adapt.instance_based.KLIEP

class adapt.instance_based.KLIEP(estimator=None, Xt=None, kernel='rbf', sigmas=None, max_centers=100, cv=5, lr=0.0001, tol=1e-06, max_iter=5000, copy=True, verbose=1, random_state=None, **params)[source]

KLIEP: Kullback–Leibler Importance Estimation Procedure

KLIEP is an instance-based method for domain adaptation.

The purpose of the algorithm is to correct the difference between input distributions of source and target domains. This is done by finding a source instances reweighting which minimizes the Kullback-Leibler divergence between source and target distributions.

The source instance weights are given by the following formula:

\[w(x) = \sum_{x_i \in X_T} \alpha_i K(x, x_i)\]

Where:

\(x, x_i\) are input instances.
\(X_T\) is the target input data.
\(\alpha_i\) are the basis functions coefficients.
\(K(x, x_i) = \text{exp}(-\gamma ||x - x_i||^2)\) for instance if kernel="rbf".

KLIEP algorithm consists in finding the optimal \(\alpha_i\) according to the following optimization problem:

\[\max_{\alpha_i } \sum_{x_j \in X_T} \log( \sum_{x_i \in X_T} \alpha_i K(x_j, x_i))\]

Subject to:

\[\sum_{x_j \in X_S} \sum_{x_i \in X_T} \alpha_i K(x_j, x_i)) = n_S\]

Where:

\(X_T\) is the source input data of size \(n_S\).

The above OP is solved through gradient ascent algorithm.

Furthemore a LCV procedure can be added to select the appropriate parameters of the kernel function \(K\) (typically, the paramter \(\gamma\) of the Gaussian kernel). The parameter is then selected using cross-validation on the \(J\) score defined as follows: \(J = \frac{1}{|\mathcal{X}|} \sum_{x \in \mathcal{X}} \text{log}(w(x))\)

Finally, an estimator is fitted using the reweighted labeled source instances.

KLIEP method has been originally introduced for unsupervised DA but it could be widen to supervised by simply adding labeled target data to the training set.

Parameters

estimatorsklearn estimator or tensorflow Model (default=None): Estimator used to learn the task. If estimator is None, a LinearRegression instance is used as estimator.
Xtnumpy array (default=None): Target input data.
kernelstr (default=”rbf”): Kernel metric. Possible values: [‘additive_chi2’, ‘chi2’, ‘linear’, ‘poly’, ‘polynomial’, ‘rbf’, ‘laplacian’, ‘sigmoid’, ‘cosine’]
sigmasfloat or list of float (default=None): Deprecated, please use the gamma parameter instead. (See below).
cvint (default=5): Cross-validation split parameter. Used only if sigmas has more than one value.
max_centersint (default=100): Maximal number of target instances use to compute kernels.
lrfloat (default=1e-4): Learning rate of the gradient ascent.
tolfloat (default=1e-6): Optimization threshold.
max_iterint (default=5000): Maximal iteration of the gradient ascent optimization.
copyboolean (default=True): Whether to make a copy of estimator or not.
verboseint (default=1): Verbosity level.
random_stateint (default=None): Seed of random generator.
paramskey, value arguments: Arguments given at the different level of the adapt object. It can be, for instance, compile or fit parameters of the estimator or kernel parameters etc… Accepted parameters can be found by calling the method _get_legal_params(params).

Yields

gammafloat or list of float

Kernel parameter gamma.

For kernel = chi2:

k(x, y) = exp(-gamma Sum [(x - y)^2 / (x + y)])

For kernel = poly or polynomial:

K(X, Y) = (gamma <X, Y> + coef0)^degree

For kernel = rbf:
```
K(x, y) = exp(-gamma ||x-y||^2)
```
For kernel = laplacian:
```
K(x, y) = exp(-gamma ||x-y||_1)
```
For kernel = sigmoid:
```
K(X, Y) = tanh(gamma <X, Y> + coef0)
```

If a list is given, the LCV process is performed to select the best parameter gamma.

coef0floaf or list of float

Kernel parameter coef0. Used for ploynomial and sigmoid kernels. See gamma parameter above for the kernel formulas. If a list is given, the LCV process is performed to select the best parameter coef0.

degreeint or list of int

Degree parameter for the polynomial kernel. (see formula in the gamma parameter description). If a list is given, the LCV process is performed to select the best parameter degree.

See also

KMM

References

1: [1] M. Sugiyama, S. Nakajima, H. Kashima, P. von Bünau and M. Kawanabe. “Direct importance estimation with model selection and its application to covariateshift adaptation”. In NIPS 2007

Examples

>>> from sklearn.linear_model import RidgeClassifier
>>> from adapt.utils import make_classification_da
>>> from adapt.instance_based import KLIEP
>>> Xs, ys, Xt, yt = make_classification_da()
>>> model = KLIEP(RidgeClassifier(), Xt=Xt, kernel="rbf", gamma=[0.1, 1.], random_state=0)
>>> model.fit(Xs, ys)
Fit weights...
Cross Validation process...
Parameter {'gamma': 0.1} -- J-score = 0.013 (0.003)
Parameter {'gamma': 1.0} -- J-score = 0.120 (0.026)
Fit Estimator...
>>> model.score(Xt, yt)
0.85

Attributes

weights_numpy array: Training instance weights.
best_params_float: Best kernel params combination deduced from the LCV procedure.
alphas_numpy array: Basis functions coefficients.
centers_numpy array: Center points for kernels.
j_scores_dict: dict of J scores with the kernel params combination as keys and the J scores as values.
estimator_object: Fitted estimator.

Methods

`__init__`([estimator, Xt, kernel, sigmas, ...])
`fit`(X, y[, Xt, yt, domains])	Fit Adapt Model.
`fit_estimator`(X, y[, sample_weight, ...])	Fit estimator on X, y.
`fit_weights`(Xs, Xt, **kwargs)	Fit importance weighting.
`get_params`([deep])	Get parameters for this estimator.
`predict`(X[, domain])	Return estimator predictions after adaptation.
`predict_estimator`(X, **predict_params)	Return estimator predictions for X.
`predict_weights`([X])	Return fitted source weights
`score`(X, y[, sample_weight, domain])	Return the estimator score.
`set_params`(**params)	Set the parameters of this estimator.
`unsupervised_score`(Xs, Xt)	Return unsupervised score.

__init__(estimator=None, Xt=None, kernel='rbf', sigmas=None, max_centers=100, cv=5, lr=0.0001, tol=1e-06, max_iter=5000, copy=True, verbose=1, random_state=None, **params)[source]

fit(X, y, Xt=None, yt=None, domains=None, **fit_params)[source]

Fit Adapt Model.

For feature-based models, the transformation of the input features Xs and Xt is first fitted. In a second stage, the estimator_ is fitted on the transformed features.

For instance-based models, source importance weights are first learned based on Xs, ys and Xt. In a second stage, the estimator_ is fitted on Xs, ys with the learned importance weights.

Parameters

Xnumpy array: Source input data.
ynumpy array: Source output data.
Xtarray (default=None): Target input data. If None, the Xt argument given in init is used.
ytarray (default=None): Target input data. Only needed for supervised and semi-supervised Adapt model. If None, the yt argument given in init is used.
domainsarray (default=None): Vector giving the domain for each source data. Can be used for multisource purpose.
fit_paramskey, value arguments: Arguments given to the fit method of the estimator.

Returns

selfreturns an instance of self

fit_estimator(X, y, sample_weight=None, random_state=None, warm_start=True, **fit_params)[source]

Fit estimator on X, y.

Parameters

Xarray: Input data.
yarray: Output data.
sample_weightarray: Importance weighting.
random_stateint (default=None): Seed of the random generator
warm_startbool (default=True): If True, continue to fit estimator_, else, a new estimator is fitted based on a copy of estimator. (Be sure to set copy=True to use warm_start=False)
fit_paramskey, value arguments: Arguments given to the fit method of the estimator and to the compile method for tensorflow estimator.

Returns

estimator_fitted estimator

fit_weights(Xs, Xt, **kwargs)[source]

Fit importance weighting.

Parameters

Xsarray: Input source data.
Xtarray: Input target data.
kwargskey, value argument: Not used, present here for adapt consistency.

Returns

weights_sample weights

get_params(deep=True)[source]

Get parameters for this estimator.

Parameters

deepbool, default=True: Not used, here for scikit-learn compatibility.

Returns

paramsdict: Parameter names mapped to their values.

predict(X, domain=None, **predict_params)[source]

Return estimator predictions after adaptation.

For feature-based method (object which implements a transform method), the input feature X are first transformed. Then the predict method of the fitted estimator estimator_ is applied on the transformed X.

Parameters

Xarray: input data
domainstr (default=None): For antisymetric feature-based method, different transformation of the input X are applied for different domains. The domain should then be specified between “src” and “tgt”. If None the default transformation is the target one.

Returns

y_predarray: prediction of the Adapt Model.

predict_estimator(X, **predict_params)[source]

Return estimator predictions for X.

Parameters

Xarray: input data

Returns

y_predarray: prediction of estimator.

predict_weights(X=None)[source]

Return fitted source weights

If None, the fitted source weights are returned. Else, sample weights are computing using the fitted alphas_ and the chosen centers_.

Parameters

Xarray (default=None): Input data.

Returns

weights_sample weights

score(X, y, sample_weight=None, domain=None)[source]

Return the estimator score.

If the object has a transform method, the estimator is applied on the transformed features X. For antisymetric transformation, a parameter domain can be set to specified between source and target transformation.

Call score on sklearn estimator and evaluate on tensorflow Model.

Parameters

Xarray: input data
yarray: output data
sample_weightarray (default=None): Sample weights
domainstr (default=None): This parameter specifies for antisymetric feature-based method which transformation will be applied between “source” and “target”. If None the transformation by default is the target one.

Returns