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AI theory, architecture, models
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Module 1
Mathematical and Statistical Foundations for AI
1
Vector and Matrix Operations for Neural Networks
Perform vector and matrix operations relevant to neural network computations
2
Eigenvalues and Eigenvectors: ML Significance
Calculate eigenvalues and eigenvectors and understand their significance in machine learning
3
Matrix Decomposition: SVD and Eigendecomposition
Apply matrix decomposition techniques such as SVD and eigendecomposition
4
Partial Derivatives and Gradients
Compute partial derivatives and gradients of multivariate functions
5
Chain Rule for Backpropagation
Apply the chain rule for differentiating composite functions in the context of backpropagation
6
Jacobians and Hessians for Optimization
Calculate Jacobians and Hessians for advanced optimization
7
Bayes' Theorem: Conditional Probability in Action
Apply Bayes' theorem to solve problems involving conditional probability
8
Common Probability Distributions and Their Applications
Describe common probability distributions (Gaussian, Bernoulli, Categorical) and their applications
9
Expectations and Variances of Random Variables
Compute expectations and variances of random variables
10
Large Numbers, Central Limit Theorem, and Statistical Justification
Apply the law of large numbers and the central limit theorem to justify statistical methods
11
MLE and MAP Estimation
Perform maximum likelihood estimation (MLE) and maximum a posteriori (MAP) estimation
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Core Machine Learning Concepts