Thema der Dissertation:
On the statistical approximation of conditional expectation operators Thema der Disputation:
Perturbation theory of linear operators in machine learning and statistics
On the statistical approximation of conditional expectation operators Thema der Disputation:
Perturbation theory of linear operators in machine learning and statistics
Abstract: The perturbation of spectral properties of linear operators is a classical topic in functional analysis. Although its inception in the early 20th century was mostly driven by the developments in quantum mechanics, it grew into a theoretical discipline in its own right.
Since then, it has greatly influenced applied mathematical disciplines such as the numerical solution of eigenvalue problems.
Over the last years, spectral perturbation theory remained an important area of research, as it led to foundational results in modern high-dimensional statistics and machine learning.
In this talk, we discuss the role of spectral perturbation in the age of "big data". We introduce some perturbation results for compact operators and apply them together with concentration bounds to prove statistical consistency of typical techniques in machine learning.
Since then, it has greatly influenced applied mathematical disciplines such as the numerical solution of eigenvalue problems.
Over the last years, spectral perturbation theory remained an important area of research, as it led to foundational results in modern high-dimensional statistics and machine learning.
In this talk, we discuss the role of spectral perturbation in the age of "big data". We introduce some perturbation results for compact operators and apply them together with concentration bounds to prove statistical consistency of typical techniques in machine learning.
Zeit & Ort
11.03.2022 | 15:00