Data science/ML/AI

12 Fundamental Math Theories Needed to Understand AI

1. Curse of Dimensionality
This phenomenon occurs when analyzing data in high-dimensional spaces. As dimensions increase, the volume of the space grows exponentially, making it challenging for algorithms to identify meaningful patterns due to the sparse nature of the data.
2. Law of Large Numbers
A cornerstone of statistics, this theorem states that as a sample size grows, its mean will converge to the expected value. This principle assures that larger datasets yield more reliable estimates, making it vital for statistical learning methods.
3. Central Limit Theorem
This theorem posits that the distribution of sample means will approach a normal distribution as the sample size increases, regardless of the original distribution. Understanding this concept is crucial for making inferences in machine learning.
4. Bayes’ Theorem
A fundamental concept in probability theory, Bayes’ Theorem explains how to update the probability of your belief based on new evidence. It is the backbone of Bayesian inference methods used in AI.
5. Overfitting and Underfitting
Overfitting occurs when a model learns the noise in training data, while underfitting happens when a model is too simplistic to capture the underlying patterns. Striking the right balance is essential for effective modeling and performance.
6. Gradient Descent
This optimization algorithm is used to minimize the loss function in machine learning models. A solid understanding of gradient descent is key to fine-tuning neural networks and AI models.
7. Information Theory
Concepts like entropy and mutual information are vital for understanding data compression and feature selection in machine learning, helping to improve model efficiency.
8. Markov Decision Processes (MDP)
MDPs are used in reinforcement learning to model decision-making scenarios where outcomes are partly random and partly under the control of a decision-maker. This framework is crucial for developing effective AI agents.
9. Game Theory
Old school AI is based off game theory. This theory provides insights into multi-agent systems and strategic interactions among agents, particularly relevant in reinforcement learning and competitive environments.
10. Statistical Learning Theory
This theory is the foundation of regression, regularization and classification. It addresses the relationship between data and learning algorithms, focusing on the theoretical aspects that govern how models learn from data and make predictions.
11. Hebbian Theory
This theory is the basis of neural networks, “Neurons that fire together, wire together”. Its a biology theory on how learning is done on a cellular level, and as you would have it — Neural Networks are based off this theory.
12. Convolution (Kernel)
Not really a theory and you don’t need to fully understand it, but this is the mathematical process on how masks work in image processing. Convolution matrix is used to combine two matrixes and describes the overlap.

Special thanks to Jiji Veronica Kim for this list.


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3.3K viewsOct 24, 2024 at 08:52

12 Fundamental Math Theories Needed to Understand AI

1. Curse of Dimensionality
This phenomenon occurs when analyzing data in high-dimensional spaces. As dimensions increase, the volume of the space grows exponentially, making it challenging for algorithms to identify meaningful patterns due to the sparse nature of the data.
2. Law of Large Numbers
A cornerstone of statistics, this theorem states that as a sample size grows, its mean will converge to the expected value. This principle assures that larger datasets yield more reliable estimates, making it vital for statistical learning methods.
3. Central Limit Theorem
This theorem posits that the distribution of sample means will approach a normal distribution as the sample size increases, regardless of the original distribution. Understanding this concept is crucial for making inferences in machine learning.
4. Bayes’ Theorem
A fundamental concept in probability theory, Bayes’ Theorem explains how to update the probability of your belief based on new evidence. It is the backbone of Bayesian inference methods used in AI.
5. Overfitting and Underfitting
Overfitting occurs when a model learns the noise in training data, while underfitting happens when a model is too simplistic to capture the underlying patterns. Striking the right balance is essential for effective modeling and performance.
6. Gradient Descent
This optimization algorithm is used to minimize the loss function in machine learning models. A solid understanding of gradient descent is key to fine-tuning neural networks and AI models.
7. Information Theory
Concepts like entropy and mutual information are vital for understanding data compression and feature selection in machine learning, helping to improve model efficiency.
8. Markov Decision Processes (MDP)
MDPs are used in reinforcement learning to model decision-making scenarios where outcomes are partly random and partly under the control of a decision-maker. This framework is crucial for developing effective AI agents.
9. Game Theory
Old school AI is based off game theory. This theory provides insights into multi-agent systems and strategic interactions among agents, particularly relevant in reinforcement learning and competitive environments.
10. Statistical Learning Theory
This theory is the foundation of regression, regularization and classification. It addresses the relationship between data and learning algorithms, focusing on the theoretical aspects that govern how models learn from data and make predictions.
11. Hebbian Theory
This theory is the basis of neural networks, “Neurons that fire together, wire together”. Its a biology theory on how learning is done on a cellular level, and as you would have it — Neural Networks are based off this theory.
12. Convolution (Kernel)
Not really a theory and you don’t need to fully understand it, but this is the mathematical process on how masks work in image processing. Convolution matrix is used to combine two matrixes and describes the overlap.

Special thanks to Jiji Veronica Kim for this list.


➖➖➖➖➖➖➖➖➖➖➖➖➖➖
Join @datascience_bds for more cool repositories.
*This channel belongs to @bigdataspecialist group

BY Data science/ML/AI