Learn Bayesian optimization and statistical modeling to tackle high-dimensional problems. Explore hyperparameter tuning, experimental design, algorithm configuration, and system optimization.

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Bayesian optimization allows developers to leverage Bayesian inference and statistical modeling to efficiently search for the optimal solution in a high-dimensional space. 

Starting with the fundamentals of statistics and Bayesian statistics, you’ll explore different concepts of machine learning and its applications in software engineering. Next, you’ll discover different strategies for optimizations. Through practical examples and hands-on exercises, you’ll gain proficiency in implementing Bayesian optimization algorithms and fine-tuning them for specific tasks. By the end of the course, you’ll have a comprehensive understanding of the entire Bayesian optimization workflow, from problem formulation to solution optimization.

By completing this course, you’ll be able to tackle complex optimization problems more efficiently and effectively. You’ll be equipped to find optimal solutions in areas such as hyperparameter tuning, experimental design, algorithm configuration, and system optimization.

Bayesian Machine Learning for Optimization in Python

import scipy.stats as stats
import matplotlib.pyplot as plt
import numpy as np

# Define the prior probabilities for each class
prior_probs = [0.4, 0.6]

# Define the class-conditional probability distributions for each feature
feature_distributions = [
    stats.norm(loc=0, scale=1),  # Class 1
    stats.norm(loc=2, scale=1)   # Class 2
]

# Define the number of features
num_features = 2

# Define the number of classes
num_classes = 2

# Generate some synthetic data
data = np.random.randn(100, num_features)
data_y=np.random.randn(100)
# Compute the log-likelihoods for each class
log_likelihoods = np.zeros((num_classes, data.shape[0]))
for c in range(num_classes):
    for i in range(data.shape[0]):
        log_likelihoods[c, i] = np.sum([
            np.log(feature_distributions[c].pdf(data[i, j]))
            for j in range(num_features)
        ])

# Compute the posterior probabilities for each class
posterior_probs = np.zeros((num_classes, data.shape[0]))
for i in range(data.shape[0]):
    posterior_probs[:, i] = prior_probs * np.exp(log_likelihoods[:, i])
    posterior_probs[:, i] /= np.sum(posterior_probs[:, i])

# Classify the data points based on the posterior probabilities
predictions = np.argmax(posterior_probs, axis=0)

# Plot the data and the class-conditional probability distributions
x = np.linspace(-5, 5, 100)
fig, (ax1, ax2) = plt.subplots(2,1,sharex=True)
ax1.plot(x, feature_distributions[0].pdf(x), 'b-', lw=2, alpha=0.6, label='class 1')
ax1.plot(x, feature_distributions[1].pdf(x), 'r-', lw=2, alpha=0.6, label='class 2')
ax1.legend()
ax1.set_xlabel("Value of feature")
ax1.set_ylabel("Probability of feature")
ax1.set_title("Distribution of Feature in term of Classes")
ax2.scatter(data[:, 0], data[:, 1], c=predictions, cmap='bwr')
ax2.set_xlabel("Value of Feature 1")
ax2.set_ylabel("Value of Feature 2")
ax2.set_title("Distribution of Predicted Labels")
plt.tight_layout()
plt.show()
plt.savefig("output/classification.png")

Learn how Bayes’ theorem is used in machine learning problems, i.e., clustering, classification, and regression.

Introduction to Bayesian Statistics

Bayesian Statistics: Knowledge Check

Bayesian Machine Learning

Regression Using Bayes’ Theorem: Knowledge Check

Optimization: An Overview

Optimization: Knowledge Check

Bayesian Optimization: From Scratch

Hyperparameter Tuning Using Bayesian Optimization

Conclusion

Overcoming Uncertainty with Bayesian Probability in Python

Bayes’ Theorem in Machine Learning