Mathematics for Artificial Intelligence

Introduction

Mathematics forms the backbone of Artificial Intelligence. While libraries simplify implementation, understanding the math improves model design and debugging skills.

1. Linear Algebra

Vectors

Vectors represent data points. For example, a house price prediction model may represent a house as:

 [Size, Bedrooms, Age] 

Matrices

Matrices store datasets where rows represent examples and columns represent features.

Matrix Multiplication

Used in neural networks to compute weighted sums.

2. Calculus

Derivatives

Derivatives measure rate of change and are used in gradient descent optimization.

Gradient Descent

An optimization algorithm used to minimize error in models.

3. Probability

Conditional Probability

Used in spam detection and Bayesian classifiers.

Bayes Theorem

Helps update probability based on new evidence.

4. Statistics

Mean and Variance

Measure central tendency and data spread.

Normal Distribution

Many natural phenomena follow a bell curve distribution.

Real Life Example

In fraud detection:

• Linear algebra processes transaction features.
• Probability estimates fraud likelihood.
• Calculus optimizes model accuracy.

Common Mistakes

• Ignoring feature scaling.
• Not understanding gradient descent convergence.
• Confusing correlation with causation.

Interview Questions

1. Why is linear algebra important in AI?
2. Explain gradient descent.
3. What is conditional probability?

Certification Practice Questions

1. What does a derivative represent?
2. What is the role of matrices in ML?
3. State Bayes Theorem.

Summary

Linear algebra structures data, calculus optimizes models, probability manages uncertainty, and statistics interprets results.

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