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Machine Learning

Machine Learningmachine learning is the process of enabling a machine to learn methods for identifying features from an existing dataset so that it can effectively recognize features in new data as well.

The above definition isn’t particularly rigorous, nor does it need to be. Simply put, a machine can be understood as a computer or programming code. The dataset already in possession and used for learning is called the training settraining set, 훈련집합. Comparing machine learning to a student studying for exams:

  • Machine: Student
  • Training set: Past exam papers
  • Features: Question patterns
  • New data: Actual exam questions
  • Learning: Solving past papers to be able to tackle actual exam questions

As of 2021, the most widely used method for implementing machine learning is deep learningdeep learning, 심층학습, which involves increasing the hidden layers of artificial neural networks. Artificial neural networks have recently seen dramatic improvements in performance, often showcasing the best results. Before deep learning achieved satisfactory performance, models based on statistical theories dominated machine learning.

To become proficient in machine learning, one needs to be skilled in mathematics, statistics, and programming. Mathematical and statistical knowledge is required to understand the theory, and programming skills are needed to implement it. Specifically, to deeply study machine learning theory, knowledge of linear algebra related to matrices, as well as measure theory, functional analysis, and others are necessary. Additionally, recent research is linking artificial intelligence with fields like geometry, graph theory, and partial differential equations1.

The following articles are written to be as accessible as possible for mathematics majors.

Basics

Learning Concepts

Optimization

Sampling

Classical Machine Learning

Linear Regression Models

Linear Classification Models

  • Linear Classification Models
    • Least Squares Method
  • Fisher’s Linear Discriminant
  • Neyman-Pearson Criterion for Binary Classification
  • Bayes Risk Classifier

Clustering

Subfields

Reinforcement Learning

Computer Vision

Deep Learning Theory

Deep Learning Frameworks

Python PyTorch

Neural Networks

Tensors

Troubleshooting

Julia

Flux

References

  • Christoper M. Bishop, Pattern Recognition annd Machine Learning (2006)
  • Simon Haykin, Neural Networks and Learning Machines (3rd Edition, 2009)
  • Trevor Hastie, The Elements of Statistical Learning: Data Mining, Inference, and Prediction (2nd Edition, 2017)
  • 오일석, 기계 학습(MACHINE LEARNING) (2017)
  • Richard S. Sutton, Reinforcement Learning: An Introduction (2nd Edition, 2018)

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