Μαθήματα

Welcome to grad course 602! This is a core graduate course, useful for people specialising in various aspects of engineering.
Throughout the semester, we derive and discuss basic theoretical tools and provide concrete examples. Even though practical
engineering problems will be analyzed, the course aims to develop solid problem solving skills applicable to more general settings.

It is hard to find a problem in digital communications, big data analytics, pattern recognition, radar/satellite engineering, bioinformatics, i.e., the broad area of signal processing that does not involve core detection and estimation theory!
Students must feel comfortable with probability and linear algebra; however, all necessary background material is taught in the class.

Pls consult "Extended Syllabus" in the "Documents" section for course content.

Χρήση στοχαστικών μεθόδων για την ανάλυση χρονοσειρών. Για περισσότερες πληροφορίες βλέπε το σχετικό αρχείο.

ΧΕΙΜΕΡΙΝΟ ΕΞΑΜΗΝΟ 2021-2022

ΑΙΘΟΥΣΑ 2041 Κτ. Επιστημών, ΚΑΘΕ ΠΕΜΠΤΗ 5μμ-8μμ

Fundamentals of programming with Python and Python libraries for data manipulation. This is a hands-on course with a substantial amount of project work. No prior knowledge of Python is needed, but a basic understanding of programming concepts (variables, types, functions, files, etc) as well as computer use skills are required.

• Part I: We will cover principles of object-oriented and structured programming, data representation via Python data structures, and fundamental data manipulation in idiomatic Python. Then, we will examine Python libraries for scientific computing (numpy and scipy).
• Part II: We will learn to work with basic software development technologies (version control, package installation, package publication) and interactive environments. A practical introduction to Jupyter, pandas, scikit-learn and matplotlib will be followed by students demonstrating their use on introductory data analysis tasks.
• Part III: An introduction to high-performance computing techniques via Python, including dask and tensorflow will be given. Students will be asked to implement all stages of a scientific workflow, demonstrating the skills acquired in the previous stages of the course.

Requirements: basic knowledge of programming in any programming language

Uncertainty and probabilistic reasoning. Robotic perception and action. Recursive state estimation: state space, belief space, prediction and correction, Bayes filter. Estimation filters: linear Kalman filter, extended Kalman filter, unscented Kalman filter, histogram filter, particle filter. Probabilistic motion models: velocity model, odometry model, sampling and probability density. Probabilistic observation models: beam model, scan model, feature model, sampling and probability density. Robot localization: Markov, Gaussian, Grid, Monte-Carlo. Robotic mapping: occupancy grid maps, feature maps, simultaneous localization and mapping (SLAM). Decision making under uncertainty, Markov decision processes (MDPs), optimal policies, value iteration, policy iteration. Partial observability, partially observable MPDs (POMDPs), augmented MDPs. Reinforcement learning, prediction and control, trial and error, approximate representations. Multi-robot planning, coordination, and learning.
syllabus

Probability spaces, Random Variables and Stochastic Processes, Conditional Probability, Expected Values, Conditional Expectations, Independence of Random Variables. The Bernoulli Stochastic Process and Sums of Independent Random Variables: Bernoulli Process, Number of Successes, Times of Successes, Sums of Independent Random Variables, Chebyshev Inequality, Weak and Strong Law of Large Numbers, Central Limit Theorem.
Basics of Inference and Testing (including maximum likelihood estimates, hypothesis testing, likelihood ratio test, and Bayesian inference), Linear regression models, Generalized linear regression models (including logistic regression), Nonparametric Regression (including Gaussian Process regression), Tree methods and Forests, Bagging and Ensemble methods, Statistical Computing.

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Probabilistic Graphical Models (PGM) are based on graph, probability, estimation, and information theory, as well as elements of machine learning and offer a fascinating unifying theoretical framework exploited in a rich variety of (challenging) engineering applications, including communications, computer vision, natural language processing, bioinformatics, social networks, and big data analysis. They are particularly useful in problems that can be described as graphs of random variables, and their theory is currently an active topic of research. More specifically, PGMs encode (conditional) dependencies among random variables on carefully crafted graphs. Such description is powerful enough to describe a variety of many famous algorithms, such as (Gaussian) Belief Propagation, Kalman Filtering, Viterbi, Expectation-Maximization. This class will offer an introduction in representation with PGMs, algorithms for exact inference, approximate inference, and learning/estimation. Directed acyclic graphs (DAGs) (Bayesian Nets) factorization theorem and semantics (I-map, d-separation, p-map). Undirected graphs (Markov Blanket, Hammersley-Clifford theorem), factor graphs (and techniques to convert), Gaussian Graphical Models. Exact Inference (elimination algorithm, sum-product/belief propagation, max-product on Trees, HMMs and Kalman Filtering, Junction Tree algorithm). Approximate Inference: Loopy Belief Propagation, Sampling Methods (Particle Filtering, Metropolis-Hastings). Intro to learning graphs: ML Techniques, Chow-Liu, BIC-based Techniques, EM. Term projects will thoroughly study application examples in diverse domains.

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Στοιχεία οπτικής και φυσικής στερεάς κατάστασης, διαμόρφωση φωτός, οθόνες, Lasers, εφαρμογές των Lasers, φωτοανιχνευτές, οπτικές ίνες, συστήματα οπτικής επικοινωνίας, προχωρημένα θέματα οπτοηλεκτρονικής

Χρήση στοχαστικών μεθόδων για την ανάλυση χρονοσειρών. Για περισσότερες πληροφορίες βλέπε το σχετικό αρχείο.

ΧΕΙΜΕΡΙΝΟ ΕΞΑΜΗΝΟ 2021-2022

ΑΙΘΟΥΣΑ 2041 Κτ. Επιστημών, ΚΑΘΕ ΠΕΜΠΤΗ 5μμ-8μμ