Machine Learning Theory Notes (1): Getting to Know Machine Learning

1 Preface: Blue is the sky's machine learning notes column

Hello, dear readers! Welcome to my new column: " Blue is the sky machine learning notes ". I couldn't be more excited to be here to share my love and exploration of machine learning with you. This column will become a warm corner for me to record machine learning knowledge and exchange ideas, and this article is the first step of the column.

1.1 The original intention and positioning of the column

As an avid enthusiast in the field of machine learning, I have always believed that the sharing and dissemination of knowledge is the key to promoting technological progress. The column " Blue is the Sky's Machine Learning Notes " will be a continuously updated platform, where I will share my understanding of the field of machine learning, my experience in the learning process and practical experience. I hope that through this column, I can explore the mysteries of machine learning with like-minded you, grow and make progress together.

1.2 Main content of this article

1. Definition and Significance of Machine Learning
   In the world of machine learning, computers no longer passively execute preset instructions, but are able to autonomously learn and optimize performance through data and experience. Machine learning has penetrated into every aspect of our lives, from intelligent assistants to recommendation algorithms, showing its powerful application potential. In this article, I will give you a detailed introduction to the definition of machine learning and its significance in modern technology.

2. Basic terminology of machine learning
   Before stepping into the field of machine learning, it is very necessary to understand some basic terminology. This article will introduce some commonly used machine learning terms, such as supervised learning, unsupervised learning, feature engineering, etc., to help you establish a preliminary understanding of these concepts and lay a solid foundation for subsequent learning.

3. Exploring NFL Theory
   NFL Theory, the "no free lunch" theorem, is an important principle in the field of machine learning. It tells us that there is no one algorithm that performs optimally in all situations, and that different problems require different approaches. In this article, I will analyze the connotation of this theory and explore its application significance in practical problems.

2 Definition of Machine Learning

In today's era of information explosion, we deal with all kinds of data every day. From likes on social media and recommendations on shopping sites, to medical diagnoses and smart driving, our world is increasingly influenced by data and technology. However, how to extract valuable information from these massive data and make intelligent decisions is a problem full of challenges. In this context, machine learning emerged as the times require, giving computers the ability to learn and adapt like humans.

2.1 The essence of machine learning

Machine learning is the discipline that allows computers to learn from experience to improve performance. Its core idea can be understood with a simple analogy: just as we predict tomorrow's weather based on past experience, or pick a good melon in the market, machine learning enables computers to gain "experience" from historical data, And generate an algorithm model by learning these experiences, so as to make effective judgments in the face of new situations.

Mitchell's formal definition

Tom Mitchell, in his classic textbook "Machine Learning", gives a formal definition of machine learning, which expresses this concept more accurately and concretely. He regards machine learning as a process of performance improvement, through the learning of historical data to improve the performance of computer programs on a certain task class. In the formal definition, he introduced three key elements:

• P (performance): Indicates the performance of a computer program on a certain task class T. This could be classification accuracy, regression error, etc., depending on the nature of the task.
• T (Task Class): Refers to the type of problem the computer program is trying to solve. This can be anything from image recognition to natural language processing.
• E (Experience): A dataset representing history, i.e. past experience. This data will be used to train a computer program to perform better on task T.

According to Mitchell's definition, if a computer program improves its performance P on task T by learning experience E, then it can be said that the program has learned E.

2.2 Classification of machine learning

Machine learning can be divided into several subfields, including but not limited to supervised learning, unsupervised learning, and reinforcement learning. In supervised learning, a computer learns from labeled data in order to be able to classify or regress on new data. In unsupervised learning, computers discover patterns and structures from unlabeled data for tasks such as clustering and dimensionality reduction. Reinforcement learning is to let the computer learn the optimal strategy through trial and error in the process of interacting with the environment.

3 Basic terminology of machine learning

In the field of machine learning, there are many basic terms used to describe data, models, and learning processes, which help us understand and communicate more accurately. Let's dive into these key concepts together.

The basic composition of data
When we want to let the computer learn, we first need a set of data as the basis for learning. Taking watermelon data as an example, each record represents the characteristic information of a watermelon:

• Dataset: The collection of all records is called a dataset, which is the source data for our learning.
• Instance/Sample: Each record is called an instance or sample, which is a single data point in the dataset.
• Features/attributes: Each individual characteristic in a dataset, such as "color" or "knock", is called a feature or attribute.
• Feature vector: A record can be represented as a feature vector, which is a point on the coordinate axis, where each dimension corresponds to a feature.

Training and testing
In machine learning, we need to use part of the data to train the model, and then use another part of the data to test the performance of the model:

• Training samples: The data samples used to train the model are called training samples, and these samples have labeled information.
• Training set: The collection of all training samples is called the training set, which is the data set used to train the model.
• Test samples: The data samples used to test the performance of the model are called test samples, and these samples usually have no label information.
• Test Set: The collection of all test samples is called the test set, which is the data set used to evaluate the performance of the model.

Generalization ability and prediction
A good machine learning model should have the ability to adapt to new data, which is the generalization ability:

• Generalization ability: The learning results of the model on the training set can be applied to unseen data, which is the generalization ability of the model.

Problem Types and Learning Tasks
Machine learning can be applied to different types of problems, depending on the nature of the predicted value:

• Classification: When the predicted values ​​are discrete values ​​such as good melon/bad melon, the problem is called classification. It can be divided into binary classification and multi-classification.
• Regression: When the predicted value is a continuous value such as population size, the problem is called regression.

Supervised learning and unsupervised learning
According to whether the training data has labeled information, we can divide machine learning tasks into two categories:

• Supervised learning: Training data is labeled, including classification and regression problems.
• Unsupervised learning: The training data has no labeled information, including tasks such as clustering and association rules.

4 Exploring the "No Free Lunch" Theorem (NFL)

In the field of machine learning, there is a widely cited theorem that reveals a common reality in a concise statement: there is no free lunch (No Free Lunch, NFL). The essence of this theorem not only has profound applications in the field of machine learning, but also applies to our personal development path. Please read a previous blog post: Life Lessons in Machine Learning: Personal Development of the "No Free Lunch" Theorem (NFL)

The NFL theorem (No Free Lunch Theorem) is a fundamental theorem in the field of machine learning that provides insight through mathematical derivation. The core idea of ​​the theorem is that for all problems and all potential learning algorithms, their performance on average is the same. This means that there is no single algorithm that performs optimally on all problems.

Concretely, suppose we have a set of learning algorithms, denoted A = {A1, A2, … , An}, which are applied to different sets of problems D = {D1, D2, … , Dm}. Then the NFL theorem gives the following conclusion:

1. For a specific problem Di, when an algorithm Aj performs well, there must be other problems Dk, in which the algorithm Aj performs relatively poorly.
2. For the average performance of any algorithm, their performance on all problems is the same, that is, the expected performance on all problems is equal.

In order to better understand the NFL theorem, we can conduct specific analysis through formula derivation.
Suppose we have two algorithms, Algorithm a and Algorithm B, which are used for hypothesis generation and random guessing respectively. Consider a discrete sample space X and hypothesis space H. We define P(h|X,a) as the probability that algorithm a produces hypothesis h based on training data X, and assume that we wish to find a true objective function f. Then, the error of algorithm a outside the training set can be expressed as:

Through formula derivation, we can clearly see the mathematical basis of NFL theorem and understand its meaning. It reminds us that no one algorithm fits all problems because there is an inherent connection between the characteristics of the problem and the algorithm.

In personal development, we can extend the thought of NFL theorem to career choice and development. Everyone has their own unique interests, skills and adaptations, and no one career or field is right for everyone. We need to explore our strengths and find opportunities and paths that work for us.

Whether in machine learning or personal development, we should understand and accept the enlightenment of NFL theorem, and find opportunities that suit us by exploring diverse fields. In this way, we can develop to our full potential and succeed in our personal development. Let's go beyond the boundaries of NFL theorem and embark on a colorful journey of personal development.

5 Conclusion

In Exploring the World of Machine Learning, we delve into the importance of the "No Free Lunch" Theorem (NFL), which not only brings new thinking to machine learning, but also points out the way forward for personal development. Just as each algorithm has its advantages on different problems, each person also has unique shining points on the stage of life. In machine learning, we are driven by data, guided by models, and constantly pursue optimization and innovation; in life, we use hard work as the driving force and dreams as the goal to move forward firmly and make continuous breakthroughs. Whether solving complex problems or realizing personal value, perseverance and a positive attitude are the keys to success.

In this blog post, we dive into basic machine learning terminology and dissect the implications of the "no free lunch" theorem in machine learning and personal development. Whether it is choosing the right algorithm or facing a sense of gap in personal development, we can draw wisdom from NFL theorems. Just as every problem in machine learning requires a unique algorithm, everyone has their own path in life. It is the direction of our common efforts to absorb experience from learning, continue to grow, and gradually move towards success.

Let us go forward bravely in the exploration of machine learning; in the journey of life, uphold the wisdom of NFL theorem, constantly surpass ourselves, and create a better tomorrow. Whether exploring the boundaries of technology or realizing personal dreams, we should firmly believe that nothing is impossible under the guidance of knowledge. Let us meet the challenges of the future together, contribute to the development of machine learning and the progress of life, and write our own wonderful chapters.