The course provides a survey of dimensionality reduction (feature extraction) and classification methods. Dimensionality reduction enhances the performance of computer vision and machine learning-based approaches, it allows to represent the data in a more efficient way, it allows to visualise high-dimensional data. Among others, we study principal component analysis (PCA), non-negative matrix factorization (NMF), independent component analysis (ICA), t-distributed Stochastic Neighbour Embedding (t- SNE). Concerning classification methods, we study many classical "shallow-learning" classifiers, e.g., nearest neighbours, naive Bayes, support vector machine (SVM), linear and quadratic discriminant analysis (LDA and QDA), decision trees. Though all details are provided for most methods, we put a strong emphasis on intuition and practical applications: we discuss (and apply the acquired knowledge to various practical problems in lab classes), e.g., classification of multidimensional data (including time series, images and texts), image compression, topic recovery, recommendation systems.

The course is devoted to discrete time Markov chains with finite state space. We gently start with fundamentals (stationary distributions, transition-matrix based simulations, reversibility) and go through monte carlo Markov chain methods (MCMC, a class of algorithms providing one of the currently most popular methods for simulating complicated stochastic systems); rate of convergence methods ("how many times should we shuffle a deck of cards?" — we study coupling methods, strong stationary times, strong stationary duality, inequalities (Cheeger and Poincaré) for bounding the second- largest eigenvalue of a transition matrix); coupling from the past (CFTP) algorithm (improvement of standard MCMC, allows to obtain an unbiased sample from given distribution on huge state space, e.g., Ising model); estimating winning probabilities in gambler ruin-like problems (first step analysis and Siegmund duality); simulated annealing (a widely used randomized algorithm for various optimization problems); basics of hidden markov models (HMM, a popular machine learning algorithm, e.g., for speech recognition); randomized polynomial time approximation schemes (MCMC- originated algorithm for approximating "the answer" to NP-hard related problem, e.g., graph coloring).

The aim of the course is to discuss the methods used in the analysis and processing of texts in natural languages, with particular emphasis on results that can be translated into effective implementation. We consider both classical methods of language modelling (Hidden Markov Models, (Probabilistic) Context Free Grammars, Finite State Transducers) and modern, neural networks based approaches: RNN, LSTM, Convolutional Neural Networks and Transformer. We show several applications of this methods, including POS-tagging, dependency parsing, Named Entity Recognition, Machine Translation, and Natural Language Generation.

In this course, we cover basic and more advanced information retrieval techniques. We also discuss data mining methods applied to texts. We discuss how to implement from scratch efficient systems gathering information from large text corpora. We analyze in detail several variants of word embeddings, and their use in computing texts similarity. We discuss text classification methods, flat and hierarchical clusterization, automatic summarisation, text comprehension methods and question answering.

This course focuses on advanced data mining algorithms for processing big, complex and unstructured data. It mainly concerns recommendation systems, dimensionality reduction with neighborhood embedding, temporal data mining and decision support systems. In recommendation systems, various approaches from simple collaborative filtering to advanced matrix factorization are presented and discussed in the context of their practical relevance, concerning not only the popular MSE or MAE measures, but also the coverage, diversity, and novelty of recommendations. In temporal data mining, beside the analysis of regular time series with machine learning methods, such as Support Vector Regression and Neural Networks, unstructured temporal data are studied. Student projects concern unstructured datasets, such as irregular multidimensional time series, GPS tracks or medical images.

This course covers the technical background useful in processing large amounts of data in a distributed environment. We discuss cloud computing basics and then introduce Hadoop Distributed File System (HDFS) architecture and MapReduce programming paradigm. The course studies in-depth Apache Spark and its ecosystem including Spark programming with Scala, Spark SQL, Spark graph processing framework GraphX, also TinkerPop and Gremlin traversals. Finally, some time is spent on stream processing technologies such as Apache Kafka and Spark Streaming.

In this course we will provide mathematical theory, which explains statistical problems in the analysis of high dimensional data. In the first part of the lecture we will concentrate on the generic problem of estimating the vector of means of multivariate normal distribution. We will discuss testing the global hypothesis that this vector is equal to zero and show a variety of methods which are optimal under different scenarios concerning the sparsity of this vector. We will also discuss the detectability curve, which provides the relationship between the sparsity and the magnitude of the elements of the vector of means, so that the signal can be identified with testing procedures. The course will also cover different procedures for multiple testing, Stein identity and James-Stein estimator of the vector of means. Finally, we will discuss the topic of selective inference and the application of the above ideas in the context of high dimensional multiple regression.

Neural Networks course provides in-depth understanding of Artificial Neural Networks and Deep Learning methods, from both a theoretical and practical standpoint. The course will neural network fundamentals and provide details on most commonly used models: convolutional architectures used for image processing, recurrent networks for sequential data, and attention-based models used in language processing. We will also study modern data generation methods, such as variational auto-encoders and generative adversarial networks, concentrating on learning features that are useful in downstream data processing tasks. Accompanying lab sessions will provide hands-on experience with the material.

Numerical programming tools and methods is an introduction to programming languages and frameworks used in data science and deep learning. Concentrating on Python ecosystem, the course teaches numpy internals, data wrangling with pandas, and efficient usage of hardware accelerators through deep learning frameworks. Techniques are illustrated using practical projects that involve physical simulations, digital signal processing, real-world data analysis and modeling using machine learning.