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SimpleMNL model

Implementation of the simple linear multinomial logit model.

It is a multi output logistic regression.

SimpleMNL

Bases: ChoiceModel

Simple MNL with one linear coefficient to estimate by feature.

Source code in choice_learn/models/simple_mnl.py 
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class SimpleMNL(ChoiceModel):
    """Simple MNL with one linear coefficient to estimate by feature."""

    def __init__(
        self,
        add_exit_choice=False,
        intercept=None,
        optimizer="lbfgs",
        lr=0.001,
        **kwargs,
    ):
        """Initialize of Simple-MNL.

        Parameters
        ----------
        add_exit_choice : bool, optional
            Whether or not to normalize the probabilities computation with an exit choice
            whose utility would be 1, by default True
        intercept: str, optional
            Type of intercept to use, by default None
        optimizer: str
            TensorFlow optimizer to be used for estimation
        lr: float
            Learning Rate to be used with optimizer.
        """
        super().__init__(add_exit_choice=add_exit_choice, optimizer=optimizer, lr=lr, **kwargs)
        self.instantiated = False
        self.intercept = intercept

    def instantiate(self, n_items, n_shared_features, n_items_features):
        """Instantiate the model from ModelSpecification object.

        Parameters
        ----------
        n_items : int
            Number of items/aternatives to consider.
        n_shared_features : int
            Number of contexts features
        n_items_features : int
            Number of contexts items features

        Returns
        -------
        list of tf.Tensor
            List of the weights created coresponding to the specification.
        """
        weights = []
        indexes = {}
        for n_feat, feat_name in zip(
            [n_shared_features, n_items_features],
            ["shared_features", "items_features"],
        ):
            if n_feat > 0:
                weights += [
                    tf.Variable(
                        tf.random_normal_initializer(0.0, 0.02, seed=42)(shape=(n_feat,)),
                        name=f"Weights_{feat_name}",
                    )
                ]
                indexes[feat_name] = len(weights) - 1
        if self.intercept is None:
            logging.info("No intercept in the model")
        elif self.intercept == "item":
            weights.append(
                tf.Variable(
                    tf.random_normal_initializer(0.0, 0.02, seed=42)(shape=(n_items - 1,)),
                    name="Intercept",
                )
            )
            indexes["intercept"] = len(weights) - 1
        elif self.intercept == "item-full":
            logging.info("Simple MNL intercept is not normalized to 0!")
            weights.append(
                tf.Variable(
                    tf.random_normal_initializer(0.0, 0.02, seed=42)(shape=(n_items,)),
                    name="Intercept",
                )
            )
            indexes["intercept"] = len(weights) - 1
        else:
            weights.append(
                tf.Variable(
                    tf.random_normal_initializer(0.0, 0.02, seed=42)(shape=(1,)),
                    name="Intercept",
                )
            )
            indexes["intercept"] = len(weights) - 1

        self.instantiated = True
        self.indexes = indexes
        self._trainable_weights = weights
        return indexes, weights

    @property
    def trainable_weights(self):
        """Trainable weights of the model."""
        return self._trainable_weights

    def compute_batch_utility(
        self,
        shared_features_by_choice,
        items_features_by_choice,
        available_items_by_choice,
        choices,
    ):
        """Compute the utility of the model. Selects the right method to compute.

        Parameters
        ----------
        shared_features_by_choice : tuple of np.ndarray (choices_features)
            a batch of shared features
            Shape must be (n_choices, n_shared_features)
        items_features_by_choice : tuple of np.ndarray (choices_items_features)
            a batch of items features
            Shape must be (n_choices, n_items, n_items_features)
        available_items_by_choice : np.ndarray
            A batch of items availabilities
            Shape must be (n_choices, n_items)
        choices : np.ndarray
            Choices
            Shape must be (n_choices, )

        Returns
        -------
        tf.Tensor
            Computed utilities of shape (n_choices, n_items).
        """
        _ = choices

        if "shared_features" in self.indexes.keys():
            if isinstance(shared_features_by_choice, tuple):
                shared_features_by_choice = tf.concat(*shared_features_by_choice, axis=1)
            shared_features_by_choice = tf.cast(shared_features_by_choice, tf.float32)
            shared_features_utilities = tf.tensordot(
                shared_features_by_choice,
                self.trainable_weights[self.indexes["shared_features"]],
                axes=1,
            )
            shared_features_utilities = tf.expand_dims(shared_features_utilities, axis=-1)
        else:
            shared_features_utilities = 0

        if "items_features" in self.indexes.keys():
            if isinstance(items_features_by_choice, tuple):
                items_features_by_choice = tf.concat([*items_features_by_choice], axis=2)
            items_features_by_choice = tf.cast(items_features_by_choice, tf.float32)
            items_features_utilities = tf.tensordot(
                items_features_by_choice,
                self.trainable_weights[self.indexes["items_features"]],
                axes=1,
            )
        else:
            items_features_utilities = tf.zeros(
                (available_items_by_choice.shape[0], available_items_by_choice.shape[1])
            )

        if "intercept" in self.indexes.keys():
            intercept = self.trainable_weights[self.indexes["intercept"]]
            if self.intercept == "item":
                intercept = tf.concat([tf.constant([0.0]), intercept], axis=0)
            if self.intercept in ["item", "item-full"]:
                intercept = tf.expand_dims(intercept, axis=0)
        else:
            intercept = 0

        return shared_features_utilities + items_features_utilities + intercept

    def fit(self, choice_dataset, get_report=False, **kwargs):
        """Fit to estimate the parameters.

        Parameters
        ----------
        choice_dataset : ChoiceDataset
            Choice dataset to use for the estimation.
        get_report: bool, optional
            Whether or not to compute a report of the estimation, by default False

        Returns
        -------
        dict
            dict with fit history.
        """
        if not self.instantiated:
            # Lazy Instantiation
            self.indexes, self._trainable_weights = self.instantiate(
                n_items=choice_dataset.get_n_items(),
                n_shared_features=choice_dataset.get_n_shared_features(),
                n_items_features=choice_dataset.get_n_items_features(),
            )
            self.instantiated = True
        fit = super().fit(choice_dataset=choice_dataset, **kwargs)
        if get_report:
            self.report = self.compute_report(choice_dataset)
        return fit

    def _fit_with_lbfgs(self, choice_dataset, sample_weight=None, get_report=False, **kwargs):
        """Specific fit function to estimate the parameters with LBFGS.

        Parameters
        ----------
        choice_dataset : ChoiceDataset
            Choice dataset to use for the estimation.
        n_epochs : int
            Number of epochs to run.
        sample_weight: Iterable, optional
            list of each sample weight, by default None meaning that all samples have weight 1.
        get_report: bool, optional
            Whether or not to compute a report of the estimation, by default False.

        Returns
        -------
        dict
            dict with fit history.
        """
        if not self.instantiated:
            # Lazy Instantiation
            self.indexes, self._trainable_weights = self.instantiate(
                n_items=choice_dataset.get_n_items(),
                n_shared_features=choice_dataset.get_n_shared_features(),
                n_items_features=choice_dataset.get_n_items_features(),
            )
            self.instantiated = True
        fit = super()._fit_with_lbfgs(
            choice_dataset=choice_dataset, sample_weight=sample_weight, **kwargs
        )
        if get_report:
            self.report = self.compute_report(choice_dataset)
        return fit

    def compute_report(self, choice_dataset):
        """Compute a report of the estimated weights.

        Parameters
        ----------
        choice_dataset : ChoiceDataset
            ChoiceDataset used for the estimation of the weights that will be
            used to compute the Std Err of this estimation.

        Returns
        -------
        pandas.DataFrame
            A DF with estimation, Std Err, z_value and p_value for each coefficient.
        """

        def phi(x):
            """Cumulative distribution function for the standard normal distribution."""
            return (1.0 + math.erf(x / math.sqrt(2.0))) / 2.0

        weights_std = self.get_weights_std(choice_dataset)

        names = []
        z_values = []
        estimations = []
        p_z = []
        i = 0
        for weight in self.trainable_weights:
            for j in range(weight.shape[0]):
                if weight.shape[0] > 1:
                    names.append(f"{weight.name[:-2]}_{j}")
                else:
                    names.append(f"{weight.name[:-2]}")
                estimations.append(weight.numpy()[j])
                z_values.append(weight.numpy()[j] / weights_std[i].numpy())
                p_z.append(2 * (1 - phi(tf.math.abs(z_values[-1]).numpy())))
                i += 1

        return pd.DataFrame(
            {
                "Coefficient Name": names,
                "Coefficient Estimation": estimations,
                "Std. Err": weights_std.numpy(),
                "z_value": z_values,
                "P(.>z)": p_z,
            },
        )

    def get_weights_std(self, choice_dataset):
        """Approximates Std Err with Hessian matrix.

        Parameters
        ----------
        choice_dataset : ChoiceDataset
            ChoiceDataset used for the estimation of the weights that will be
            used to compute the Std Err of this estimation.

        Returns
        -------
        tf.Tensor
            Estimation of the Std Err for the weights.
        """
        # Loops of differentiation
        with tf.GradientTape() as tape_1:
            with tf.GradientTape(persistent=True) as tape_2:
                model = self.clone()
                w = tf.concat(self.trainable_weights, axis=0)
                tape_2.watch(w)
                tape_1.watch(w)
                mw = []
                index = 0
                for _w in self.trainable_weights:
                    mw.append(w[index : index + _w.shape[0]])
                    index += _w.shape[0]
                model._trainable_weights = mw
                for batch in choice_dataset.iter_batch(batch_size=-1):
                    utilities = model.compute_batch_utility(*batch)
                    probabilities = tf.nn.softmax(utilities, axis=-1)
                    loss = tf.keras.losses.CategoricalCrossentropy(reduction="sum")(
                        y_pred=probabilities,
                        y_true=tf.one_hot(choice_dataset.choices, depth=probabilities.shape[-1]),
                    )
            # Compute the Jacobian
            jacobian = tape_2.jacobian(loss, w)
        # Compute the Hessian from the Jacobian
        hessian = tape_1.jacobian(jacobian, w)
        hessian = tf.linalg.inv(tf.squeeze(hessian))
        return tf.sqrt([hessian[i][i] for i in range(len(tf.squeeze(hessian)))])

    def clone(self):
        """Return a clone of the model."""
        clone = SimpleMNL(
            add_exit_choice=self.add_exit_choice,
            optimizer=self.optimizer_name,
        )
        if hasattr(self, "history"):
            clone.history = self.history
        if hasattr(self, "is_fitted"):
            clone.is_fitted = self.is_fitted
        if hasattr(self, "instantiated"):
            clone.instantiated = self.instantiated
        clone.loss = self.loss
        clone.label_smoothing = self.label_smoothing
        if hasattr(self, "report"):
            clone.report = self.report
        if hasattr(self, "trainable_weights"):
            clone._trainable_weights = self.trainable_weights
        if hasattr(self, "indexes"):
            clone.indexes = self.indexes
        if hasattr(self, "intercept"):
            clone.intercept = self.intercept
        if hasattr(self, "lr"):
            clone.lr = self.lr
        if hasattr(self, "_items_features_names"):
            clone._items_features_names = self._items_features_names
        if hasattr(self, "_shared_features_names"):
            clone._shared_features_names = self._shared_features_names
        return clone

trainable_weights property

Trainable weights of the model.

__init__(add_exit_choice=False, intercept=None, optimizer='lbfgs', lr=0.001, **kwargs)

Initialize of Simple-MNL.

Parameters:

Name Type Description Default
add_exit_choice bool

Whether or not to normalize the probabilities computation with an exit choice whose utility would be 1, by default True

 False
intercept

Type of intercept to use, by default None

 None
optimizer

TensorFlow optimizer to be used for estimation

 'lbfgs'
lr

Learning Rate to be used with optimizer.

 0.001
Source code in choice_learn/models/simple_mnl.py 
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def __init__(
    self,
    add_exit_choice=False,
    intercept=None,
    optimizer="lbfgs",
    lr=0.001,
    **kwargs,
):
    """Initialize of Simple-MNL.

    Parameters
    ----------
    add_exit_choice : bool, optional
        Whether or not to normalize the probabilities computation with an exit choice
        whose utility would be 1, by default True
    intercept: str, optional
        Type of intercept to use, by default None
    optimizer: str
        TensorFlow optimizer to be used for estimation
    lr: float
        Learning Rate to be used with optimizer.
    """
    super().__init__(add_exit_choice=add_exit_choice, optimizer=optimizer, lr=lr, **kwargs)
    self.instantiated = False
    self.intercept = intercept

clone()

Return a clone of the model.

Source code in choice_learn/models/simple_mnl.py 
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def clone(self):
    """Return a clone of the model."""
    clone = SimpleMNL(
        add_exit_choice=self.add_exit_choice,
        optimizer=self.optimizer_name,
    )
    if hasattr(self, "history"):
        clone.history = self.history
    if hasattr(self, "is_fitted"):
        clone.is_fitted = self.is_fitted
    if hasattr(self, "instantiated"):
        clone.instantiated = self.instantiated
    clone.loss = self.loss
    clone.label_smoothing = self.label_smoothing
    if hasattr(self, "report"):
        clone.report = self.report
    if hasattr(self, "trainable_weights"):
        clone._trainable_weights = self.trainable_weights
    if hasattr(self, "indexes"):
        clone.indexes = self.indexes
    if hasattr(self, "intercept"):
        clone.intercept = self.intercept
    if hasattr(self, "lr"):
        clone.lr = self.lr
    if hasattr(self, "_items_features_names"):
        clone._items_features_names = self._items_features_names
    if hasattr(self, "_shared_features_names"):
        clone._shared_features_names = self._shared_features_names
    return clone

compute_batch_utility(shared_features_by_choice, items_features_by_choice, available_items_by_choice, choices)

Compute the utility of the model. Selects the right method to compute.

Parameters:

Name Type Description Default
shared_features_by_choice tuple of np.ndarray (choices_features)

a batch of shared features Shape must be (n_choices, n_shared_features)

 required
items_features_by_choice tuple of np.ndarray (choices_items_features)

a batch of items features Shape must be (n_choices, n_items, n_items_features)

 required
available_items_by_choice ndarray

A batch of items availabilities Shape must be (n_choices, n_items)

 required
choices ndarray

Choices Shape must be (n_choices, )

 required

Returns:

Type Description
Tensor

Computed utilities of shape (n_choices, n_items).
Source code in choice_learn/models/simple_mnl.py 
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def compute_batch_utility(
    self,
    shared_features_by_choice,
    items_features_by_choice,
    available_items_by_choice,
    choices,
):
    """Compute the utility of the model. Selects the right method to compute.

    Parameters
    ----------
    shared_features_by_choice : tuple of np.ndarray (choices_features)
        a batch of shared features
        Shape must be (n_choices, n_shared_features)
    items_features_by_choice : tuple of np.ndarray (choices_items_features)
        a batch of items features
        Shape must be (n_choices, n_items, n_items_features)
    available_items_by_choice : np.ndarray
        A batch of items availabilities
        Shape must be (n_choices, n_items)
    choices : np.ndarray
        Choices
        Shape must be (n_choices, )

    Returns
    -------
    tf.Tensor
        Computed utilities of shape (n_choices, n_items).
    """
    _ = choices

    if "shared_features" in self.indexes.keys():
        if isinstance(shared_features_by_choice, tuple):
            shared_features_by_choice = tf.concat(*shared_features_by_choice, axis=1)
        shared_features_by_choice = tf.cast(shared_features_by_choice, tf.float32)
        shared_features_utilities = tf.tensordot(
            shared_features_by_choice,
            self.trainable_weights[self.indexes["shared_features"]],
            axes=1,
        )
        shared_features_utilities = tf.expand_dims(shared_features_utilities, axis=-1)
    else:
        shared_features_utilities = 0

    if "items_features" in self.indexes.keys():
        if isinstance(items_features_by_choice, tuple):
            items_features_by_choice = tf.concat([*items_features_by_choice], axis=2)
        items_features_by_choice = tf.cast(items_features_by_choice, tf.float32)
        items_features_utilities = tf.tensordot(
            items_features_by_choice,
            self.trainable_weights[self.indexes["items_features"]],
            axes=1,
        )
    else:
        items_features_utilities = tf.zeros(
            (available_items_by_choice.shape[0], available_items_by_choice.shape[1])
        )

    if "intercept" in self.indexes.keys():
        intercept = self.trainable_weights[self.indexes["intercept"]]
        if self.intercept == "item":
            intercept = tf.concat([tf.constant([0.0]), intercept], axis=0)
        if self.intercept in ["item", "item-full"]:
            intercept = tf.expand_dims(intercept, axis=0)
    else:
        intercept = 0

    return shared_features_utilities + items_features_utilities + intercept

compute_report(choice_dataset)

Compute a report of the estimated weights.

Parameters:

Name Type Description Default
choice_dataset ChoiceDataset

ChoiceDataset used for the estimation of the weights that will be used to compute the Std Err of this estimation.

 required

Returns:

Type Description
DataFrame

A DF with estimation, Std Err, z_value and p_value for each coefficient.
Source code in choice_learn/models/simple_mnl.py 
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def compute_report(self, choice_dataset):
    """Compute a report of the estimated weights.

    Parameters
    ----------
    choice_dataset : ChoiceDataset
        ChoiceDataset used for the estimation of the weights that will be
        used to compute the Std Err of this estimation.

    Returns
    -------
    pandas.DataFrame
        A DF with estimation, Std Err, z_value and p_value for each coefficient.
    """

    def phi(x):
        """Cumulative distribution function for the standard normal distribution."""
        return (1.0 + math.erf(x / math.sqrt(2.0))) / 2.0

    weights_std = self.get_weights_std(choice_dataset)

    names = []
    z_values = []
    estimations = []
    p_z = []
    i = 0
    for weight in self.trainable_weights:
        for j in range(weight.shape[0]):
            if weight.shape[0] > 1:
                names.append(f"{weight.name[:-2]}_{j}")
            else:
                names.append(f"{weight.name[:-2]}")
            estimations.append(weight.numpy()[j])
            z_values.append(weight.numpy()[j] / weights_std[i].numpy())
            p_z.append(2 * (1 - phi(tf.math.abs(z_values[-1]).numpy())))
            i += 1

    return pd.DataFrame(
        {
            "Coefficient Name": names,
            "Coefficient Estimation": estimations,
            "Std. Err": weights_std.numpy(),
            "z_value": z_values,
            "P(.>z)": p_z,
        },
    )

fit(choice_dataset, get_report=False, **kwargs)

Fit to estimate the parameters.

Parameters:

Name Type Description Default
choice_dataset ChoiceDataset

Choice dataset to use for the estimation.

 required
get_report

Whether or not to compute a report of the estimation, by default False

 False

Returns:

Type Description
dict

dict with fit history.
Source code in choice_learn/models/simple_mnl.py 
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def fit(self, choice_dataset, get_report=False, **kwargs):
    """Fit to estimate the parameters.

    Parameters
    ----------
    choice_dataset : ChoiceDataset
        Choice dataset to use for the estimation.
    get_report: bool, optional
        Whether or not to compute a report of the estimation, by default False

    Returns
    -------
    dict
        dict with fit history.
    """
    if not self.instantiated:
        # Lazy Instantiation
        self.indexes, self._trainable_weights = self.instantiate(
            n_items=choice_dataset.get_n_items(),
            n_shared_features=choice_dataset.get_n_shared_features(),
            n_items_features=choice_dataset.get_n_items_features(),
        )
        self.instantiated = True
    fit = super().fit(choice_dataset=choice_dataset, **kwargs)
    if get_report:
        self.report = self.compute_report(choice_dataset)
    return fit

get_weights_std(choice_dataset)

Approximates Std Err with Hessian matrix.

Parameters:

Name Type Description Default
choice_dataset ChoiceDataset

ChoiceDataset used for the estimation of the weights that will be used to compute the Std Err of this estimation.

 required

Returns:

Type Description
Tensor

Estimation of the Std Err for the weights.
Source code in choice_learn/models/simple_mnl.py 
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def get_weights_std(self, choice_dataset):
    """Approximates Std Err with Hessian matrix.

    Parameters
    ----------
    choice_dataset : ChoiceDataset
        ChoiceDataset used for the estimation of the weights that will be
        used to compute the Std Err of this estimation.

    Returns
    -------
    tf.Tensor
        Estimation of the Std Err for the weights.
    """
    # Loops of differentiation
    with tf.GradientTape() as tape_1:
        with tf.GradientTape(persistent=True) as tape_2:
            model = self.clone()
            w = tf.concat(self.trainable_weights, axis=0)
            tape_2.watch(w)
            tape_1.watch(w)
            mw = []
            index = 0
            for _w in self.trainable_weights:
                mw.append(w[index : index + _w.shape[0]])
                index += _w.shape[0]
            model._trainable_weights = mw
            for batch in choice_dataset.iter_batch(batch_size=-1):
                utilities = model.compute_batch_utility(*batch)
                probabilities = tf.nn.softmax(utilities, axis=-1)
                loss = tf.keras.losses.CategoricalCrossentropy(reduction="sum")(
                    y_pred=probabilities,
                    y_true=tf.one_hot(choice_dataset.choices, depth=probabilities.shape[-1]),
                )
        # Compute the Jacobian
        jacobian = tape_2.jacobian(loss, w)
    # Compute the Hessian from the Jacobian
    hessian = tape_1.jacobian(jacobian, w)
    hessian = tf.linalg.inv(tf.squeeze(hessian))
    return tf.sqrt([hessian[i][i] for i in range(len(tf.squeeze(hessian)))])

instantiate(n_items, n_shared_features, n_items_features)

Instantiate the model from ModelSpecification object.

Parameters:

Name Type Description Default
n_items int

Number of items/aternatives to consider.

 required
n_shared_features int

Number of contexts features

 required
n_items_features int

Number of contexts items features

 required

Returns:

Type Description
list of tf.Tensor

List of the weights created coresponding to the specification.
Source code in choice_learn/models/simple_mnl.py 
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def instantiate(self, n_items, n_shared_features, n_items_features):
    """Instantiate the model from ModelSpecification object.

    Parameters
    ----------
    n_items : int
        Number of items/aternatives to consider.
    n_shared_features : int
        Number of contexts features
    n_items_features : int
        Number of contexts items features

    Returns
    -------
    list of tf.Tensor
        List of the weights created coresponding to the specification.
    """
    weights = []
    indexes = {}
    for n_feat, feat_name in zip(
        [n_shared_features, n_items_features],
        ["shared_features", "items_features"],
    ):
        if n_feat > 0:
            weights += [
                tf.Variable(
                    tf.random_normal_initializer(0.0, 0.02, seed=42)(shape=(n_feat,)),
                    name=f"Weights_{feat_name}",
                )
            ]
            indexes[feat_name] = len(weights) - 1
    if self.intercept is None:
        logging.info("No intercept in the model")
    elif self.intercept == "item":
        weights.append(
            tf.Variable(
                tf.random_normal_initializer(0.0, 0.02, seed=42)(shape=(n_items - 1,)),
                name="Intercept",
            )
        )
        indexes["intercept"] = len(weights) - 1
    elif self.intercept == "item-full":
        logging.info("Simple MNL intercept is not normalized to 0!")
        weights.append(
            tf.Variable(
                tf.random_normal_initializer(0.0, 0.02, seed=42)(shape=(n_items,)),
                name="Intercept",
            )
        )
        indexes["intercept"] = len(weights) - 1
    else:
        weights.append(
            tf.Variable(
                tf.random_normal_initializer(0.0, 0.02, seed=42)(shape=(1,)),
                name="Intercept",
            )
        )
        indexes["intercept"] = len(weights) - 1

    self.instantiated = True
    self.indexes = indexes
    self._trainable_weights = weights
    return indexes, weights