Contents

- Importing, summarizing, and visualizing data
- Statistical learning
- Monte carlo methods
- Unsupervised learning
- Regression
- Regularization and kernel methods
- Classification
- Decision trees and ensemble methods
- Deep learning

Only some subjects are as timely as **data science** and **machine learning** in today's world of **automation**, **cloud computing**, **algorithms**, **AI**, and **big data**. They have recently gained popularity because solutions can be applied to problems in many different fields, from **mathematics** and **statistics** to **computer science** and **engineering** to natural science and finance.

If you are learning about these subjects, you might feel overwhelmed by how many computational methods and mathematical ideas there are. Some would be content to learn how to apply premade formulas to real-world problems. But what if the black-box recipe's assumptions are wrong? Is it still possible to have faith in the findings? Is there a recommended tweak to the algorithm? One must be familiar with the mathematics and statistics that form the basis of **data science** and **machine learning** to grasp the fields and their resulting algorithms fully.

Data science gives us the words and methods to understand and work with data. It involves planning, collecting, analyzing, and figuring out what the numbers mean to find patterns and other helpful information. **Machine learning**, closely related to **data science**, is the design of computer programs and algorithms that can learn from data. The book is put together in a way that is similar to how most data science projects are put together:

- Collecting data to learn more about a research question.
- Cleaning, summarizing, and displaying the data.
- Modeling and analyzing the data.
- Turning decisions about the model into decisions and predictions about the research question.

Since this is a book about math and statistics, modeling and analysis will get the most attention.

How to locate helpful data sets, import them into Python, and (re)organize them are all covered in this chapter. Different methods of summarizing the data in tables and figures are also discussed. The nature of the relevant variables dictates the form of the resulting plots and numerical summaries.

This chapter aims to familiarize the reader with some of the more fundamental ideas and themes used in statistical learning. We compare supervised and unsupervised *learning* and discuss how to evaluate supervised learning's ability to predict outcomes. Also, we take a close look at how linear and Gaussian characteristics play a significant role in data modeling.

Many machine learning and data science algorithms use Monte Carlo methods. This chapter provides an overview of the three primary applications of Monte Carlo simulation:

- Simulating random objects and processes to study their behavior.
- Estimating numerical quantities by repeated sampling.
- Solving complex optimization problems via randomized algorithms.

Unsupervised methods are necessary for *learning* the data structure when there is no separation between response and explanatory variables. Several unsupervised learning methods, including density estimation, clustering, and principal component analysis, are discussed in this chapter. The cross-entropy training loss, mixture models, the Expectation-Maximization algorithm, and the Singular Value Decomposition are all vital tools in unsupervised learning.

Under the umbrella term of "regression," many different supervised learning methods are categorized. For that reason, this chapter will focus on regression models' theoretical and methodological foundations. We comprehensively analyze the underlying linear model and expand our discussion to include nonlinear and generalized linear models.

This chapter introduces the reader to regularization and kernel methods, two essential tools in contemporary data science and machine learning. Overfitting can be prevented naturally by regularization, and linear models can be generalized in various ways using kernel methods. As a transition into the core concepts of kernel methods, we introduce regularized regression (ridge, lasso). We present the idea of reproducing kernel Hilbert spaces and demonstrate that finding the optimal prediction function is a convex optimization problem with finite dimensions. Numerous examples are provided, including their use in spline fitting, regression using the Gaussian process, and principal component analysis with the kernel.

Common classification strategies are introduced in this chapter, including the naive Bayes method, linear and quadratic discriminant analysis, logistic/softmax classification, the K-nearest neighbor's method, and support vector machines, and their underlying mathematical ideas are explained.

Decision tree-based statistical learning methods have become very popular because of their clarity, accessibility, and predictive power. The basics of making and using such trees are covered in this chapter. We also go over bootstrap aggregation and boosting, two important ensemble methods that can increase the effectiveness of decision trees and other learning techniques.

This section presents a method for building neural networks, a general category of approximating functions. Since the training of neural-network class learners is computationally feasible. Since their complexity can be easily controlled and fine-tuned, they have become ubiquitous in modern machine-learning applications.

Description : | Download ebook Data Science and Machine Learning Mathematical and Statistical Methods, free PDF on 533 pages. |

Level : | Advanced |

Created : | October 11, 2022 |

Size : | 13.75 MB |

File type : | |

Pages : | 533 |

Author : | Dirk P. Kroese, Zdravko I. Botev, Thomas Taimre, Radislav Vaisman |

Downloads : | 1924 |

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