In this thesis, we propose to formally derive amplitude equations governing the weakly nonlinear evolution of non-normal dynamical systems, when they respond to harmonic or stochastic forcing, or to an initial condition. This approach reconciles the non-mo ...
Computer systems rely heavily on abstraction to manage the exponential growth of complexity across hardware and software. Due to practical considerations of compatibility between components of these complex systems across generations, developers have favou ...
We consider the problem of comparing several samples of stochastic processes with respect to their second-order structure, and describing the main modes of variation in this second order structure, if present. These tasks can be seen as an Analysis of Vari ...
We derive confidence intervals (CIs) and confidence sequences (CSs) for the classical problem of estimating a bounded mean. Our approach generalizes and improves on the celebrated Chernoff method, yielding the best closed-form "empirical-Bernstein" CSs and ...
Random Fourier features (RFFs) provide a promising way for kernel learning in a spectral case. Current RFFs-based kernel learning methods usually work in a two-stage way. In the first-stage process, learn-ing an optimal feature map is often formulated as a ...
We consider the problem of learning a target function corresponding to a deep, extensive-width, non-linear neural network with random Gaussian weights. We consider the asymptotic limit where the number of samples, the input dimension and the network width ...
A kernel method for estimating a probability density function from an independent and identically distributed sample drawn from such density is presented. Our estimator is a linear combination of kernel functions, the coefficients of which are determined b ...
This thesis is situated at the crossroads between machine learning and control engineering. Our contributions are both theoretical, through proposing a new uncertainty quantification methodology in a kernelized context; and experimental, through investigat ...
Fuzzing reliably and efficiently finds bugs in software, including operating system kernels. In general, higher code coverage leads to the discovery of more bugs. This is why most existing kernel fuzzers adopt strategies to generate a series of inputs that ...
The progress towards intelligent systems and digitalization relies heavily on the use of automation technology. However, the growing diversity of control objects presents significant challenges for traditional control approaches, as they are highly depende ...
