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Bachelor

Artificial Intelligence & Data Science

Linear Methods of AI

Mathematical backbone transforming data patterns into intelligent predictions.

Definition of Determinant

Determinant Calculation

Laplace Expansion Theorem

Cramer's Rule

Complex Vector Space

Complex Matrix

Eigenvalues, Eigenvectors, and Eigenspaces

Characteristic Polynomial

Eigenvalues of Diagonal and Triangular Matrices

Orthogonal and Unitary Matrices

Symmetric and Hermitian Matrices

Positive Definite Matrix

Scalar Product

Matrix Condition

LU Decomposition

Cholesky Decomposition

QR Decomposition

Linear Model

System of Linear Equations

Linear Equilibrium Problem

Normal Equation System

Normal Equation System Solution

Identifiability and Ranking Capability

Regularization

Statistical Analysis

Best Approximation in Function and Polynomial Spaces

Orthogonal Projection

Orthogonal Polynomials

Matrix Similarity

Matrix Diagonalization

Basic Procedure for Diagonalization

Spectral Theorem

Spectral Theorem for Complex Matrices

Spectral Theorem for Real Matrices

Real Axis Transformation

Principal Component Analysis

Triangularization and Jordan Normal Form

Numerical Calculation of Eigenvalues

Individual Eigenvalue Calculation

All Eigenvalues Calculation

AI Programming

Coding intelligence that teaches machines to think and solve complex problems.

Neural Networks

Digital brains mimicking human neurons to recognize patterns and make decisions.

Problems of Supervised Learning

Types of Supervised Learning

Linear Regression

Function Space

Loss Function

Normal Equation

Basic Linear Function

Binary Classifier

Binary Cross-Entropy Loss

Optimization

Multi-Class Classifier

Cross-Entropy Loss

Multi-Layer Perceptron

Partial Derivative

Partial Derivative Example

Learning in Vector Form

Activation Function for Hidden Layer

Optimization Challenge

Gradient Descent Variants

Adaptive Learning Rate

Exponential Weighted Average

Momentum

Root Mean Squared Propagation

Adaptive Moment Estimation

Overfitting and Underfitting

Regularization

Parameter Penalties

Dropout

Training, Validation, and Testing

Preprocessing and Initialization

Batch Normalization

Hyperparameter Search

Convolution for Time Series

Pooling for Time Series

Convolutional Neural Networks for Time Series

Convolution for Images

Convolution on Volume

Convolution Block

Convolutional Neural Network

Machine Learning

Algorithms that learn from experience to predict future outcomes automatically.

What is Machine Learning?

What is Supervised Learning?

Formal Setting for Supervised Learning

Empirical Risk Minimization

Regularized Risk Minimization

K-Nearest Neighbor Classifier

Maximum A Posteriori Rule

Bayesian Decision Rule

Discriminant Function

Proof of Bayes Optimal Classifier

Univariate Normal Distribution

Probability vs Likelihood

Maximum Likelihood Estimation

Maximum Likelihood Estimation Example

Maximum Likelihood Method

Parameter Fitting for Normal Distribution

Covariance

Eigendecomposition of Covariance Matrix

Gaussian Model

Discriminant Function for Gaussian Model

Mahalanobis Distance

Point Estimation

Unbiased Estimator

Consistency

Mean Squared Error

Bias-Variance Decomposition of Mean Squared Error

Model Selection for Maximum Likelihood Estimation

Kullback-Leibler Divergence

Akaike Information Criterion

Cross Validation

Gaussian Mixture Model

Expectation Maximization Algorithm

Nonlinear Optimization for AI

Advanced mathematics finding optimal solutions in complex AI problem spaces.

Advanced Machine Learning

Cutting-edge techniques pushing the boundaries of artificial intelligence capabilities.

Computer Vision

Teaching machines to see and understand the visual world like humans.

Natural Language Processing

Bridging human language and machine understanding for seamless communication.