from itertools import combinations
import logging

import numpy as np
from sklearn.utils import check_random_state

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 PairedCombinatorialLogit(DiscreteObjectChooser, Learner):
def __init__(
self,
loss_function="",
regularization="l2",
alpha=5e-2,
random_state=None,
**kwd,
):
"""
Create an instance of the Paired Combinatorial Logit model for learning the discrete choice function. This
model considering each pair of objects as a different nest allowing unique covariances for each pair of objects,
and each object is a member of :math:n - 1 nests. This model structure is 1-layer of hierarchy and the
:math:\\lambda for each nest :math:B_k signifies the degree of independence and  :math:1-\\lambda signifies
the correlations between the object in it. We learn two weight vectors and the  :math:\\lambda s.
* **weights** (:math:w): Weights to get the utility of the object :math:Y_i = U(x_i) = w \\cdot x_i
* **lambda_k** (:math:\\lambda_k): Lambda for nest nest :math:B_k for correlations between the obejcts.

The probability of choosing an object :math:x_i from the given query set :math:Q is defined by product
of choosing the nest in which :math:x_i exists and then choosing the the object from the nest.

.. math::

P(x_i \\lvert Q) = P_i = \\sum_{\\substack{B_k \\in \\mathcal{B} \\ i \\in B_k}}P_{i \\lvert B_k} P_{B_k} \\enspace ,

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_objects: int
Number of objects in each query set
n_nests : int range : [2,n_objects/2]
The number of nests/subsets in which the objects are divided
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
alpha: float (range : [0,1])
The lower bound of the correlations between the objects in a nest
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 GEV, pp. 87–111.

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

[3] Chaushie Chu. „A paired combinatorial logit model for travel demand analysis“. In: Proceedings of the fifth world conference on transportation research. Vol. 4.1989, pp. 295–309
"""
self.logger = logging.getLogger(PairedCombinatorialLogit.__name__)
self.alpha = alpha
self.random_state = random_state
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.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** : Weights 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)

Returns
-------
configuration : dict
Dictionary containing the priors applies on the weights
"""
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 get_probabilities(self, utility, lambda_k):
"""
This method calculates the probability of choosing an object from the query set using the following parameters of the model which are used:

* **weights** (:math:w): Weights to get the utility of the object :math:Y_i = U(x_i) = w \\cdot x_i
* **lambda_k** (:math:\\lambda_k): Lambda is the measure of independence amongst the obejcts in the nest :math:B_k

The probability of choosing the object  :math:x_i from the query set :math:Q:

.. math::
P_i = \\sum_{j \\in I \\setminus i} P_{{i} \\lvert {ij}} P_{ij} \\enspace where, \\\\
P_{i \\lvert ij} = \\frac{\\boldsymbol{e}^{^{Y_i} /_{\\lambda_{ij}}}}{\\boldsymbol{e}^{^{Y_i} /_{\\lambda_{ij}}} + \\boldsymbol{e}^{^{Y_j} /_{\\lambda_{ij}}}} \\enspace ,\\\\
P_{ij} = \\frac{{\\left( \\boldsymbol{e}^{^{V_i}/{\\lambda_{ij}}} + \\boldsymbol{e}^{^{V_j}/{\\lambda_{ij}}}  \\right)}^{\\lambda_{ij}}}{\\sum_{k=1}^{n-1} \\sum_{\\ell = k + 1}^{n} {\\left( \\boldsymbol{e}^{^{V_k}/{\\lambda_{k\\ell}}} + \\boldsymbol{e}^{^{V_{\\ell}}/{\\lambda_{k\\ell}}}  \\right)}^{\\lambda_{k\\ell}}}

Parameters
----------
utility : theano tensor
(n_instances, n_objects)
Utility :math:Y_i of the objects :math:x_i \\in Q in the query sets
lambda_k : theano tensor (range : [alpha, 1.0])
(n_nests)
Measure of independence amongst the obejcts in each nests

Returns
-------
p : theano tensor
(n_instances, n_objects)
Choice probabilities :math:P_i of the objects :math:x_i \\in Q in the query sets

"""
n_objects = self.n_objects_fit_
nests_indices = self.nests_indices
n_nests = self.n_nests
lambdas = tt.ones((n_objects, n_objects), dtype=np.float)
for i, p in enumerate(nests_indices):
r = [p[0], p[1]]
c = [p[1], p[0]]
lambdas = tt.set_subtensor(lambdas[r, c], lambda_k[i])
uti_per_nest = tt.transpose(utility[:, None, :] / lambdas, (0, 2, 1))
ind = np.array([[[i1, i2], [i2, i1]] for i1, i2 in nests_indices])
ind = ind.reshape(2 * n_nests, 2)
x = uti_per_nest[:, ind[:, 0], ind[:, 1]].reshape((-1, 2))
log_sum_exp_nest = ttu.logsumexp(x).reshape((-1, n_nests))
pnk = tt.exp(
log_sum_exp_nest * lambda_k - ttu.logsumexp(log_sum_exp_nest * lambda_k)
)
p = tt.zeros(tuple(utility.shape), dtype=float)
for i in range(n_nests):
i1, i2 = nests_indices[i]
x1 = tt.exp(uti_per_nest[:, i1, i2] - log_sum_exp_nest[:, i]) * pnk[:, i]
x2 = np.exp(uti_per_nest[:, i2, i1] - log_sum_exp_nest[:, i]) * pnk[:, i]
p = tt.set_subtensor(p[:, i1], p[:, i1] + x1)
p = tt.set_subtensor(p[:, i2], p[:, i2] + x2)
return p

def _get_probabilities_np(self, utility, lambda_k):
n_objects = self.n_objects_fit_
nests_indices = self.nests_indices
n_nests = self.n_nests
temp_lambdas = np.ones((n_objects, n_objects), lambda_k.dtype)
temp_lambdas[nests_indices[:, 0], nests_indices[:, 1]] = temp_lambdas.T[
nests_indices[:, 0], nests_indices[:, 1]
] = lambda_k
uti_per_nest = np.transpose((utility[:, None] / temp_lambdas), (0, 2, 1))
ind = np.array([[[i1, i2], [i2, i1]] for i1, i2 in nests_indices])
ind = ind.reshape(2 * n_nests, 2)
x = uti_per_nest[:, ind[:, 0], ind[:, 1]].reshape(-1, 2)
log_sum_exp_nest = npu.logsumexp(x).reshape(-1, n_nests)
pnk = np.exp(
log_sum_exp_nest * lambda_k - npu.logsumexp(log_sum_exp_nest * lambda_k)
)
p = np.zeros(tuple(utility.shape), dtype=float)
for i in range(n_nests):
i1, i2 = nests_indices[i]
p[:, i1] += (
np.exp(uti_per_nest[:, i1, i2] - log_sum_exp_nest[:, i]) * pnk[:, i]
)
p[:, i2] += (
np.exp(uti_per_nest[:, i2, i1] - log_sum_exp_nest[:, i]) * pnk[:, i]
)
return p

def construct_model(self, X, Y):
"""
Constructs the nested logit model by applying priors on weight vectors **weights** as per :meth:model_configuration.
Then we apply a uniform prior to the :math:\\lambda s, i.e. :math:\\lambda s \\sim Uniform(\\text{alpha}, 1.0).
The probability of choosing the object :math:x_i from the query set :math:Q = \\{x_1, \\ldots ,x_n\\} is
evaluated in :meth:get_probabilities.

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_}
weights_dict = create_weight_dictionary(self.model_configuration, shapes)
lambda_k = pm.Uniform("lambda_k", self.alpha, 1.0, shape=self.n_nests)
utility = tt.dot(self.Xt, weights_dict["weights"])
self.p = self.get_probabilities(utility, lambda_k)
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 paired combinatorial 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
"""
self.random_state_ = check_random_state(self.random_state)
_n_instances, self.n_objects_fit_, self.n_object_features_fit_ = X.shape
self.nests_indices = np.array(
list(combinations(np.arange(self.n_objects_fit_), 2))
)
self.n_nests = len(self.nests_indices)
self.construct_model(X, Y)
fit_pymc3_model(self, sampler, draws, tune, vi_params, **kwargs)

def _predict_scores_fixed(self, X, **kwargs):
mean_trace = dict(pm.summary(self.trace)["mean"])
weights = np.array(
[
mean_trace["weights[{}]".format(i)]
for i in range(self.n_object_features_fit_)
]
)
lambda_k = np.array(
[mean_trace["lambda_k[{}]".format(i)] for i in range(self.n_nests)]
)
utility = np.dot(X, weights)
p = self._get_probabilities_np(utility, lambda_k)
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, alpha=5e-2, loss_function=None, regularization="l2", **point
):
"""
Set tunable parameters of the Paired Combinatorial logit model to the values provided.

Parameters
----------
alpha: float (range : [0,1])
The lower bound of the correlations between the objects in a nest
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 alpha is not None:
self.alpha = alpha
if loss_function is not None:
if loss_function not in likelihood_dict:
raise ValueError(
f"Loss function {loss_function} is unknown. Must be one of {set(likelihood_dict.keys())}"
)
self.loss_function = loss_function
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))
)