Mathematical Methods of Machine Learning and Data Science

Aim

After completing the course, the student shall be able to:

• Apply concepts from linear algebra to learning tasks, e.g., for fitting data to a model.
• Apply concepts from probability to learning tasks, e.g., for modeling noise in data.
• Implement, and apply basic data science algorithms, e.g., k-means for classification tasks.
• Solve a practical problem related to the course contents and account for this solution.

Content

• Applications of linear algebra in learning and data science: Matrices and vectors. Rank and solvability of linear systems, least-squares (underdetermined and overdetermined case), vectorization and Kronecker product. Quadratic forms and eigenvalues/eigenvectors, singular value decomposition.
• Applications of probability and statistics in learning and data science: Random variables, expectation and moments, conditional probability and Bayes’ theorem. Mixture distributions. Multivariate normal distribution and other important distributions. Probabilistic modeling based on data and paradoxes in probability, e.g., Simpson’s paradox.
• Basic learning theory and algorithms: Fitting data to a model. Principal component analysis. k-means clustering. Gradient descent. Convergence concepts.