Search result: Catalogue data in Spring Semester 2023
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| Number | Title | Type | ECTS | Hours | Lecturers | |||||||||||||||||||||||||||||||||||||||||||
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| 261-5110-00L | Optimization for Data Science | W | 10 credits | 3V + 2U + 4A | B. Gärtner, N. He | |||||||||||||||||||||||||||||||||||||||||||
| Abstract | This course provides an in-depth theoretical treatment of optimization methods that are relevant in data science. | |||||||||||||||||||||||||||||||||||||||||||||||
| Learning objective | Understanding the guarantees and limits of relevant optimization methods used in data science. Learning theoretical paradigms and techniques to deal with optimization problems arising in data science. | |||||||||||||||||||||||||||||||||||||||||||||||
| Content | This course provides an in-depth theoretical treatment of classical and modern optimization methods that are relevant in data science. After a general discussion about the role that optimization has in the process of learning from data, we give an introduction to the theory of (convex) optimization. Based on this, we present and analyze algorithms in the following four categories: first-order methods (gradient and coordinate descent, Frank-Wolfe, subgradient and mirror descent, stochastic and incremental gradient methods); second-order methods (Newton and quasi Newton methods); non-convexity (local convergence, provable global convergence, cone programming, convex relaxations); min-max optimization (extragradient methods). The emphasis is on the motivations and design principles behind the algorithms, on provable performance bounds, and on the mathematical tools and techniques to prove them. The goal is to equip students with a fundamental understanding about why optimization algorithms work, and what their limits are. This understanding will be of help in selecting suitable algorithms in a given application, but providing concrete practical guidance is not our focus. | |||||||||||||||||||||||||||||||||||||||||||||||
| Prerequisites / Notice | A solid background in analysis and linear algebra; some background in theoretical computer science (computational complexity, analysis of algorithms); the ability to understand and write mathematical proofs. | |||||||||||||||||||||||||||||||||||||||||||||||
| 263-3710-00L | Machine Perception  | W | 8 credits | 3V + 2U + 2A | O. Hilliges, J. Song | |||||||||||||||||||||||||||||||||||||||||||
| Abstract | Recent developments in neural networks have drastically advanced the performance of machine perception systems in a variety of areas including computer vision, robotics, and human shape modeling This course is a deep dive into deep learning algorithms and architectures with applications to a variety of perceptual and generative tasks. | |||||||||||||||||||||||||||||||||||||||||||||||
| Learning objective | Students will learn about fundamental aspects of modern deep learning approaches for perception and generation. Students will learn to implement, train and debug their own neural networks and gain a detailed understanding of cutting-edge research in learning-based computer vision, robotics, and shape modeling. The optional final project assignment will involve training a complex neural network architecture and applying it to a real-world dataset. The core competency acquired through this course is a solid foundation in deep-learning algorithms to process and interpret human-centric signals. In particular, students should be able to develop systems that deal with the problem of recognizing people in images, detecting and describing body parts, inferring their spatial configuration, performing action/gesture recognition from still images or image sequences, also considering multi-modal data, among others. | |||||||||||||||||||||||||||||||||||||||||||||||
| Content | We will focus on teaching: how to set up the problem of machine perception, the learning algorithms, network architectures, and advanced deep learning concepts in particular probabilistic deep learning models. The course covers the following main areas: I) Foundations of deep learning. II) Advanced topics like probabilistic generative modeling of data (latent variable models, generative adversarial networks, auto-regressive models, invertible neural networks, diffusion models). III) Deep learning in computer vision, human-computer interaction, and robotics. Specific topics include: I) Introduction to Deep Learning: a) Neural Networks and training (i.e., backpropagation) b) Feedforward Networks c) Timeseries modelling (RNN, GRU, LSTM) d) Convolutional Neural Networks II) Advanced topics: a) Latent variable models (VAEs) b) Generative adversarial networks (GANs) c) Autoregressive models (PixelCNN, PixelRNN, TCN, Transformer) d) Invertible Neural Networks / Normalizing Flows e) Coordinate-based networks (neural implicit surfaces, NeRF) f) Diffusion models III) Applications in machine perception and computer vision: a) Fully Convolutional architectures for dense per-pixel tasks (i.e., instance segmentation) b) Pose estimation and other tasks involving human activity c) Neural shape modeling (implicit surfaces, neural radiance fields) d) Deep Reinforcement Learning and Applications in Physics-Based Behavior Modeling | |||||||||||||||||||||||||||||||||||||||||||||||
| Literature | Deep Learning Book by Ian Goodfellow and Yoshua Bengio | |||||||||||||||||||||||||||||||||||||||||||||||
| Prerequisites / Notice | This is an advanced grad-level course that requires a background in machine learning. Students are expected to have a solid mathematical foundation, in particular in linear algebra, multivariate calculus, and probability. The course will focus on state-of-the-art research in deep learning and will not repeat the basics of machine learning Please take note of the following conditions: 1) Students must have taken the exam in Machine Learning (252-0535-00) or have acquired equivalent knowledge 2) All practical exercises will require basic knowledge of Python and will use libraries such as Pytorch, scikit-learn, and scikit-image. We will provide introductions to Pytorch and other libraries that are needed but will not provide introductions to basic programming or Python. The following courses are strongly recommended as prerequisites: * "Visual Computing" or "Computer Vision" The course will be assessed by a final written examination in English. No course materials or electronic devices can be used during the examination. Note that the examination will be based on the contents of the lectures, the associated reading materials, and the exercises. The exam will be a 3-hour end-of-term exam and take place at the end of the teaching period. | |||||||||||||||||||||||||||||||||||||||||||||||
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| Number | Title | Type | ECTS | Hours | Lecturers | |||||||||||||||||||||||||||||||||||||||||||
| 252-0526-00L | Statistical Learning Theory | W | 8 credits | 3V + 2U + 2A | J. M. Buhmann | |||||||||||||||||||||||||||||||||||||||||||
| Abstract | The course covers advanced methods of statistical learning: - Variational methods and optimization. - Deterministic annealing. - Clustering for diverse types of data. - Model validation by information theory. | |||||||||||||||||||||||||||||||||||||||||||||||
| Learning objective | The course surveys recent methods of statistical learning. The fundamentals of machine learning, as presented in the courses "Introduction to Machine Learning" and "Advanced Machine Learning", are expanded from the perspective of statistical learning. | |||||||||||||||||||||||||||||||||||||||||||||||
| Content | - Variational methods and optimization. We consider optimization approaches for problems where the optimizer is a probability distribution. We will discuss concepts like maximum entropy, information bottleneck, and deterministic annealing. - Clustering. This is the problem of sorting data into groups without using training samples. We discuss alternative notions of "similarity" between data points and adequate optimization procedures. - Model selection and validation. This refers to the question of how complex the chosen model should be. In particular, we present an information theoretic approach for model validation. - Statistical physics models. We discuss approaches for approximately optimizing large systems, which originate in statistical physics (free energy minimization applied to spin glasses and other models). We also study sampling methods based on these models. | |||||||||||||||||||||||||||||||||||||||||||||||
| Lecture notes | A draft of a script will be provided. Lecture slides will be made available. | |||||||||||||||||||||||||||||||||||||||||||||||
| Literature | Hastie, Tibshirani, Friedman: The Elements of Statistical Learning, Springer, 2001. L. Devroye, L. Gyorfi, and G. Lugosi: A probabilistic theory of pattern recognition. Springer, New York, 1996 | |||||||||||||||||||||||||||||||||||||||||||||||
| Prerequisites / Notice | Knowledge of machine learning (introduction to machine learning and/or advanced machine learning) Basic knowledge of statistics. | |||||||||||||||||||||||||||||||||||||||||||||||
| 252-0579-00L | 3D Vision | W | 5 credits | 3G + 1A | M. Pollefeys, D. B. Baráth | |||||||||||||||||||||||||||||||||||||||||||
| Abstract | The course covers camera models and calibration, feature tracking and matching, camera motion estimation via simultaneous localization and mapping (SLAM) and visual odometry (VO), epipolar and mult-view geometry, structure-from-motion, (multi-view) stereo, augmented reality, and image-based (re-)localization. | |||||||||||||||||||||||||||||||||||||||||||||||
| Learning objective | After attending this course, students will: 1. understand the core concepts for recovering 3D shape of objects and scenes from images and video. 2. be able to implement basic systems for vision-based robotics and simple virtual/augmented reality applications. 3. have a good overview over the current state-of-the art in 3D vision. 4. be able to critically analyze and asses current research in this area. | |||||||||||||||||||||||||||||||||||||||||||||||
| Content | The goal of this course is to teach the core techniques required for robotic and augmented reality applications: How to determine the motion of a camera and how to estimate the absolute position and orientation of a camera in the real world. This course will introduce the basic concepts of 3D Vision in the form of short lectures, followed by student presentations discussing the current state-of-the-art. The main focus of this course are student projects on 3D Vision topics, with an emphasis on robotic vision and virtual and augmented reality applications. | |||||||||||||||||||||||||||||||||||||||||||||||
| 261-5120-00L | Machine Learning for Health Care | W | 5 credits | 2V + 2A | V. Boeva, J. Vogt, M. Kuznetsova | |||||||||||||||||||||||||||||||||||||||||||
| Abstract | The course will review the most relevant methods and applications of Machine Learning in Biomedicine, discuss the main challenges they present and their current technical problems. | |||||||||||||||||||||||||||||||||||||||||||||||
| Learning objective | During the last years, we have observed a rapid growth in the field of Machine Learning (ML), mainly due to improvements in ML algorithms, the increase of data availability and a reduction in computing costs. This growth is having a profound impact in biomedical applications, where the great variety of tasks and data types enables us to get benefit of ML algorithms in many different ways. In this course we will review the most relevant methods and applications of ML in biomedicine, discuss the main challenges they present and their current technical solutions. | |||||||||||||||||||||||||||||||||||||||||||||||
| Content | The course will consist of four topic clusters that will cover the most relevant applications of ML in Biomedicine: 1) Structured time series: Temporal time series of structured data often appear in biomedical datasets, presenting challenges as containing variables with different periodicities, being conditioned by static data, etc. 2) Medical notes: Vast amount of medical observations are stored in the form of free text, we will analyze stategies for extracting knowledge from them. 3) Medical images: Images are a fundamental piece of information in many medical disciplines. We will study how to train ML algorithms with them. 4) Genomics data: ML in genomics is still an emerging subfield, but given that genomics data are arguably the most extensive and complex datasets that can be found in biomedicine, it is expected that many relevant ML applications will arise in the near future. We will review and discuss current applications and challenges. | |||||||||||||||||||||||||||||||||||||||||||||||
| Prerequisites / Notice | Data Structures & Algorithms, Introduction to Machine Learning, Statistics/Probability, Programming in Python, Unix Command Line Relation to Course 261-5100-00 Computational Biomedicine: This course is a continuation of the previous course with new topics related to medical data and machine learning. The format of Computational Biomedicine II will also be different. It is helpful but not essential to attend Computational Biomedicine before attending Computational Biomedicine II. | |||||||||||||||||||||||||||||||||||||||||||||||
| 263-5000-00L | Computational Semantics for Natural Language Processing | W | 6 credits | 2V + 1U + 2A | M. Sachan | |||||||||||||||||||||||||||||||||||||||||||
| Abstract | This course presents an introduction to Natural language processing (NLP) with an emphasis on computational semantics i.e. the process of constructing and reasoning with meaning representations of natural language text. | |||||||||||||||||||||||||||||||||||||||||||||||
| Learning objective | The objective of the course is to learn about various topics in computational semantics and its importance in natural language processing methodology and research. Exercises and the project will be key parts of the course so the students will be able to gain hands-on experience with state-of-the-art techniques in the field. | |||||||||||||||||||||||||||||||||||||||||||||||
| Content | We will take a modern view of the topic, and focus on various statistical and deep learning approaches for computation semantics. We will also overview various primary areas of research in language processing and discuss how the computational semantics view can help us make advances in NLP. | |||||||||||||||||||||||||||||||||||||||||||||||
| Lecture notes | Lecture slides will be made available at the course Web site. | |||||||||||||||||||||||||||||||||||||||||||||||
| Literature | No textbook is required, but there will be regularly assigned readings from research literature, linked to the course website. | |||||||||||||||||||||||||||||||||||||||||||||||
| Prerequisites / Notice | The student should have successfully completed a graduate level class in machine learning (252-0220-00L), deep learning (263-3210-00L) or natural language processing (252-3005-00L) before. Similar courses from other universities are acceptable too. | |||||||||||||||||||||||||||||||||||||||||||||||
| 263-5051-00L | AI Center Projects in Machine Learning Research Last cancellation/deregistration date for this ungraded semester performance: Friday, 17 March 2023! Please note that after that date no deregistration will be accepted and the course will be considered as "fail". | W | 4 credits | 2V + 1A | A. Ilic, N. Davoudi, M. El-Assady, F. Engelmann, S. Gashi, T. Kontogianni, A. Marx, B. Moseley, G. Ramponi, X. Shen, M. Sorbaro Sindaci | |||||||||||||||||||||||||||||||||||||||||||
| Abstract | The course will give students an overview of selected topics in advanced machine learning that are currently subjects of active research. The course concludes with a final project. | |||||||||||||||||||||||||||||||||||||||||||||||
| Learning objective | The overall objective is to give students a concrete idea of what working in contemporary machine learning research is like and inform them about current research performed at ETH. In this course, students will be able to get an overview of current research topics in different specialized areas. In the final project, students will be able to build experience in practical aspects of machine learning research, including research literature, aspects of implementation, and reproducibility challenges. | |||||||||||||||||||||||||||||||||||||||||||||||
| Content | The course will be structured as sections taught by different postdocs specialized in the relevant fields. Each section will showcase an advanced research topic in machine learning, first introducing it and motivating it in the context of current technological or scientific advancement, then providing practical applications that students can experiment with, ideally with the aim of reproducing a known result in the specific field. A tentative list of topics for this year: - fully supervised 3D scene understanding - weakly supervised 3D scene understanding - causal discovery - biological and artificial neural networks - reinforcement learning - visual text analytics - human-centered AI - representation learning. The last weeks of the course will be reserved for the implementation of the final project. The students will be assigned group projects in one of the presented areas, based on their preferences. The outcomes will be made into a scientific poster and students will be asked to present the projects to the other groups in a joint poster session. | |||||||||||||||||||||||||||||||||||||||||||||||
| Prerequisites / Notice | Participants should have basic knowledge about machine learning and statistics (e.g. Introduction to Machine Learning course or equivalent) and programming. | |||||||||||||||||||||||||||||||||||||||||||||||
| 263-5052-00L | Interactive Machine Learning: Visualization & Explainability | W | 5 credits | 3G + 1A | M. El-Assady | |||||||||||||||||||||||||||||||||||||||||||
| Abstract | Visual Analytics supports the design of human-in-the-loop interfaces that enable human-machine collaboration. In this course, will go through the fundamentals of designing interactive visualizations, later applying them to explain and interact with machine leaning models. | |||||||||||||||||||||||||||||||||||||||||||||||
| Learning objective | The goal of the course is to introduce techniques for interactive information visualization and to apply these on understanding, diagnosing, and refining machine learning models. | |||||||||||||||||||||||||||||||||||||||||||||||
| Content | Interactive, mixed-initiative machine learning promises to combine the efficiency of automation with the effectiveness of humans for a collaborative decision-making and problem-solving process. This can be facilitated through co-adaptive visual interfaces. This course will first introduce the foundations of information visualization design based on data charecteristics, e.g., high-dimensional, geo-spatial, relational, temporal, and textual data. Second, we will discuss interaction techniques and explanation strategies to enable explainable machine learning with the tasks of understanding, diagnosing, and refining machine learning models. Tentative list of topics: 1. Visualization and Perception 2. Interaction and Explanation 3. Systems Overview | |||||||||||||||||||||||||||||||||||||||||||||||
| Lecture notes | Course material will be provided in form of slides. | |||||||||||||||||||||||||||||||||||||||||||||||
| Literature | Will be provided during the course. | |||||||||||||||||||||||||||||||||||||||||||||||
| Prerequisites / Notice | Basic understanding of machine learning as taught at the Bachelor's level. | |||||||||||||||||||||||||||||||||||||||||||||||
| 263-5255-00L | Foundations of Reinforcement Learning | W | 7 credits | 3V + 3A | N. He | |||||||||||||||||||||||||||||||||||||||||||
| Abstract | Reinforcement learning (RL) has been in the limelight of many recent breakthroughs in artificial intelligence. This course focuses on theoretical and algorithmic foundations of reinforcement learning, through the lens of optimization, modern approximation, and learning theory. The course targets M.S. students with strong research interests in reinforcement learning, optimization, and control. | |||||||||||||||||||||||||||||||||||||||||||||||
| Learning objective | This course aims to provide students with an advanced introduction of RL theory and algorithms as well as bring them near the frontier of this active research field. By the end of the course, students will be able to - Identify the strengths and limitations of various reinforcement learning algorithms; - Formulate and solve sequential decision-making problems by applying relevant reinforcement learning tools; - Generalize or discover “new” applications, algorithms, or theories of reinforcement learning towards conducting independent research on the topic. | |||||||||||||||||||||||||||||||||||||||||||||||
| Content | Basic topics include fundamentals of Markov decision processes, approximate dynamic programming, linear programming and primal-dual perspectives of RL, model-based and model-free RL, policy gradient and actor-critic algorithms, Markov games and multi-agent RL. If time allows, we will also discuss advanced topics such as batch RL, inverse RL, causal RL, etc. The course keeps strong emphasis on in-depth understanding of the mathematical modeling and theoretical properties of RL algorithms. | |||||||||||||||||||||||||||||||||||||||||||||||
| Lecture notes | Lecture notes will be posted on Moodle. | |||||||||||||||||||||||||||||||||||||||||||||||
| Literature | Dynamic Programming and Optimal Control, Vol I & II, Dimitris Bertsekas Reinforcement Learning: An Introduction, Second Edition, Richard Sutton and Andrew Barto. Algorithms for Reinforcement Learning, Csaba Czepesvári. Reinforcement Learning: Theory and Algorithms, Alekh Agarwal, Nan Jiang, Sham M. Kakade. | |||||||||||||||||||||||||||||||||||||||||||||||
| Prerequisites / Notice | Students are expected to have strong mathematical background in linear algebra, probability theory, optimization, and machine learning. | |||||||||||||||||||||||||||||||||||||||||||||||
| 263-5351-00L | Machine Learning for Genomics The deadline for deregistering expires at the end of the third week of the semester. Students who are still registered after that date, but do not provide project work, do not participate in paper presentation sessions and/or do not show up for the exam, will officially fail the course. | W | 5 credits | 2V + 1U + 1A | V. Boeva | |||||||||||||||||||||||||||||||||||||||||||
| Abstract | The course reviews solutions that machine learning provides to the most challenging questions in human genomics. | |||||||||||||||||||||||||||||||||||||||||||||||
| Learning objective | Over the last few years, the parallel development of machine learning methods and molecular profiling technologies for human cells, such as sequencing, created an extremely powerful tool to get insights into the cellular mechanisms in healthy and diseased contexts. In this course, we will discuss the state-of-the-art machine learning methodology solving or attempting to solve common problems in human genomics. At the end of the course, you will be familiar with (1) classical and advanced machine learning architectures used in genomics, (2) bioinformatics analysis of human genomic and transcriptomic data, and (3) data types used in this field. | |||||||||||||||||||||||||||||||||||||||||||||||
| Content | - Short introduction to major concepts of molecular biology: DNA, genes, genome, central dogma, transcription factors, epigenetic code, DNA methylation, signaling pathways - Prediction of transcription factor binding sites, open chromatin, histone marks, promoters, nucleosome positioning (convolutional neural networks, position weight matrices) - Prediction of variant effects and gene expression (hidden Markov models, topic models) - Deconvolution of mixed signal - DNA, RNA and protein folding (RNN, LSTM, transformers) - Data imputation for single cell RNA-seq data, clustering and annotation (diffusion and methods on graphs) - Batch correction (autoencoders, optimal transport) - Survival analysis (Cox proportional hazard model, regularization penalties, multi-omics, multi-tasking) | |||||||||||||||||||||||||||||||||||||||||||||||
| Prerequisites / Notice | Introduction to Machine Learning, Statistics/Probability, Programming in Python, Unix Command Line | |||||||||||||||||||||||||||||||||||||||||||||||
| 263-5352-00L | Advanced Formal Language Theory | W | 6 credits | 4G + 1A | R. Cotterell | |||||||||||||||||||||||||||||||||||||||||||
| Abstract | This course serves as an introduction to various advanced topics in formal language theory. | |||||||||||||||||||||||||||||||||||||||||||||||
| Learning objective | The objective of the course is to learn and understand a variety of topics in advanced formal language theory. | |||||||||||||||||||||||||||||||||||||||||||||||
| Content | This course serves as an introduction to various advanced topics in formal language theory. The primary focus of the course is on weighted formalisms, which can easily be applied in machine learning. Topics include finite-state machines as well as the algorithms that are commonly used for their manipulation. We will also cover weighted context-free grammars, weighted tree automata, and weighted mildly context-sensitive formalisms. | |||||||||||||||||||||||||||||||||||||||||||||||
| 263-5353-10L | Philosophy of Language and Computation II (with Case Study) | W | 5 credits | 2V + 1U + 1A | R. Cotterell, J. L. Gastaldi | |||||||||||||||||||||||||||||||||||||||||||
| Abstract | Understand the philosophical underpinnings of language-based artificial intelligence. | |||||||||||||||||||||||||||||||||||||||||||||||
| Learning objective | This graduate class, taught like a seminar, is designed to help you understand the philosophical underpinnings of modern work in natural language processing (NLP), most of which is centered around statistical machine learning applied to natural language data. | |||||||||||||||||||||||||||||||||||||||||||||||
| Content | This graduate class, taught like a seminar, is designed to help you understand the philosophical underpinnings of modern work in natural language processing (NLP), most of which is centered around statistical machine learning applied to natural language data. The course is a year-long journey, but the second half (Spring 2023) does not depend on the first (Fall 2022) and thus either half may be taken independently. In each semester, we divide the class time into three modules. Each module is centered around a philosophical topic. After discussing logical, structuralist, and generative approaches to language in the first semester, in the second semester we will focus on information, language games, and pragmatics. The modules will be four weeks long. During the first two weeks of a module, we will read and discuss original texts and supplementary criticism. During the second two weeks, we will read recent NLP papers and discuss how the authors of those works are building on philosophical insights into our conception of language—perhaps implicitly or unwittingly. | |||||||||||||||||||||||||||||||||||||||||||||||
| Literature | The literature will be provided by the instructors on the class website | |||||||||||||||||||||||||||||||||||||||||||||||
| 263-5354-00L | Large Language Models | W | 8 credits | 3V + 2U + 2A | R. Cotterell, M. Sachan, F. Tramèr, C. Zhang | |||||||||||||||||||||||||||||||||||||||||||
| Abstract | Large language models have become one of the most commonly deployed NLP inventions. In the past half-decade, their integration into core natural language processing tools has dramatically increased the performance of such tools, and they have entered the public discourse surrounding artificial intelligence. | |||||||||||||||||||||||||||||||||||||||||||||||
| Learning objective | To understand the mathematical foundations of large language models as well as how to implement them. | |||||||||||||||||||||||||||||||||||||||||||||||
| Content | We start with the probabilistic foundations of language models, i.e., covering what constitutes a language model from a formal, theoretical perspective. We then discuss how to construct and curate training corpora, and introduce many of the neural-network architectures often used to instantiate language models at scale. The course covers aspects of systems programming, discussion of privacy and harms, as well as applications of language models in NLP and beyond. | |||||||||||||||||||||||||||||||||||||||||||||||
| Literature | The lecture notes will be supplemented with various readings from the literature. | |||||||||||||||||||||||||||||||||||||||||||||||
| 227-0434-10L | Mathematics of Information | W | 8 credits | 3V + 2U + 2A | H. Bölcskei | |||||||||||||||||||||||||||||||||||||||||||
| Abstract | The class focuses on mathematical aspects of 1. Information science: Sampling theorems, frame theory, compressed sensing, sparsity, super-resolution, spectrum-blind sampling, subspace algorithms, dimensionality reduction 2. Learning theory: Approximation theory, greedy algorithms, uniform laws of large numbers, Rademacher complexity, Vapnik-Chervonenkis dimension | |||||||||||||||||||||||||||||||||||||||||||||||
| Learning objective | The aim of the class is to familiarize the students with the most commonly used mathematical theories in data science, high-dimensional data analysis, and learning theory. The class consists of the lecture and exercise sessions with homework problems. | |||||||||||||||||||||||||||||||||||||||||||||||
| Content | Mathematics of Information 1. Signal representations: Frame theory, wavelets, Gabor expansions, sampling theorems, density theorems 2. Sparsity and compressed sensing: Sparse linear models, uncertainty relations in sparse signal recovery, super-resolution, spectrum-blind sampling, subspace algorithms (ESPRIT), estimation in the high-dimensional noisy case, Lasso 3. Dimensionality reduction: Random projections, the Johnson-Lindenstrauss Lemma Mathematics of Learning 4. Approximation theory: Nonlinear approximation theory, best M-term approximation, greedy algorithms, fundamental limits on compressibility of signal classes, Kolmogorov-Tikhomirov epsilon-entropy of signal classes, optimal compression of signal classes 5. Uniform laws of large numbers: Rademacher complexity, Vapnik-Chervonenkis dimension, classes with polynomial discrimination | |||||||||||||||||||||||||||||||||||||||||||||||
| Lecture notes | Detailed lecture notes will be provided at the beginning of the semester. | |||||||||||||||||||||||||||||||||||||||||||||||
| Prerequisites / Notice | This course is aimed at students with a background in basic linear algebra, analysis, statistics, and probability. We encourage students who are interested in mathematical data science to take both this course and "401-4944-20L Mathematics of Data Science" by Prof. A. Bandeira. The two courses are designed to be complementary. H. Bölcskei and A. Bandeira | |||||||||||||||||||||||||||||||||||||||||||||||
| 401-3632-00L | Computational Statistics | W | 8 credits | 3V + 1U | M. Mächler | |||||||||||||||||||||||||||||||||||||||||||
| Abstract | We discuss modern statistical methods for data analysis, including methods for data exploration, prediction and inference. We pay attention to algorithmic aspects, theoretical properties and practical considerations. The class is hands-on and methods are applied using the statistical programming language R. | |||||||||||||||||||||||||||||||||||||||||||||||
| Learning objective | The student obtains an overview of modern statistical methods for data analysis, including their algorithmic aspects and theoretical properties. The methods are applied using the statistical programming language R. | |||||||||||||||||||||||||||||||||||||||||||||||
| Content | See the class website | |||||||||||||||||||||||||||||||||||||||||||||||
| Prerequisites / Notice | At least one semester of (basic) probability and statistics. Programming experience is helpful but not required. | |||||||||||||||||||||||||||||||||||||||||||||||
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