Μαθήματα

Supervised learning: least mean squares (LMS), logistic regression, perceptron, Gaussian discriminant analysis, naive Bayes, support vector machines, model selection and feature selection, ensemble methods (bagging, boosting). Deep Neural Networks & Modern Tools (e.g., Tensorflow, AutoML). Generative Adversarial Neural Networks (GANN) & Applications. Learning theory: bias/variance tradeoff, union and Chernoff/Hoeffding bounds, VC dimension. Unsupervised learning: clustering, k-means, EM, mixture of Gaussians, factor analysis, principal components analysis (PCA), independent component analysis (ICA). Reinforcement learning: Markov decision processes (MDPs), algorithms for POMDPs.

Course topics

Supervised learning: least mean squares (LMS), logistic regression, perceptron, Gaussian discriminant analysis, naive Bayes, support vector machines, model selection and feature selection, ensemble methods (bagging, boosting). Deep Neural Networks & Modern Tools (e.g., Tensorflow, AutoML). Generative Adversarial Neural Networks (GANN) & Applications. Learning theory: bias/variance tradeoff, union and Chernoff/Hoeffding bounds, VC dimension. Unsupervised learning: clustering, k-means, EM, mixture of Gaussians, factor analysis, principal components analysis (PCA), independent component analysis (ICA). Reinforcement learning: Markov decision processes (MDPs), algorithms for POMDPs.

Course Syllabus

Course Outline

State vector Hilbert spaces, Qubit. Theory of quantum measurements, orthonormal complete bases, projectors, positive operator-valued probability measures (POVM). Density matrix, spectral decomposition, convex decomposition. Bloch sphere and vector. Introduction to quantum entanglement. Quantum correlations, Biorthogonal analysis, Schmidt numbers. Measures of entanglement, Quantum entropy measures. Quantum information. The Schroedinger–HJW theorem. Quantum channels (single qubit, collective channels). Quantum algorithms, Computational and communicational algorithms. The Deutsch–Jozsa algorithm. Quantum teleportation algorithm for states, gates, channels. The LOCC protocol. Quantum walks (QW). Coin-walker Hilbert spaces. The QW channel maps. Quadratic speed ups. Introduction to the Helstrom-Holevo quantum estimation theory. Cramer-Rao bound and quantum Fisher information. Optimal measurements and the symmetric logarithmic derivative operator. Phase estimation problems of quantum states. Temperature estimation and qubit thermometry for closed and open quantum systems.

Χώροι Hilbert καταστατικών διανυσμάτων - Qubit. Θεωρία κβαντικών μετρήσεων, ορθοκανονικές βάσεις, προβολικοί τελεστές. Θετικά τελεστικά μέτρα πιθανότητας POVM. Πίνακας πυκνότητας, φασματική ανάλυση, κυρτοί συνδυασμοί. Σφαίρα κα διάνυσμα Bloch. Εισαγωγή στο κβαντικό εναγκαλισμό. Κβαντικές συσχετίσεις - Διορθογώνια ανάλυση - Αριθμοί Schmidt. Μετρήσεις εναγκαλισμού- Μέτρα κβαντικής εντροπίας. Κβαντική Πληροφορία. Το θεώρημα Schroedinger -HJW. Κβαντικά κανάλια (1-qubit, συλλογικά κανάλια). Κβαντικοί αλγόριθμοι - Αλγόριθμοι υπολογισμών και επικοινωνίας. Ο αλγόριθμος Deutsch--Jozsa. Κβαντική τηλεμεταφορά καταστάσεων, πυλών, καναλιών. Το πρωτόκολο LOCC. Κβαντικοί περίπατοι (QW). Χώροι Hilbert νομίσματος-περιπατητή. Κανάλια τύπου QW. Τετραγωνικές επιταχύνσεις. Εισαγωγή στη θεωρία κβαντικής εκτιμητικής Helstrom-Holevo. Φράγμα Cramér-Rao και κβαντική πληροφορία Fisher. Βέλτιστες μετρήσεις και ο συμμετρικός τελεστής λογαριθμικής παραγώγου. Προβλήματα εκτιμητικής γωνίας φάσης σε κβαντικές καταστάσεις. Εκτιμητική θερμοκρασίας και θερμιδομετρία  qubit για κλειστά και ανοιχτά κβαντικά συστήματα.

 Photo: Jing Liu et al 2020 J. Phys. A: Math. Theor. 53 023001

Διαλέξεις/Lectures

Πέμπτη/Thu,           12:00-13:00  αιθ./Classroom 2041
Παρασκευή/Fri,      12:00-15:00 αιθ.Classroom 2041

Ώρες γραφείου :   Μία ώρα μετά το τέλος των διαλέξεων Πέμπτης και Παρασκευής ή μετά από συνεννόηση

The course will cover tools for optimization problems, where a sequence of (inter-dependent) decisions must be made (dynamically), often under uncertainty about the environment to be optimized (requires learning). Problems like this arise in many modern applications, ranging from autonomous driving and robotics, to game playing (chess, poker, go) and wired/wireless network management. The specific topics covered will be the following: Quick revision of first order optimization methods (gradient descent and stochastic gradient descent); Multi-armed Bandits; First order algorithms for Online Convex Optimization; Online Convex Optimization with instantaneous and long-term constraints; Distributed online convex optimization; backpressure algorithms for Stochastic Network Optimization; Markov Decision Processes; Tabular Reinforcement Learning - RL (Q-Learning, SARSA); Policy gradient methods; Approximate (e.g. Deep) RL solutions such as Deep Q Networks, Actor-Critic methods, and the recent AlphaGo and AlphaZero algorithms, that have been very successful in popular strategic games; Generalized policy rollout for online learning; The class will include both take home exercises, as well as a programming assignment.

Time series data are indexed by the time dimension. This feature imposes a natural order and distinguishes time series from "static" data.  Every data scientist is bound to face at some point in their career time series data.  This course focuses on the fundamental concepts underlying the analysis of time series and some of the methods that can be used to model such data. 

Time series analysis has a long history which led to the development of classical methods such as ARIMA. The machine learning revolution has introduced new tools for time series analysis which are based on deep neural networks (DNNs). However, for most of the everyday problems faced by data scientists, ARIMA and its generalizations perform as well (or even better) than DNN methods which require a very large amount of data in order to achieve their full potential.

This course will focus on classical methodologies of time series analysis.  While the latter are not based on DNNs, they are today considered components of the broad machine learning framework.

SPRING SEMESTER 2023-2024

Tuesday 7-9pm

Wednesday 5-7pm

ROOM 145.Π58

Time series data are indexed by the time dimension. This feature imposes a natural order and distinguishes time series from "static" data.  Every data scientist is bound to face at some point in their career time series data.  This course focuses on the fundamental concepts underlying the analysis of time series and some of the methods that can be used to model such data. 

Time series analysis has a long history which led to the development of classical methods such as ARIMA. The machine learning revolution has introduced new tools for time series analysis which are based on deep neural networks (DNNs). However, for most of the everyday problems faced by data scientists, ARIMA and its generalizations perform as well (or even better) than DNN methods which require a very large amount of data in order to achieve their full potential.

This course will focus on classical methodologies of time series analysis.  While the latter are not based on DNNs, they are today considered components of the broad machine learning framework.

SPRING SEMESTER 2022-2023

Tuesday 5-7pm

Thursday 5-7pm

ROOM 145.Π58