi_params, **kwargs)

def _predict_scores_fixed(self, X, **kwargs):
summary = dict(pm.summary(self.trace)["mean"])
weights = np.zeros((self.n_object_features_fit_, self.n_mixtures))
for i, k in product(range(self.n_object_features_fit_), range(self.n_mixtures)):
weights[i][k] = summary["weights[{},{}]".format(i, k)]
utility = np.dot(X, weights)
p = np.mean(npu.softmax(utility, axis=1), axis=2)
return p

def predict(self, X, **kwargs):
return super().predict(X, **kwargs)

def predict_scores(self, X, **kwargs):
return super().predict_scores(X, **kwargs)

def predict_for_scores(self, scores, **kwargs):
return DiscreteObjectChooser.predict_for_scores(self, scores, **kwargs)

def set_tunable_parameters(
self, n_mixtures=4, loss_function="", regularization="l1", **point
):
"""
Set tunable parameters of the Mixed Logit model to the values provided.

Parameters
----------
n_mixtures: int (range : [2, inf])
The number of logit models (:math:R) which are used to estimate the choice probability
loss_function : string , {‘categorical_crossentropy’, ‘binary_crossentropy’, ’categorical_hinge’}
Loss function to be used for the discrete choice decision from the query set
regularization : string, {‘l1’, ‘l2’}, string
Regularizer function (L1 or L2) applied to the kernel weights matrix
point: dict
Dictionary containing parameter values which are not tuned for the network
"""
if loss_function in likelihood_dict:
self.loss_function = loss_function
self.n_mixtures = n_mixtures
self.regularization = regularization
self.model = None
self.trace = None
self.trace_vi = None
self.Xt = None
self.Yt = None
self.p = None
self._config = None
if len(point) > 0:
self.logger.warning(
"This ranking algorithm does not support"
" tunable parameters called: {}".format(print_dictionary(point))
)