Concept
Reproducing kernel Hilbert space
Related publications (72)
Multigraded algebras and multigraded linear series
Leonid Monin, Fatemeh Mohammadi, Yairon Cid Ruiz
This paper is devoted to the study of multigraded algebras and multigraded linear series. For an Ns-graded algebra A, we define and study its volume function FA:N+s -> R, which computes the ...
Wiley2024Quantum circuits for solving local fermion-to-qubit map- pings
Giuseppe Carleo, Jannes Willy E. Nys
Local Hamiltonians of fermionic systems on a lattice can be mapped onto local qubit Hamiltonians. Maintaining the lo-cality of the operators comes at the ex-pense of increasing the Hilbert space with auxiliary degrees of freedom. In order to retrieve the l ...
VEREIN FORDERUNG OPEN ACCESS PUBLIZIERENS QUANTENWISSENSCHAF2023Positive Definite Completions and Continuous Graphical Models
This thesis concerns the theory of positive-definite completions and its mutually beneficial connections to the statistics of function-valued or continuously-indexed random processes, better known as functional data analysis. In particular, it dwells upon ...
EPFL2023Data-driven Methods for Control: from Linear to Lifting
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 ...
EPFL2023TimeEvolver: A program for time evolution with improved error bound
We present TimeEvolver, a program for computing time evolution in a generic quantum system. It relies on well-known Krylov subspace techniques to tackle the problem of multiplying the exponential of a large sparse matrix iH, where His the Hamiltonian, with ...
ELSEVIER2022Convex optimization in sums of Banach spaces
Michaël Unser, Shayan Aziznejad
We characterize the solution of a broad class of convex optimization problems that address the reconstruction of a function from a finite number of linear measurements. The underlying hypothesis is that the solution is decomposable as a finite sum of compo ...
2021Many-body localization in a fragmented Hilbert space
We study many-body localization (MBL) in a pair-hopping model exhibiting strong fragmentation of the Hilbert space. We show that several Krylov subspaces have both ergodic statistics in the thermodynamic limit and a dimension that scales much slower than t ...
2021Deterministic error bounds for kernel-based learning techniques under bounded noise
Colin Neil Jones, Paul Scharnhorst, Emilio Maddalena
We consider the problem of reconstructing a function from a finite set of noise-corrupted samples. Two kernel algorithms are analyzed, namely kernel ridge regression and epsilon-support vector regression. By assuming the ground-truth function belongs to th ...
PERGAMON-ELSEVIER SCIENCE LTD2021A kernel‐based change detection method to map shifts in phytoplankton communities measured by flow cytometry
Automated, ship-board flow cytometers provide high-resolution maps of phytoplankton composition over large swaths of the world's oceans. They therefore pave the way for understanding how environmental conditions shape community structure. Identification o ...
2021Multikernel Regression with Sparsity Constraint
Michaël Unser, Shayan Aziznejad
In this paper, we provide a Banach-space formulation of supervised learning with generalized total-variation (gTV) regularization. We identify the class of kernel functions that are admissible in this framework. Then, we propose a variation of supervised l ...
2021