expectation-reflection 0.0.10

Expectation Reflection (ER) is a multiplicative optimization method that trains the interaction weights from features to target according to the ratio of target observations to their corresponding model expectations. This approach completely separates model updates from minimization of a cost function measuring goodness of fit, so that it can take the cost function as an effective stopping criterion of the iteration.

Advantages of this method: (1) working relatively well even in the regime of small sample sizes; (2) using only one hyper-parameter; (3) being able to demonstrate the system mechanism.

In the current version, ER classification can work as a classifier (for both binary and multinomial tasks). The extension to regression will be appeared shortly.

Installation

From PyPI

pip install expectation-reflection

From Repository

git clone https://github.com/danhtaihoang/expectation-reflection.git

Usage

The implementation of ER is very similar to that of other classifiers in sklearn, bassically it consists of the following steps.

• Import the expectation_reflection package into your python script:

from expectation_reflection import classification as ER

• Select a model:

model = ER.model(max_iter=100,reg=0.01,random_state=1)

• Import your dataset.txt into python script.

Xy = np.loadtxt('dataset.txt')

• Select the features and target from the dataset. If the target is the last column then

X, y = Xy[:,:-1], Xy[:,-1]

• Import train_test_split from sklearn to split data into training and test sets:

from sklearn.model_selection import train_test_split

X_train,X_test,y_train,y_test = train_test_split(X,y,test_size=0.5,random_state = 1)

• Train the model with (X_train, y_train) set:

model.fit(X_train, y_train)

• Predict the output class y_pred and its probability p_pred of a new dataset X_test:

y_pred = model.predict(X_test)
print('predicted output:', y_pred)

p_pred = model.predict_proba(X_test)
print('predicted probability:', p_pred)

• Intercept and interaction weights:

print('intercept:', model.intercept_)
print('interaction weights:', model.coef_)

Hyper-Parameter Optimization

ER has only one hyper-parameter, reg, which can be optimized by using GridSearchCV from sklearn:

from sklearn.model_selection import GridSearchCV

model = ER.model(max_iter=100, random_state = 1)

reg = [0.0001, 0.001, 0.01, 0.1, 0.5, 1.]

hyper_parameters = dict(reg=reg)

clf = GridSearchCV(model, hyper_parameters, cv=4, n_jobs=-1, iid='deprecated')

best_model = clf.fit(X_train, y_train)

• Best hyper-parameters:

print('best_hyper_parameters:',best_model.best_params_)

• Predict the output y_pred and its probability p_pred:

y_pred = best_model.best_estimator_.predict(X_test)
print('predicted output:', y_pred)

p_pred = best_model.best_estimator_.predict_proba(X_test)
print('predicted probability:', p_pred)

Performance Evaluation

We can measure the model performance by using metrics from sklearn:

from sklearn.metrics import accuracy_score,precision_score,recall_score,f1_score,\
roc_auc_score,roc_curve,auc

acc = accuracy_score(y_test,y_pred)
print('accuracy:', acc)

precision = precision_score(y_test,y_pred)
print('precision:', precision)

recall = recall_score(y_test,y_pred)
print('recall:', recall)

f1score = f1_score(y_test,y_pred)
print('f1score:', f1score)

roc_auc = roc_auc_score(y_test,p_pred) ## note: it is p_pred, not y_pred
print('roc auc:', roc_auc)

ROC AUC can be also calculated as

fp,tp,thresholds = roc_curve(y_test, p_pred, drop_intermediate=False)
roc_auc = auc(fp,tp)
print('roc auc:', roc_auc)

Citation

Please cite the following papers if you use this package in your work:

• Danh-Tai Hoang, Juyong Song, Vipul Periwal, and Junghyo Jo, Network inference in stochastic systems from neurons to currencies: Improved performance at small sample size, Physical Review E, 99, 023311 (2019)

• Danh-Tai Hoang, Junghyo Jo, and Vipul Periwal, Data-driven inference of hidden nodes in networks, Physical Review E, 99, 042114 (2019)