Related papers: Unique Reconstruction From Mean-Field Measurements
The task of reconstructing a low rank matrix from incomplete linear measurements arises in areas such as machine learning, quantum state tomography and in the phase retrieval problem. In this note, we study the particular setup that the…
We study large but finite neural networks that, in the thermodynamic limit, admit an exact low-dimensional mean-field description. We assume that the governing mean-field equations describing macroscopic quantities such as the mean firing…
Network reconstruction consists in retrieving the hidden interaction structure of a system from observations. Many reconstruction algorithms have been proposed, although less research has been devoted to describe their theoretical…
Reconstructing a quantum system's Hamiltonian from limited yet experimentally observable information is interesting both as a practical task and from a fundamental standpoint. We pose and investigate the inverse problem of reconstructing a…
We use the annealed formulation of complex networks to study the dynamical behavior of disease spreading on both static and adaptive networked systems. This unifying approach relies on the annealed adjacency matrix, representing one network…
This paper considers the problem of inferring an unknown network of dynamical systems driven by unknown, intrinsic, noise inputs. Equivalently we seek to identify direct causal dependencies among manifest variables only from observations of…
We present a data-driven model to reconstruct nonlinear dynamics from a very sparse times series data, which relies on the strength of the echo state network (ESN) in learning nonlinear representation of data. With an assumption of the…
Accurately reconstructing a global spatial field from sparse data has been a longstanding problem in several domains, such as Earth Sciences and Fluid Dynamics. Historically, scientists have approached this problem by employing complex…
This work deals with the problem of distributed data acquisition under non-linear communication constraints. More specifically, we consider a model setup where $M$ distributed nodes take individual measurements of an unknown structured…
Empirical data on real complex systems are becoming increasingly available. Parallel to this is the need for new methods of reconstructing (inferring) the topology of networks from time-resolved observations of their node-dynamics. The…
This work examines the multi-view compressive phase retrieval problem in a distributed sensor network, where each sensor device, limited by storage and sensing capabilities, can access only intensity measurements from an unknown part of the…
A major problem in the study of complex socioeconomic systems is represented by privacy issues$-$that can put severe limitations on the amount of accessible information, forcing to build models on the basis of incomplete knowledge. In this…
Recovery of support of a sparse vector from simple measurements is a widely-studied problem, considered under the frameworks of compressed sensing, 1-bit compressed sensing, and more general single index models. We consider generalizations…
An important problem in many areas of science is that of recovering interaction networks from simultaneous time-series of many interacting dynamical processes. A common approach is to use the elements of the correlation matrix or its…
Recovering microscopic couplings directly from data provides a route to solving the inverse problem in statistical field theories, one that complements the traditional-often computationally intractable-forward approach of predicting…
This paper considers the problem of inferring the structure of a network from indirect observations. Each observation (a "trace") is the unordered set of nodes which are activated along a path through the network. Since a trace does not…
We investigate the reconstruction of time series from dynamical networks that are partially observed. In particular, we address the extent to which the time series at a node of the network can be successfully reconstructed when measuring…
We propose and analyze an online algorithm for reconstructing a sequence of signals from a limited number of linear measurements. The signals are assumed sparse, with unknown support, and evolve over time according to a generic nonlinear…
This paper determines to within a single measurement the minimum number of measurements required to successfully reconstruct a signal drawn from a Gaussian mixture model in the low-noise regime. The method is to develop upper and lower…
In many applications sampled data are collected in irregular fashion or are partly lost or unavailable. In these cases it is required to convert irregularly sampled signals to regularly sampled ones or to restore missing data. In this…