Adding IsoReg folder and files

content/sklearn/concepts/isotonic-regression/isotonic-regression.md

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+---
+Title: 'Isotonic Regression'
+Description: 'Isotonic Regression is a technique of using a fre-form line to establish a non-linear path, created by a set of data points.' 
+Subjects:
+  - 'Data Science'
+  - 'Data Visualization'
+Tags:
+  - 'Booleans'
+  - 'Datasets'
+  - 'Matplotlib'
+  - 'Numpy'
+  - 'Scikit-learn'
+CatalogContent:
+  - 'learn-python-3'
+  - 'paths/intermediate-machine-learning-skill-path'
+---
+
+***Isotonic Regression*** is a technique of using a free-form line to establish a non-linear path. The path is created by a set of data points. In this technique, predictor variables and target vairables increase or decrease, monotonically, in a non-oscilatory manner. The word "isotonic" (*iso* and *tonos*) comes from the Greek, meaning *equal* and *to stretch*, respectively.
+
+## Syntax
+
+This is the basic syntax for implementing Isotonic Regression in Python:
+
+```pseudo
+import numpy as np
+from sklearn.isotonic import IsotonicRegression
+import matplotlib.pyplot as plt
+
+# Define predictor and target data
+X = [list of predictor values]
+Y = [list of target values]
+
+# Initialize Isotonic Regression model
+model = IsotonicRegression(increasing=True or False)
+
+# Fit the model and transform the target data
+Y_transformed = model.fit_transform(X, Y)
+
+# Visualize the original data and the regression fit
+plot.scatter(X, Y, label="Original Data")
+plot.line(X, Y_transformed, label="Isotonic Fit", color="red")
+plot.title("Isotonic Regression Example")
+plot.xlabel("Predictor Variable")
+plot.ylabel("Target Variable")
+plot.legend()
+plot.show()
+```
+
+- `increasing`: This is a boolean parameter that specifies whether the fitted values should increase monotonically (`True`) or decrease monotonically (`False`). 
+- `increasing=True` enforces a non-decreasing relationship between the predictor (`x`) and the target (`y`) variables.
+
+## Example
+
+The following is an example of Isotonic Regression in action:
+
+```py
+import numpy as np
+import matplotlib.pyplot as plt
+from sklearn.isotonic import IsotonicRegression
+
+# Generate synthetic data with a non-monotonic relationship
+np.random.seed(123)
+x = np.linspace(0, 10, 15) # Predictor variables
+y = np.sin(x) + np.random.normal(0, 0.2, len(x)) # Non-monotonic target variable with noise
+
+# Initialize and fit isotonic regression model
+iso_reg = IsotonicRegression(increasing=True)
+y_isotonic = iso_reg.fit_transform(x, y)
+
+# Plot the original data and isotonic regression fit
+plt.figure(figsize=(8, 6))
+plt.scatter(x, y, color='green', label='Original Data', marker='o')
+plt.step(x, y_isotonic, color-'orange', label='Isotonic Fit', where='post', linewidth=2)
+plt.title('Isotonic Regression on Non-Monotonic Data')
+plt.xlabel('Predictor Variable (X)')
+plt.ylabel('Target Variable (Y)')
+plt.legend()
+plt.grid(True)
+plt.show()
+```
+
+The example results in the following output:
+
+![Isotonic Regression Example] (https://github.com/S3an28/docs/blob/SK_5305/content/sklearn/concepts/isotonic-regression/isotonic-regression-example.jpg)
+
+## Codebyte
+
+```codebyte/python
+import numpy as np
+import matplotlib.pyplot as plt
+from sklearn.isotonic import IsotonicRegression
+
+# Generate some synthetic data
+np.random.seed(0)
+x = np.arange(1, 11)
+y = np.array([1, 2, 1.5, 3, 2.5, 3.5, 4, 4.5, 5, 6]) + np.random.normal(0, 0.3, 10)
+
+# Fit isotonic regression
+iso_reg = IsotonicRegression(increasing=True)
+y_pred = iso_reg.fit_transform(x, y)
+
+# Plot
+plt.figure(figsize=(8, 6))
+plt.scatter(x, y, color='blue', label='Original Data')
+plt.plot(x, y_pred, color='red', label='Isotonic Regression Fit', linewidth=2)
+plt.title("Isotonic Regression")
+plt.xlabel("X")
+plt.ylabel("Y")
+plt.legend()
+plt.grid(True)
+plt.show()
+```