Python for Probability, Statistics, and Machine Learning

Using a novel integration of mathematics and Python codes, this book illustrates the fundamental concepts that link probability, statistics, and machine learning, so that the reader can not only employ statistical and machine learning models using modern Python modules, but also understand their relative strengths and weaknesses. To clearly connect theoretical concepts to practical implementations, the author provides many worked-out examples along with "Programming Tips" that encourage the reader to write quality Python code. The entire text, including all the figures and numerical results, is reproducible using the Python codes provided, thus enabling readers to follow along by experimenting with the same code on their own computers.Modern Python modules like Pandas, Sympy, Scikit-learn, Statsmodels, Scipy, Xarray, Tensorflow, and Keras are used to implement and visualize important machine learning concepts like the bias/variance trade-off, cross-validation, interpretability, and regularization. Many abstract mathematical ideas, such as modes of convergence in probability, are explained and illustrated with concrete numerical examples. This book is suitable for anyone with undergraduate-level experience with probability, statistics, or machine learning and with rudimentary knowledge of Python programming.

Interessenniveau: 06, Professional and scholarly: For an expert adult audience, including academic research. (06).

Introduction.- Part 1 Getting Started with Scientific Python.- Installation and Setup.- Numpy.- Matplotlib.- Ipython.- Jupyter Notebook.- Scipy.- Pandas.- Sympy.- Interfacing with Compiled Libraries.- Integrated Development Environments.- Quick Guide to Performance and Parallel Programming.- Other Resources.- Part 2 Probability.- Introduction.- Projection Methods.- Conditional Expectation as Projection.- Conditional Expectation and Mean Squared Error.- Worked Examples of Conditional Expectation and Mean Square Error Optimization.- Useful Distributions.- Information Entropy.- Moment Generating Functions.- Monte Carlo Sampling Methods.- Useful Inequalities.- Part 3 Statistics.- Python Modules for Statistics.- Types of Convergence.- Estimation Using Maximum Likelihood.- Hypothesis Testing and P-Values.- Confidence Intervals.- Linear Regression.- Maximum A-Posteriori.- Robust Statistics.- Bootstrapping.- Gauss Markov.- Nonparametric Methods.- Survival Analysis.- Part 4 Machine Learning.- Introduction.- Python Machine Learning Modules.- Theory of Learning.- Decision Trees.- Boosting Trees.- Logistic Regression.- Generalized Linear Models.- Regularization.- Support Vector Machines.- Dimensionality Reduction.- Clustering.- Ensemble Methods.- Deep Learning.- Notation.- References.- Index.