Research
If you are interested in my research, I recommend the presentation in my defense as an introduction. The first page is left blank intentionally. You can download it Here.
List of publications and preprints
2024
- F. Kuchelmeister On the probability of linear separability through intrinsic volumes ArXiv Preprint, 2024.
A dataset with two labels is linearly separable if it can be split into its two classes with a hyperplane. This inflicts a curse on some statistical tools (such as logistic regression) but forms a blessing for others (e.g. support vector machines). Recently, the following question has regained interest: What is the probability that the data are linearly separable?
We provide a formula for the probability of linear separability for Gaussian features and labels depending only on one marginal of the features (as in generalized linear models). In this setting, we derive an upper bound that complements the recent result by Hayakawa, Lyons, and Oberhauser [2023], and a sharp upper bound for sign-flip noise.
To prove our results, we exploit that this probability can be expressed as a sum of the intrinsic volumes of a polyhedral cone of the form
2023
- F. Kuchelmeister, S. van de Geer Finite sample rates for logistic regression with small noise or few samples Sankhya A, 2024.
Presentation at the European Meeting of Statisticians in Warsaw 2023.
The logistic regression estimator is known to inflate the magnitude of its coefficients if the sample size
We distinguish between two regimes.
In the low-noise/small-sample regime (
2022
- G. Chinot, F. Kuchelmeister, M. Löffler, S. van de Geer AdaBoost and robust one-bit compressed sensing Mathematical Statistics and Learning 5, 117-158, 2022.
This paper studies binary classification in robust one-bit compressed sensing with adversarial errors. It is assumed that the model is overparameterized and that the parameter of interest is effectively sparse. AdaBoost is considered, and, through its relation to the max-