Course description
Instructor
Santiago Toledo Cortés
Assistant Professor
Department of Information Technology and Process Optimization
Universidad de La Sabana
Course goal
Machine learning (ML) aims to build systems capable of learning from experience and adapting their behavior accordingly. It offers powerful methods for extracting insights from large volumes of data and has become a cornerstone in fields such as bioinformatics, information retrieval, business analytics, and autonomous systems.
This course emphasizes the mathematical, statistical, and computational principles that underpin machine learning. These core concepts are critical for analyzing current algorithms, designing new models, and applying ML effectively to real-world challenges.
Course topics
1 Introduction to Machine Learning
1.1 History of ML
1.2 The learning problem
1.3 Design and analysis of ML experiments
2 Probabilistic models
2.1 Bayesian decision theory
2.2 Parametric estimation
2.3 Non-parametric estimation
3 Instance based learning
3.1 K-nearest neighbors
3.2 Kernel methods
3.3 Support vector machines
4 Function approximation and neural networks
4.1 Neural networks
4.2 Differentiable programming
4.3 Deep learning
4.4 Convolutional neural networks
5 Generative models
5.1 Autoencoders
5.2 Variational autoencoders
5.3 Diffusion models
5.4 Attention mechanisms
5.5 Transformers
5.6 Language models
6 Kernel density matrices
6.1 Density matrices
6.2 KDM for density estimation
6.3 KDM for classification and regression
6.4 KDM for generative modeling
Evaluation and grading policy
- Assignments 20%
- Quizzes 20%
- Exam 30%
- Final project 30%
Course resources
References
- [Alp14] Alpaydin, E. Introduction to Machine Learning, 3Ed. The MIT Press, 2014
- [Bis24] Bishop, C. M. & Bishop H, Deep Learning: Foundations and Principles, Springer, 2024.
- [Mur12] Murphy, Kevin P. Machine learning: a probabilistic perspective. The MIT Press, 2012.
- [Sha14] Shalev-Shwartz, S., & Ben-David, S. (2014). Understanding machine learning: From theory to algorithms. Cambridge university press.
- [Dei20] Deisenroth, M. P., Faisal, A. A., & Ong, C. S. (2020). Mathematics for machine learning. Cambridge University Press.
- [Bar13] Barber, David, Bayesian Reasoning and Machine Learning, Cambridge University Press, 2013.
- [Bis06] Bishop, C. Pattern Recognition and Machine Learning. Springer-Verlag, 2006
- [HTF09] Hastie, T. and Tibshirani, R. and Friedman. The elements of statistical learning: data mining, inference, and prediction, Springer, 2009
- [GBC16] Goodfellow, Ian, Yoshua Bengio, and Aaron Courville. Deep learning. MIT press, 2016.
- [DHS00] Duda, R. O., Hart, P. E., and Stork, D. G. 2000 Pattern Classification (2nd Edition). Wiley-Interscience.
- [SC04] Shawe-Taylor, J. and Cristianini, N. 2004 Kernel Methods for Pattern Analysis. Cambridge University Press.
- [SS02] Scholkopf, B. and Smola, A.J., 2002, Learning with kernels, MIT Press.
Additional resources
- SciPy: scientific, mathematical, and engineering package for Python
- scikit-learn: machine learning Scipy add-on
- Kaggle: datascience competition, many interesting data sets and different competitions with prizes.
- TensorFlow: open source software library for dataflow and differentiable programming across a range of tasks.
- PyTorch: open source machine learning library based on the Torch library.
- Keras: high-level neural networks API, written in Python and capable of running on top of TensorFlow, PyTorch, or Jax.
- Coursera Machine Learning Course: one of the first (and still one of the best) machine learning MOOCs taught by Andrew Ng.
- [MIT-IntroDL] MIT 6.S191 Introduction to Deep Learning, Spring 2025, MIT
- [FundDL] Raúl Ramos, Fundamentos de Deep Learning, Universidad de Antioquia, 2021
Course schedule
| Week | Topic | Material | Assignments |
|---|---|---|---|
| Jul 22 | Course presentation 1.1 History of ML | Reading material and resources Linear Algebra and Probability Review (part 1 Linear Algebra, part 2 Probability) [GBC16] Chap 2, Chap 3 | Practice problems 1 |
| Jul 29 | 1.2 The learning problem | Synchronous Class: - Different approaches to solve a classification problem (notebook, video ) - The learning problem ( slides, video) Reading material and resources [Alp14] Chap 1 (slides) [Dei20] Chap 8 (book) | Practice problems 2 |
| Aug 4 | 1.3 Design and analysis of ML experiments | Asynchronous class - 1. Introduction (video 2m) - 2. Algorithm preference (video 8m) - 3. Factors and response (video 6.5m) - 4. Strategies of experimentation (video 12m) - 5. ML experiments (video 2m) - 6. Cross-validation (video 18.5m) - 7. Bootstrapping (video 15m) - 8. Performance measures (video 9m) - 9. ROC curve (video 24m) - 10. Precision and recall (video 10m) - 11. Interval estimation (video 14m) - 12. Hypothesis testing (video 23.5m) - 13. Error types (video 8.5m) - 14. Statistics (video 2m) - 15. Binomial tests (video 2m) - 16. Normal approximation (video 1m) - 17. Paired t-test (video 3m) - 18. McNemar's test (video 3.5m) - 19. K-fold CV paired t-test (video 3m) - 20. Anova (video 13.5m) - 21. Post-hoc tests (video 9m) Reading material and resources [Alp14] Chap 19 (slides) Synchronous class Meet recording: video | Practice problems 2.5 |
| Aug 11 | 2.1 Bayesian decision theory | Asynchronous class - 1. Probability and inference (video 8.5m) - 2. Example MLE derivation (video 18m) - 3. Classification (video 4m) - 4. Bayes' rule (video 13m) - 5. Bayes' rule K > 2 (video 1m) - 6. Losses and risks (video 7.5m) - 7. 0/1 loss (video 10m) - 8. Rejection (video 18.5m) - 9. Different losses (video 8.5m) - 10. Discriminant functions (video 9m) - 11. K=2 classes (video 4m) Reading material and resources [Alp14] Chap 3 (slides) | Practice problems 3 Optional additional exercises: [Alp14] Chap 3 Ex. 1-6 |
| Aug 18 | 2.2 Parametric estimation | Asynchronous class - 1. Parametric estimation (video 1m) - 2. Maximum likelihood estimation (video 2m) - 3. Bernoulli/multinomial (video 3m) - 4. Gaussian distribution (video 1.5m) - 5. Bias and variance (video 5.5m) - 6. Bias and variance example (video 31m) Reading material and resources [Alp14] Chap 4, 5 (slides) Bias and variance (Jupyter notebook) | Practice problems 4 Optional additional exercises: [Alp14] Chap 4 Sect 4.10 Ex. 1-8 |
| Sept 9 | 3.2 Kernel methods | Asynchronous class - 1. Introduction (video 7.5m) - 2. Input and feature space (video 9m) - 3. The kernel trick (video 12m) - 4. Kernel induced feature space (video 8m) - 5. Kernel approach to ML (video 6.5m) - 6. Kernel functions (video 12m) - 7. Embeddings and kernels (video 9.5m) - 8. Visualizing kernel induced spaces (video 16.5m) - 9. Kernel algorithms (video 1m) - 10. Example: linear regression (video 9.5m) - 11. Solution using optimization (video 4.5m) - 12. Linear regression as a kernel method (video 7m) - 13. Dual linear regression (video 8m) - 14. Solution of dual linear regression (video 10m) - 15. Coding primal linear regression (video 8m) - 16. Regularization (video 9m) - 17. Ridge regression (video 5m) - 18. Ridge regression as a kernel method (video 8m) - 19. Different kernel functions (video 19.5m) Reading material and resources Introduction to kernel methods (slides) [Alp14] Chap 13 (slides) [SC04] Chap 1 and 2 | Practice problems 5 Assignment 1 |
| Sept 29 | 4.1 Neural networks | Asynchronous class - 1. History: the perceptron (video 3m) - 2. History: artificial neuron (video 4m) - 3. History: NN criticism (video 3.5m) - 4. History: backpropagation (video 6.5m) - 5. History: SVM's and kernels (video 11.5m) - 6. History: beginning of deep learning (video 3m) - 7. History: UNNeuro (video 3m) - 8. Practical example (video 28.5m) - 9. Backpropagation derivation (video )45m Reading material and resources Neural networks, Representation Learning and Deep Learning (slides) [Alp14] Chap 11 (slides) Quick and dirty introduction to neural networks (Colab notebook) Backpropagation derivation handout | Practice problems 7 |
| Sept | 4.2 Differentiable programming | Asynchronous class - 1. Deep learning frameworks (video 22.5m) - 2. Tensorflow example (video 35m) - 3. Keras example (video 34.5m) Reading material and resources Deep learning frameworks (slides) Introduction to TensorFlow (Jupyter notebook) Neural Networks in Keras (Jupyter notebook) Neural Networks in PyTorch (Jupyter notebook) | Practice problems 8 |
| Oct | 4.3 Deep learning 4.4 Convolutional neural networks | Asynchronous class - 1. Introduction to deep learning (video) - 2. Convolutional neural networks (video ) - 3. CNN in Keras example (video ) Reading material and resources Representation Learning and Deep Learning (slides) [GBC2016] (Chap 9) CNN for image classification in Keras (Jupyter notebook) ConvNetJS demos Feature visualization | Practice problems 9 |
| Oct | 5.1 Autoencoders 5.2 Variational autoencoders | Synchronous class Autoencoders and variational autoencoders (video, ELBO derivation notes) Reading material and resources [Bis24] Chap 19 Autoencoders Ava Amini, Deep generative models (slides, video) (from MIT 6.S191) Autoencoders and variational autoencoders (Jupyter notebook) | Practice problems 10 Project proposal: 3 persons per group, pdf with maximum 2 pages describing problem, objectives and method (16/06/25) Assignment 2 |
| Oct | 5.4 Attention mechanisms 5.5 Transformers | Synchronous class Introduction to Transformers (video, Jupyter notebook) Reading material and resources [Bis24] Chap 12 Transformers | Practice problems 11 |
| Oct | 5.6 Language models | Synchronous class Reading material and resources [Bis24] Chap 12 Transformers | |
| Oct | 5.6 Kernel density matrices | Reading material and resources - González, F. A., Ramos-Pollán, R., & Gallego-Mejia, J. A. Kernel Density Matrices for Probabilistic Deep Learning, arXiv: 2305.18204. - An Introduction to Kernel Density Matrices (notebook) - Kernel Density Matrices Library https://github.com/fagonzalezo/kdm | |
| Nov | Final Project | Final project |