# Methods - HLT-ISTI/QuaPy GitHub Wiki

# Quantification Methods

Quantification methods can be categorized as belonging to
`aggregative`

and `non-aggregative`

groups.
Most methods included in QuaPy at the moment are of type `aggregative`

(though we plan to add many more methods in the near future), i.e.,
are methods characterized by the fact that
quantification is performed as an aggregation function of the individual
products of classification.

Any quantifier in QuaPy shoud extend the class `BaseQuantifier`

,
and implement some abstract methods:

```
@abstractmethod
def fit(self, data: LabelledCollection): ...
@abstractmethod
def quantify(self, instances): ...
```

The meaning of those functions should be familiar to those
used to work with scikit-learn since the class structure of QuaPy
is directly inspired by scikit-learn's *Estimators*. Functions
`fit`

and `quantify`

are used to train the model and to provide
class estimations (the reason why
scikit-learn' structure has not been adopted *as is* in QuaPy responds to
the fact that scikit-learn's `predict`

function is expected to return
one output for each input element --e.g., a predicted label for each
instance in a sample-- while in quantification the output for a sample
is one single array of class prevalences).
Quantifiers also extend from scikit-learn's `BaseEstimator`

, in order
to simplify the use of `set_params`

and `get_params`

used in
model selector.

## Aggregative Methods

All quantification methods are implemented as part of the
`qp.method`

package. In particular, `aggregative`

methods are defined in
`qp.method.aggregative`

, and extend `AggregativeQuantifier(BaseQuantifier)`

.
The methods that any `aggregative`

quantifier must implement are:

```
@abstractmethod
def aggregation_fit(self, classif_predictions: LabelledCollection, data: LabelledCollection):
@abstractmethod
def aggregate(self, classif_predictions:np.ndarray): ...
```

These two functions replace the `fit`

and `quantify`

methods, since those
come with default implementations. The `fit`

function is provided and amounts to:

```
def fit(self, data: LabelledCollection, fit_classifier=True, val_split=None):
self._check_init_parameters()
classif_predictions = self.classifier_fit_predict(data, fit_classifier, predict_on=val_split)
self.aggregation_fit(classif_predictions, data)
return self
```

Note that this function fits the classifier, and generates the predictions. This is assumed
to be a routine common to all aggregative quantifiers, and is provided by QuaPy. What remains
ahead is to define the `aggregation_fit`

function, that takes as input the classifier predictions
and the original training data (this latter is typically unused). The classifier predictions
can be:

- confidence scores: quantifiers inheriting directly from
`AggregativeQuantifier`

- crips predictions: quantifiers inheriting from
`AggregativeCrispQuantifier`

- posterior probabilities: quantifiers inheriting from
`AggregativeSoftQuantifier`

*anything*: custom quantifiers overriding the`classify`

method

Note also that the `fit`

method also calls `_check_init_parameters`

; this function is meant to be
overriden (if needed) and allows the method to quickly raise any exception based on any inconsistency
found in the `__init__`

arguments, thus avoiding to break after training the classifier and generating
predictions.

Similarly, the function `quantify`

is provided, and amounts to:

```
def quantify(self, instances):
classif_predictions = self.classify(instances)
return self.aggregate(classif_predictions)
```

in which only the function `aggregate`

is required to be overriden in most cases.

Aggregative quantifiers are expected to maintain a classifier (which is
accessed through the `@property`

`classifier`

). This classifier is
given as input to the quantifier, and can be already fit
on external data (in which case, the `fit_learner`

argument should
be set to False), or be fit by the quantifier's fit (default).

The above patterns (in training: fit the classifier, then fit the aggregation;
in test: classify, then aggregate) allows QuaPy to optimize many internal procedures.
In particular, the model selection routing takes advantage of this two-step process
and generates classifiers only for the valid combinations of hyperparameters of the
classifier, and then *clones* these classifiers and explores the combinations
of hyperparameters that are specific to the quantifier (this can result in huge
time savings).
Concerning the inference phase, this two-step process allow the evaluation of many
standard protocols (e.g., the artificial sampling protocol) to be
carried out very efficiently. The reason is that the entire set can be pre-classified
once, and the quantification estimations for different samples can directly
reuse these predictions, without requiring to classify each element every time.
QuaPy leverages this property to speed-up any procedure having to do with
quantification over samples, as is customarily done in model selection or
in evaluation.

### The Classify & Count variants

QuaPy implements the four CC variants, i.e.:

*CC*(Classify & Count), the simplest aggregative quantifier; one that simply relies on the label predictions of a classifier to deliver class estimates.*ACC*(Adjusted Classify & Count), the adjusted variant of CC.*PCC*(Probabilistic Classify & Count), the probabilistic variant of CC that relies on the soft estimations (or posterior probabilities) returned by a (probabilistic) classifier.*PACC*(Probabilistic Adjusted Classify & Count), the adjusted variant of PCC.

The following code serves as a complete example using CC equipped with a SVM as the classifier:

```
import quapy as qp
import quapy.functional as F
from sklearn.svm import LinearSVC
training, test = qp.datasets.fetch_twitter('hcr', pickle=True).train_test
# instantiate a classifier learner, in this case a SVM
svm = LinearSVC()
# instantiate a Classify & Count with the SVM
# (an alias is available in qp.method.aggregative.ClassifyAndCount)
model = qp.method.aggregative.CC(svm)
model.fit(training)
estim_prevalence = model.quantify(test.instances)
```

The same code could be used to instantiate an ACC, by simply replacing the instantiation of the model with:

```
model = qp.method.aggregative.ACC(svm)
```

Note that the adjusted variants (ACC and PACC) need to estimate
some parameters for performing the adjustment (e.g., the
*true positive rate* and the *false positive rate* in case of
binary classification) that are estimated on a validation split
of the labelled set. In this case, the `__init__`

method of
ACC defines an additional parameter, `val_split`

. If this parameter
is set to a float in [0,1] representing a fraction (e.g., 0.4)
then that fraction of labelled data (e.g., 40%)
will be used for estimating the parameters for adjusting the
predictions. This parameters can also be set with an integer,
indicating that the parameters should be estimated by means of
*k*-fold cross-validation, for which the integer indicates the
number *k* of folds (the default value is 5). Finally, `val_split`

can be set to a
specific held-out validation set (i.e., an instance of `LabelledCollection`

).

The specification of `val_split`

can be
postponed to the invokation of the fit method (if `val_split`

was also
set in the constructor, the one specified at fit time would prevail),
e.g.:

```
model = qp.method.aggregative.ACC(svm)
# perform 5-fold cross validation for estimating ACC's parameters
# (overrides the default val_split=0.4 in the constructor)
model.fit(training, val_split=5)
```

The following code illustrates the case in which PCC is used:

```
model = qp.method.aggregative.PCC(svm)
model.fit(training)
estim_prevalence = model.quantify(test.instances)
print('classifier:', model.classifier)
```

In this case, QuaPy will print:

```
The learner LinearSVC does not seem to be probabilistic. The learner will be calibrated.
classifier: CalibratedClassifierCV(base_estimator=LinearSVC(), cv=5)
```

The first output indicates that the learner (`LinearSVC`

in this case)
is not a probabilistic classifier (i.e., it does not implement the
`predict_proba`

method) and so, the classifier will be converted to
a probabilistic one through calibration.
As a result, the classifier that is printed in the second line points
to a `CalibratedClassifier`

instance. Note that calibration can only
be applied to hard classifiers when `fit_learner=True`

; an exception
will be raised otherwise.

Lastly, everything we said aboud ACC and PCC applies to PACC as well.

*New in v0.1.8*: quantifiers ACC and PACC now have one additional argument
in the constructor: `solver`

, that specifies how to resolve the adjustment problem.
The options are `exact`

, which tries to solve the system of linear equations
(as originally proposed), and `minimize`

, which instead tries to minimize a loss
function. The latter to yield better results in cases in which
the misclassification rate matrix is ill-defined (see
Bunse, M. "On Multi-Class Extensions of Adjusted Classify and Count",
on proceedings of the 2nd International Workshop on Learning to Quantify: Methods and Applications (LQ 2022),
ECML/PKDD 2022, Grenoble (France))
and has become the default behavior in QuaPy.

### Expectation Maximization (EMQ)

The Expectation Maximization Quantifier (EMQ), also known as
the SLD, is available at `qp.method.aggregative.EMQ`

or via the
alias `qp.method.aggregative.ExpectationMaximizationQuantifier`

.
The method is described in:

*Saerens, M., Latinne, P., and Decaestecker, C. (2002). Adjusting the outputs of a classifier
to new a priori probabilities: A simple procedure. Neural Computation, 14(1):21–41.*

EMQ works with a probabilistic classifier (if the classifier given as input is a hard one, a calibration will be attempted). Although this method was originally proposed for improving the posterior probabilities of a probabilistic classifier, and not for improving the estimation of prior probabilities, EMQ ranks almost always among the most effective quantifiers in the experiments we have carried out.

An example of use can be found below:

```
import quapy as qp
from sklearn.linear_model import LogisticRegression
dataset = qp.datasets.fetch_twitter('hcr', pickle=True)
model = qp.method.aggregative.EMQ(LogisticRegression())
model.fit(dataset.training)
estim_prevalence = model.quantify(dataset.test.instances)
```

*New in v0.1.7*: EMQ now accepts two new parameters in the construction method, namely
`exact_train_prev`

which allows to use the true training prevalence as the departing
prevalence estimation (default behaviour), or instead an approximation of it as
suggested by Alexandari et al. (2020)
(by setting `exact_train_prev=False`

).
The other parameter is `recalib`

which allows to indicate a calibration method, among those
proposed by Alexandari et al. (2020),
including the Bias-Corrected Temperature Scaling, Vector Scaling, etc.
See the API documentation for further details.

### Hellinger Distance y (HDy)

Implementation of the method based on the Hellinger Distance y (HDy) proposed by González-Castro, V., Alaiz-Rodrı́guez, R., and Alegre, E. (2013). Class distribution estimation based on the Hellinger distance. Information Sciences, 218:146–164.

It is implemented in `qp.method.aggregative.HDy`

(also accessible
through the allias `qp.method.aggregative.HellingerDistanceY`

).
This method works with a probabilistic classifier (hard classifiers
can be used as well and will be calibrated) and requires a validation
set to estimate parameter for the mixture model. Just like
ACC and PACC, this quantifier receives a `val_split`

argument
in the constructor (or in the fit method, in which case the previous
value is overridden) that can either be a float indicating the proportion
of training data to be taken as the validation set (in a random
stratified split), or a validation set (i.e., an instance of
`LabelledCollection`

) itself.

HDy was proposed as a binary classifier and the implementation provided in QuaPy accepts only binary datasets.

The following code shows an example of use:

```
import quapy as qp
from sklearn.linear_model import LogisticRegression
# load a binary dataset
dataset = qp.datasets.fetch_reviews('hp', pickle=True)
qp.data.preprocessing.text2tfidf(dataset, min_df=5, inplace=True)
model = qp.method.aggregative.HDy(LogisticRegression())
model.fit(dataset.training)
estim_prevalence = model.quantify(dataset.test.instances)
```

*New in v0.1.7:* QuaPy now provides an implementation of the generalized
"Distribution Matching" approaches for multiclass, inspired by the framework
of Firat (2016). One can instantiate
a variant of HDy for multiclass quantification as follows:

```
mutliclassHDy = qp.method.aggregative.DMy(classifier=LogisticRegression(), divergence='HD', cdf=False)
```

*New in v0.1.7:* QuaPy now provides an implementation of the "DyS"
framework proposed by Maletzke et al (2020)
and the "SMM" method proposed by Hassan et al (2019)
(thanks to *Pablo González* for the contributions!)

### Threshold Optimization methods

*New in v0.1.7:* QuaPy now implements Forman's threshold optimization methods;
see, e.g., (Forman 2006)
and (Forman 2008).
These include: T50, MAX, X, Median Sweep (MS), and its variant MS2.

### Explicit Loss Minimization

The Explicit Loss Minimization (ELM) represent a family of methods based on structured output learning, i.e., quantifiers relying on classifiers that have been optimized targeting a quantification-oriented evaluation measure. The original methods are implemented in QuaPy as classify & count (CC) quantifiers that use Joachim's SVMperf as the underlying classifier, properly set to optimize for the desired loss.

In QuaPy, this can be more achieved by calling the functions:

`newSVMQ`

: returns the quantification method called SVM(Q) that optimizes for the metric*Q*defined in*Barranquero, J., Díez, J., and del Coz, J. J. (2015). Quantification-oriented learning based on reliable classifiers. Pattern Recognition, 48(2):591–604.*`newSVMKLD`

and`newSVMNKLD`

: returns the quantification method called SVM(KLD) and SVM(nKLD), standing for Kullback-Leibler Divergence and Normalized Kullback-Leibler Divergence, as proposed in*Esuli, A. and Sebastiani, F. (2015). Optimizing text quantifiers for multivariate loss functions. ACM Transactions on Knowledge Discovery and Data, 9(4):Article 27.*`newSVMAE`

and`newSVMRAE`

: returns a quantification method called SVM(AE) and SVM(RAE) that optimizes for the (Mean) Absolute Error and for the (Mean) Relative Absolute Error, as first used by*Moreo, A. and Sebastiani, F. (2021). Tweet sentiment quantification: An experimental re-evaluation. PLOS ONE 17 (9), 1-23.*

the last two methods (SVM(AE) and SVM(RAE)) have been implemented in QuaPy in order to make available ELM variants for what nowadays are considered the most well-behaved evaluation metrics in quantification.

In order to make these models work, you would need to run the script
`prepare_svmperf.sh`

(distributed along with QuaPy) that
downloads `SVMperf`

' source code, applies a patch that
implements the quantification oriented losses, and compiles the
sources.

If you want to add any custom loss, you would need to modify
the source code of `SVMperf`

in order to implement it, and
assign a valid loss code to it. Then you must re-compile
the whole thing and instantiate the quantifier in QuaPy
as follows:

```
# you can either set the path to your custom svm_perf_quantification implementation
# in the environment variable, or as an argument to the constructor of ELM
qp.environ['SVMPERF_HOME'] = './path/to/svm_perf_quantification'
# assign an alias to your custom loss and the id you have assigned to it
svmperf = qp.classification.svmperf.SVMperf
svmperf.valid_losses['mycustomloss'] = 28
# instantiate the ELM method indicating the loss
model = qp.method.aggregative.ELM(loss='mycustomloss')
```

All ELM are binary quantifiers since they rely on `SVMperf`

, that
currently supports only binary classification.
ELM variants (any binary quantifier in general) can be extended
to operate in single-label scenarios trivially by adopting a
"one-vs-all" strategy (as, e.g., in
*Gao, W. and Sebastiani, F. (2016). From classification to quantification in tweet sentiment
analysis. Social Network Analysis and Mining, 6(19):1–22*).
In QuaPy this is possible by using the `OneVsAll`

class.

There are two ways for instantiating this class, `OneVsAllGeneric`

that works for
any quantifier, and `OneVsAllAggregative`

that is optimized for aggregative quantifiers.
In general, you can simply use the `newOneVsAll`

function and QuaPy will choose
the more convenient of the two.

```
import quapy as qp
from quapy.method.aggregative import SVMQ
# load a single-label dataset (this one contains 3 classes)
dataset = qp.datasets.fetch_twitter('hcr', pickle=True)
# let qp know where svmperf is
qp.environ['SVMPERF_HOME'] = '../svm_perf_quantification'
model = newOneVsAll(SVMQ(), n_jobs=-1) # run them on parallel
model.fit(dataset.training)
estim_prevalence = model.quantify(dataset.test.instances)
```

Check the examples *explicit_loss_minimization.py*
and one_vs_all.py for more details.

### Kernel Density Estimation methods (KDEy)

*New in v0.1.8*: QuaPy now provides implementations for the three variants
of KDE-based methods proposed in
*Moreo, A., González, P. and del Coz, J.J., 2023.
Kernel Density Estimation for Multiclass Quantification.
arXiv preprint arXiv:2401.00490.*.
The variants differ in the divergence metric to be minimized:

- KDEy-HD: minimizes the (squared) Hellinger Distance and solves the problem via a Monte Carlo approach
- KDEy-CS: minimizes the Cauchy-Schwarz divergence and solves the problem via a closed-form solution
- KDEy-ML: minimizes the Kullback-Leibler divergence and solves the problem via maximum-likelihood

These methods are specifically devised for multiclass problems (although they can tackle binary problems too).

All KDE-based methods depend on the hyperparameter `bandwidth`

of the kernel. Typical values
that can be explored in model selection range in [0.01, 0.25]. The methods' performance
vary smoothing with smooth variations of this hyperparameter.

## Meta Models

By *meta* models we mean quantification methods that are defined on top of other
quantification methods, and that thus do not squarely belong to the aggregative nor
the non-aggregative group (indeed, *meta* models could use quantifiers from any of those
groups).
*Meta* models are implemented in the `qp.method.meta`

module.

### Ensembles

QuaPy implements (some of) the variants proposed in:

*Pérez-Gállego, P., Quevedo, J. R., & del Coz, J. J. (2017). Using ensembles for problems with characterizable changes in data distribution: A case study on quantification. Information Fusion, 34, 87-100.**Pérez-Gállego, P., Castano, A., Quevedo, J. R., & del Coz, J. J. (2019). Dynamic ensemble selection for quantification tasks. Information Fusion, 45, 1-15.*

The following code shows how to instantiate an Ensemble of 30 *Adjusted Classify & Count* (ACC)
quantifiers operating with a *Logistic Regressor* (LR) as the base classifier, and using the
*average* as the aggregation policy (see the original article for further details).
The last parameter indicates to use all processors for parallelization.

```
import quapy as qp
from quapy.method.aggregative import ACC
from quapy.method.meta import Ensemble
from sklearn.linear_model import LogisticRegression
dataset = qp.datasets.fetch_UCIBinaryDataset('haberman')
model = Ensemble(quantifier=ACC(LogisticRegression()), size=30, policy='ave', n_jobs=-1)
model.fit(dataset.training)
estim_prevalence = model.quantify(dataset.test.instances)
```

Other aggregation policies implemented in QuaPy include:

- 'ptr' for applying a dynamic selection based on the training prevalence of the ensemble's members
- 'ds' for applying a dynamic selection based on the Hellinger Distance
*any valid quantification measure*(e.g., 'mse') for performing a static selection based on the performance estimated for each member of the ensemble in terms of that evaluation metric.

When using any of the above options, it is important to set the `red_size`

parameter, which
informs of the number of members to retain.

Please, check the model selection wiki if you want to optimize the hyperparameters of ensemble for classification or quantification.

### The QuaNet neural network

QuaPy offers an implementation of QuaNet, a deep learning model presented in:

This model requires `torch`

to be installed.
QuaNet also requires a classifier that can provide embedded representations
of the inputs.
In the original paper, QuaNet was tested using an LSTM as the base classifier.
In the following example, we show an instantiation of QuaNet that instead uses CNN as a probabilistic classifier, taking its last layer representation as the document embedding:

```
import quapy as qp
from quapy.method.meta import QuaNet
from quapy.classification.neural import NeuralClassifierTrainer, CNNnet
# use samples of 100 elements
qp.environ['SAMPLE_SIZE'] = 100
# load the kindle dataset as text, and convert words to numerical indexes
dataset = qp.datasets.fetch_reviews('kindle', pickle=True)
qp.data.preprocessing.index(dataset, min_df=5, inplace=True)
# the text classifier is a CNN trained by NeuralClassifierTrainer
cnn = CNNnet(dataset.vocabulary_size, dataset.n_classes)
learner = NeuralClassifierTrainer(cnn, device='cuda')
# train QuaNet
model = QuaNet(learner, device='cuda')
model.fit(dataset.training)
estim_prevalence = model.quantify(dataset.test.instances)
```