<table>
<tbody>
<tr>
<td>Week</td>
<td></td>
<tr>
<tr>
<td>1</td>
<td>Mathematical Basics 1 – Introduction to Machine Learning, Linear Algebra
Introduction to Machine Learning:
Overview of Machine Learning (ML),Types of ML: Supervised, Unsupervised, Reinforcement Learning,Key applications and examples of ML
Linear Algebra:
Vectors, matrices, and their operations,Matrix multiplication, determinants, and inverses
Eigenvalues and eigenvectors,Singular Value Decomposition (SVD),Applications of linear algebra in ML
</td>
</tr>
<tr>
<td>2</td>
<td> Mathematical Basics 2 – Probability
Probability Theory: Basic probability concepts (events, sample spaces, conditional probability)
Random variables, probability distributions (discrete and continuous)
Expectation, variance, and standard deviation
Common probability distributions: Bernoulli, Binomial, Poisson, Normal, Exponential
Central Limit Theorem
Applications in Machine Learning: Probabilistic models,Bayesian inference basics
</td>
</tr>
<tr>
<td>3</td>
<td>Computational Basics – Numerical Computation and Optimization, Introduction to Machine Learning Packages
Numerical Computation:
Basics of numerical analysis, Floating-point arithmetic and errors,Numerical integration and differentiation,
Optimization:
Gradient Descent and its variants (Stochastic, Mini batch) , Convex optimization, Optimization challenges in ML (saddle points, local minima)
Machine Learning Packages:
Introduction to Python and Jupyter Notebooks, Overview of ML libraries: NumPy, SciPy, sci-kit-learn, TensorFlow, Keras, PyTorch
Hands-on exercises with basic ML algorithms using these libraries
</td>
</tr>
<tr>
<td>4</td>
<td>Week 4: Linear and Logistic Regression – Bias/Variance Tradeoff, Regularization, Variants of Gradient Descent, MLE, MAP, Applications
Linear Regression:
Model representation, assumptions,Ordinary Least Squares (OLS) method
Cost function and Gradient Descent for Linear Regression,Evaluation metrics: RMSE, R²
Logistic Regression:
Model representation, assumptions,Sigmoid function, cost function,Gradient Descent for Logistic Regression,Evaluation metrics: Accuracy, Precision, Recall, F1 Score, ROC-AUC
Bias/Variance Tradeoff:
Understanding bias and variance
Strategies to balance bias and variance
Regularization:
L1 (Lasso) and L2 (Ridge) regularization,Regularization impact on model complexity
Variants of Gradient Descent:
Stochastic Gradient Descent (SGD),Mini-batch Gradient Descent
</td>
</tr>
<tr>
<td>5</td>
<td>Neural Networks – Multilayer Perceptron, Backpropagation, Applications
Multilayer Perceptron (MLP):
Architecture and components
Activation functions (ReLU, Sigmoid, Tanh)
Forward propagation, Backpropagation, Derivation and intuition, Chain rule for gradients
Implementation of backpropagation in MLPs,Applications:
</td>
</tr>
<tr>
<td>6</td>
<td>Convolutional Neural Networks 1 – CNN Operations, CNN Architectures
CNN Operations:
Convolution operation, Pooling (Max, Average), Padding and Stride
CNN Architectures:
Layer types and their roles (Convolutional layers, Pooling layers, Fully Connected layers)
Classic architectures: LeNet, AlexNet, VGG, GoogLeNet, ResNet
Hands-on Implementation:
Building simple CNN models using ML libraries
</td>
</tr>
<tr>
<td>7</td>
<td>Convolutional Neural Networks 2 – Training, Transfer Learning, Applications
Training CNNs:
Techniques for improving training (Data Augmentation, Dropout, Batch Normalization)
Overfitting and regularization in CNNs
Transfer Learning:
Concept and benefits
Pre-trained models and fine-tuning
Applications:
Practical applications of CNNs in image classification, object detection, segmentation
Sequence modeling applications (text generation, language translation, time series prediction)
Application in clustering and density estimation
Applications:
Practical examples and use cases of clustering and density estimation techniques.
</td>
</tr>
<tr>
<td>8</td>
<td>Recurrent Neural Networks (RNN), LSTM, GRU, Applications
Recurrent Neural Networks (RNN):
Architecture and functionality
Challenges (vanishing/exploding gradients)
Long Short-Term Memory (LSTM):
LSTM cell architecture and components
Advantages over standard RNNs
Gated Recurrent Unit (GRU):
GRU cell architecture and components
Comparison with LSTM
Applications:
</td>
</tr>
<tr>
<td>9</td>
<td>Classical Techniques 1 – Bayesian Regression, Binary Trees, Random Forests, SVM, Naïve Bayes, Applications
Bayesian Regression:
Bayesian approach to linear regression
Predictive distribution
Decision Trees:
Tree structure, splitting criteria.
Pruning and overfitting
Random Forests:
Ensemble method, bagging
Feature importance
Support Vector Machines (SVM):
Hyperplanes and margins
Kernel trick
Naïve Bayes:
Assumptions, likelihoods
Variants (Gaussian, Multinomial)
</td>
</tr>
<tr>
<td>10</td>
<td> Classical Techniques 2 – k-Means, kNN, GMM, Expectation Maximization, Applications
k-Means Clustering:
Algorithm steps, choosing k
Evaluation metrics (Inertia, Silhouette Score)
k-Nearest Neighbors (kNN):
Distance metrics (Euclidean, Manhattan)
Weighting and voting schemes
Gaussian Mixture Models (GMM):
Mixture of Gaussians, responsibilities
</td>
</tr>
</tbody>
</table>