Added example comparing ai.linear_model.LogisticRegression estimato…

…r against `sklearn.linear_model.LogisticRegression`

Since there's no implementation of closed-form solution for linear regression
which is internally used by the logistic regression as hypothesis function
sklearn clearly out-performs in terms of speed but shows nearly the same
accuracy.

Signed-off-by: Ayush Joshi <ayush854032@gmail.com>

examples/linear_model/linear.py

@@ -70,6 +70,10 @@
 plt.show()
 
 print("Calculating using ai api...")
+print(
+  "Since there's no implementation of the closed-form solution for linear"
+  " regression in ai; sklearn api beats us in terms of speed..."
+)
 
 # Create linear regression object using ai api
 # Since there's no implementation of the closed-form solution for linear

examples/linear_model/logistic.py

@@ -0,0 +1,129 @@
+# Copyright 2023 The AI Authors. All Rights Reserved.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+# pylint: disable=too-many-function-args, invalid-name, missing-module-docstring
+# pylint: disable=missing-class-docstring
+
+import matplotlib.pyplot as plt
+import numpy as np
+
+from scipy.special import expit
+from sklearn.linear_model import LinearRegression
+from sklearn.linear_model import LogisticRegression
+
+from ai import linear_model
+
+# Generate a toy dataset, it's just a straight line with some Gaussian noise:
+xmin, xmax = -5, 5
+n_samples = 100
+np.random.seed(0)
+X = np.random.normal(size=n_samples)
+y = (X > 0).astype(float)
+X[X > 0] *= 4
+X += 0.3 * np.random.normal(size=n_samples)
+
+X = X[:, np.newaxis]
+
+print('Estimation using sklearn api...')
+
+# Fit the classifier
+clf = LogisticRegression(C=1e5)
+clf.fit(X, y)
+
+# and plot the result
+plt.figure(1, figsize=(4, 3))
+plt.clf()
+plt.scatter(X.ravel(), y, label="example data", color="black", zorder=20)
+X_test = np.linspace(-5, 10, 300)
+
+loss = expit(X_test * clf.coef_ + clf.intercept_).ravel()
+plt.plot(
+  X_test,
+  loss,
+  label="Logistic Regression Model (sklearn)",
+  color="red",
+  linewidth=3
+)
+
+ols = LinearRegression()
+ols.fit(X, y)
+plt.plot(
+  X_test,
+  ols.coef_ * X_test + ols.intercept_,
+  label="Linear Regression Model",
+  linewidth=1,
+)
+plt.axhline(0.5, color=".5")
+
+plt.ylabel("y")
+plt.xlabel("X")
+plt.xticks(range(-5, 10))
+plt.yticks([0, 0.5, 1])
+plt.ylim(-0.25, 1.25)
+plt.xlim(-4, 10)
+plt.legend(
+  loc="lower right",
+  fontsize="small",
+)
+plt.tight_layout()
+plt.show()
+
+print('Estimation using ai api...')
+print(
+  "Since there's no implementation of the closed-form solution for linear"
+  " regression in ai; sklearn api beats us in terms of speed..."
+)
+
+# Fit the classifier
+# LogisticRegression internally uses LinearRegression for making the hypothesis,
+# so wait for a while before the estimation pops up
+clf = linear_model.LogisticRegression(n_iters=1_000_000)
+clf.fit(X, y)
+
+# and plot the result
+plt.figure(1, figsize=(4, 3))
+plt.clf()
+plt.scatter(X.ravel(), y, label="example data", color="black", zorder=20)
+X_test = np.linspace(-5, 10, 300)
+
+loss = expit(X_test * clf._weights + clf._bias).ravel()
+plt.plot(
+  X_test,
+  loss,
+  label="Logistic Regression Model (ai)",
+  color="red",
+  linewidth=3
+)
+
+ols = LinearRegression()
+ols.fit(X, y)
+plt.plot(
+  X_test,
+  ols.coef_ * X_test + ols.intercept_,
+  label="Linear Regression Model",
+  linewidth=1,
+)
+plt.axhline(0.5, color=".5")
+
+plt.ylabel("y")
+plt.xlabel("X")
+plt.xticks(range(-5, 10))
+plt.yticks([0, 0.5, 1])
+plt.ylim(-0.25, 1.25)
+plt.xlim(-4, 10)
+plt.legend(
+  loc="lower right",
+  fontsize="small",
+)
+plt.tight_layout()
+plt.show()