Students select project theme and work in groups to complete the project. Students present their midterm progress and results. Students complete the Project with a public presentation of their work.

Project themes are compiled by the lecturer from proposals by faculty members and industry.**Matrix and tensor algebra. **Notation. Differentiation.

**Theory.**
Gradient. Convexity. Strong convexity. Lipschitz continuity. Limits on
convergence rate. Constrained optimization. Dual function. Dual problem. Strong
duality. Slater’s condition. Karush-Kuhn-Tucker condition.

**Optimization methods.**Gradient. Stochastic gradient. Conjugate gradient. Quasi-Newton. Subgradient. Proximal gradient. Accelerated gradient. Interior-point methods. ADMM. Adaptive gradient methods.

- nosilec: Gašper Fijavž
- nosilec: Polona Oblak
- nosilec: Žiga Virk

**Data. **Summarizing data. Visualizing
data. The fundamental problem of data analysis: uncertainty in our
understanding of the data generating process.

**Probability.** The axiomatic, Bayesian
and classical (frequentist) views of probability. Joint, marginal and
conditional densities. Bayes theorem.

**Distributions.** Common probability
distributions. Distributions as a means for expressing probabilistic opinions.
Distributions as data generators.

**Fundamental statistical techniques.**
Monte Carlo integration. Bootstrap. Maximum likelihood estimation. Bayesian
inference.

**Basic statistical tasks.** Hypothesis
testing vs Bayesian estimation.

**The multivariate normal distribution.**As a linear transformation. Linear regression. PCA.

- nosilec: Erik Štrumbelj

The course is an introductory overview of topics relevant to data science. The following topics will be presented to students through lectures by faculty members and guest lecturers from industry and research institutions:

**Working
with data. **Getting.
Processing. Storing. Cleaning. Summarizing. Visualizing.

**Analytics.
**Prediction.
Clustering. Statistical inference.

**Business
and social aspects**.
Privacy. Security. Ethics. Licensing. Intellectual property.

**Best practices (tools).**Programming, coding standards (Python). Versioning (Github). Reproducibility (Jupyter). Typsetting (LaTeX). Public repositories (ArXiv, Zenodo).

- nosilec: Tomaž Curk
- nosilec: Slavko Žitnik

**Linear models. **Linear regression.
Linear discriminant analysis. Logistic regression. Gradient descent. Stochastic
gradient descent.

**The machine learning approach. **Cost
functions. Empirical risk minimization. Maximum likelihood estimation. Model
evaluation. Cross-validation.

**Feature selection. **Search-based feature
selection. Regularization.

**Tree-based models. **Decision trees.
Random forest. Bagging. Gradient tree boosting.

**Clustering. **k-means. Expectation
Maximization.

**Non-linear regression. **Basis functions.
Splines. Support vector machines. Kernel trick.

**Neural networks.**Perceptron. Activation functions. Backpropagation.

- nosilec: Blaž Zupan