Related papers: Learning of Statistical Field Theories
We present a computational and statistical approach for fitting isotonic models under convex differentiable loss functions. We offer a recursive partitioning algorithm which provably and efficiently solves isotonic regression under any such…
Recovering continuous-time dynamics from discrete observations is difficult because local supervision (e.g., pointwise regression targets, derivative approximations, or equation residuals) loses fidelity as the observation interval grows.…
In this work, we investigate the use of normalizing flows to model conditional distributions. In particular, we use our proposed method to analyze inverse problems with invertible neural networks by maximizing the posterior likelihood. Our…
Similar to the obstacle or medium scattering problems, an important property of the phaseless far field patterns for source scattering problems is the translation invariance. Thus it is impossible to reconstruct the location of the…
In many physical systems, inputs related by intrinsic system symmetries are mapped to the same output. When inverting such systems, i.e., solving the associated inverse problems, there is no unique solution. This causes fundamental…
Extracting information from nonlinear measurements is a fundamental challenge in data analysis. In this work, we consider separable inverse problems, where the data are modeled as a linear combination of functions that depend nonlinearly on…
We devise a {\sl non--perturbative} method, called {\sl Parametric Perturbation Theory} (PPT), which is alternative to the ordinary perturbation theory. The method relies on a principle of simplicity for the observable solutions, which are…
We introduce an RG-inspired coarse-graining for extracting the collective features of data. The key to successful coarse-graining lies in finding appropriate pairs of data sets. We coarse-grain the two closest data in a regular real-space…
We derive for generally covariant theories the generic dependency of observables on the original fields, corresponding to coordinate-dependent gauge fixings. This gauge choice is equivalent to a choice of intrinsically defined coordinates…
The problem of reconstructing nonlinear and complex dynamical systems from measured data or time series is central to many scientific disciplines including physical, biological, computer, and social sciences, as well as engineering and…
Recovering jointly sparse signals in the multiple measurement vectors (MMV) setting is a fundamental problem in machine learning, but traditional methods often require careful parameter tuning or prior knowledge of the sparsity of the…
We introduce in this document a direct method allowing to solve numerically inverse type problems for linear hyperbolic equations. We first consider the reconstruction of the full solution of the wave equation posed in $\Omega\times (0,T)$…
A new sampling method for inverse scattering problems is proposed to process far field data of one incident wave. As the linear sampling method, the method sets up ill-posed integral equations and uses the (approximate) solutions to…
Structured prediction can be thought of as a simultaneous prediction of multiple labels. This is often done by maximizing a score function on the space of labels, which decomposes as a sum of pairwise and unary potentials. The above is…
The inverse problem method is tested for a class of mean field statistical mechanics models representing a mixture of particles of different species. The robustness of the inversion is investigated for different values of the physical…
We show that the problem of recovering the topology and admittance of an electrical network from power and voltage data at all vertices is often ill-posed, and sometimes it even has multiple solutions. We reformulate the problem to seek for…
Networks of coupled phase oscillators are one of the most studied dynamical systems with numerous applications in physics, chemistry, biology, and engineering. Their behaviour is often characterized by the emergence of various partially…
Reconstructing an infinite-dimensional signal from a finite set of measurements is a fundamental problem in approximation theory and signal processing. While the generalized sampling (GS) framework provides a robust methodology for…
We study a systematic improvement of perturbation theory for gauge fields on the lattice [hep-lat/0606001]; the improvement entails resumming, to all orders in the coupling constant, a dominant subclass of tadpole diagrams. This method,…
Inferring network topology from dynamical observations is a fundamental problem pervading research on complex systems. Here, we present a simple, direct method to infer the structural connection topology of a network, given an observation…