Recognizing handwritten digits with Ridge2Classifier

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This post is about Ridge2Classifier, a classifier that I presented 5 years ago in this document. It’s now possible to choose starting values of the (likelihood) optimization algorithm which are solutions from least squares regression. Not always better,
but can be seen as a new hyperparameter. Also, Ridge2Classifier used to fail miserably on digits data sets but now, with nnetsauce’s maturity, Ridge2Classifier is doing much better on this type of data, as demonstrated below.

0 – Install and load packages

!pip install nnetsauce
!pip install GPopt
import GPopt as gp
import nnetsauce as ns
import numpy as np

from sklearn.datasets import load_digits
from sklearn.model_selection import cross_val_score, train_test_split
from sklearn import metrics
from time import time

1 – Cross-validation and hyperparameter tuning

def ridge2_cv(X_train, y_train,
              lambda1 = 0.1,
              lambda2 = 0.1,
              dropout = 0.8,
              solver="L-BFGS-B"): # 'solver' is the optimization algorithm

  estimator  = ns.Ridge2Classifier(lambda1 = lambda1,
                                   lambda2 = lambda2,
                                   dropout = dropout,

  return -cross_val_score(estimator, X_train, y_train,
                          cv=5, n_jobs=None,

def optimize_ridge2(X_train, y_train, solver="L-BFGS-B"):
  # objective function for hyperparams tuning
  def crossval_objective(x):
    return ridge2_cv(X_train=X_train,
                  lambda1 = 10**x[0],
                  lambda2 = 10**x[1],
                  dropout = x[4],
                  solver = solver)
  gp_opt = gp.GPOpt(objective_func=crossval_objective,
                    lower_bound = np.array([ -10, -10,   3, 2, 0.6]),
                    upper_bound = np.array([  10,  10, 100, 5,   1]),
                    params_names=["lambda1", "lambda2", "n_hidden_features", "n_clusters", "dropout"],
                    n_init=10, n_iter=90, seed=3137)
  return gp_opt.optimize(verbose=2, abs_tol=1e-3)

dataset = load_digits()
X =
y =

# split data into training test and test set
X_train, X_test, y_train, y_test = train_test_split(X, y,
                                                    test_size=0.2, random_state=3137)

# hyperparams tuning
res_opt1 = optimize_ridge2(X_train, y_train, solver="L-BFGS-B")

# hyperparams tuning with different starting values for the optimization algorithm
res_opt2 = optimize_ridge2(X_train, y_train, solver="L-BFGS-B-lstsq")
res_opt1.best_params["lambda1"] = 10**(res_opt1.best_params["lambda1"])
res_opt1.best_params["lambda2"] = 10**(res_opt1.best_params["lambda2"])
res_opt1.best_params["n_hidden_features"] = int(res_opt1.best_params["n_hidden_features"])
res_opt1.best_params["n_clusters"] = int(res_opt1.best_params["n_clusters"])

res_opt2.best_params["lambda1"] = 10**(res_opt2.best_params["lambda1"])
res_opt2.best_params["lambda2"] = 10**(res_opt2.best_params["lambda2"])
res_opt2.best_params["n_hidden_features"] = int(res_opt2.best_params["n_hidden_features"])
res_opt2.best_params["n_clusters"] = int(res_opt2.best_params["n_clusters"])
{'lambda1': 5.243297406977503e-10, 'lambda2': 1.2433817601870388e-05, 'n_hidden_features': 14, 'n_clusters': 2, 'dropout': 0.94100341796875}
{'lambda1': 1.747558169384434e-08, 'lambda2': 1360.0188315151736, 'n_hidden_features': 14, 'n_clusters': 2, 'dropout': 0.7794189453125}

2 – Out-of-sample scores

from time import time

clf1 = ns.Ridge2Classifier(**res_opt1.best_params,
start = time(), y_train)
print(f"Elapsed: {time()-start}")
print(clf1.score(X_test, y_test))

clf2 = ns.Ridge2Classifier(**res_opt2.best_params,
start = time(), y_train)
print(f"Elapsed: {time()-start}")
print(clf2.score(X_test, y_test))
Elapsed: 2.6086528301239014
Elapsed: 1.2307183742523193
# confusion matrix
import matplotlib.pyplot as plt
import seaborn as sns
from sklearn.metrics import confusion_matrix

y_pred = clf2.predict(X_test)
cm = confusion_matrix(y_test, y_pred)

fig, ax = plt.subplots(figsize=(10, 8))
ax = sns.heatmap(cm, annot=True, cmap='Blues', fmt='g', xticklabels=np.arange(0, 10), yticklabels=np.arange(0, 10))
ax.set_xlabel('Predicted labels')
ax.set_ylabel('True labels')
ax.set_title('Confusion Matrix')


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