Použití randomizovaných metod nejmenších čtverců
| Název práce v češtině: | Použití randomizovaných metod nejmenších čtverců |
|---|---|
| Název v anglickém jazyce: | Randomized Least Squares Methods |
| Klíčová slova: | metoda nejmenších čtverců|randomizované metody|numerické metody|lineární algebry |
| Klíčová slova anglicky: | randomized methods|least squares|numerical methods|numerical linear algebra|scientific computing|numerical mathematics|data science |
| Akademický rok vypsání: | 2023/2024 |
| Typ práce: | bakalářská práce |
| Jazyk práce: | |
| Ústav: | Katedra numerické matematiky (32-KNM) |
| Vedoucí / školitel: | Erin Claire Carson, Ph.D. |
| Řešitel: |
| Zásady pro vypracování |
| The project will involve writing a background on methods for solving least squares problems, both using randomized and deterministic algorithms. It will also involve writing implementations of randomized least squares routines, performing tuning of parameters, and comparing randomized and non-randomized approaches within a particular data analysis application. Broader questions include:
1. How is the accuracy of the final answer affected by the use of a randomized method? 2. Can the performance of a particular data analysis application area be improved by replacing the standard least squares solution with a randomized method? |
| Seznam odborné literatury |
| * Michael W. Mahoney. Randomized Algorithms for Matrices and Data. Foundation and Trends in Machine Learning, vol. 3, no. 2, pp. 123-224, 2010. http://dx.doi.org/10.1561/2200000035
* Petros Drineas and Michael W. Mahoney. Lectures on Randomized Numerical Linear Algebra. https://arxiv.org/pdf/1712.08880.pdf * Ravindran Kannan and Santosh Vempala. Randomized algorithms in numerical linear algebra. Acta Numerica, pp. 95-135, 2017. https://www.cc.gatech.edu/~vempala/papers/acta_survey.pdf |
| Předběžná náplň práce v anglickém jazyce |
| Least squares problems arise when we have a linear system with more equations than unknowns. Such problems frequently arise in the context of optimization and data science applications. A recent hot topic is randomized numerical linear algebra methods. In particular, there now exist randomized methods for computing least squares solutions. This project will involve investigating randomized methods for solving least squares problems and evaluating their performance, usability, and applicability in practice. |