Related papers: Recursive Filters as Linear Time-Invariant Systems
This paper presents an efficient algorithm for robust network reconstruction of Linear Time-Invariant (LTI) systems in the presence of noise, estimation errors and unmodelled nonlinearities. The method here builds on previous work on robust…
In visual recognition tasks, such as image classification, unsupervised learning exploits cheap unlabeled data and can help to solve these tasks more efficiently. We show that the recursive autoconvolution operator, adopted from physics,…
Many machine learning systems utilize latent factors as internal representations for making predictions. Since these latent factors are largely uninterpreted, however, predictions made using them are opaque. Collaborative filtering via…
We present a decomposition of finitely supported filters ( aka instrument function PSF) as a composition of invertible and non-invertible filters. The invertible component can be inverted directly and the non-invertible component is shown…
In this paper, we introduce the notion of recurrence entropy in the context of nonlinear control systems. A set is said to be ($\tau$-)recurrent if every trajectory that starts in the set returns to it (within at most $\tau$ units of time).…
Recently it has been shown, in several settings, how to carry out adaptive control for an LTI plant so that a convolution bound holds on the closed-loop behavior; this, in turn, has been leveraged to prove robustness of the closed-loop…
A scattering transform defines a signal representation which is invariant to translations and Lipschitz continuous relatively to deformations. It is implemented with a non-linear convolution network that iterates over wavelet and modulus…
Functors with an instance of the Traversable type class can be thought of as data structures which permit a traversal of their elements. This has been made precise by the correspondence between traversable functors and finitary containers…
This paper is concerned with the analysis of the $L_{2}$ induced norm of continuous-time LTI systems where the input signals are restricted to be nonnegative. This induced norm is referred to as the $L_{2+}$ induced norm in this paper. It…
Time series observations can be seen as realizations of an underlying dynamical system governed by rules that we typically do not know. For time series learning tasks, we need to understand that we fit our model on available data, which is…
We completely describe a new domain for abstract interpretation of numerical programs. Fixpoint iteration in this domain is proved to converge to finite precise invariants for (at least) the class of stable linear recursive filters of any…
This paper presents a system identification framework -- inspired by multi-task learning -- to estimate the dynamics of a given number of linear time-invariant (LTI) systems jointly by leveraging structural similarities across the systems.…
Time independent convolution yields circulant matrices whose eigenvectors are the Fourier exponentials with the eigenvalues being the Fourier transform of the mask. The case of time dependent convolution, the non-stationary case, no longer…
This paper introduces a novel representation of convolutional Neural Networks (CNNs) in terms of 2-D dynamical systems. To this end, the usual description of convolutional layers with convolution kernels, i.e., the impulse responses of…
A class of left-invariant second order reversible systems with functional parameter is introduced which exhibits the phenomenon of robust integrability: an open and dense subset of the phase space is filled with invariant tori carrying…
In this note, we propose a method to under-approximate finite-time reachable sets and tubes for a class of continuous-time linear uncertain systems. The class under consideration is the linear time-varying (LTV) class with integrable…
This paper presents a new approach for analysing structural properties of time series from complex systems. Starting from the concept of recurrences in phase space, the recurrence matrix of a time series is interpreted as the adjacency…
After reviewing commutativity of second-order linear time-varying analog systems, the inverse commutativity conditions are derived for these systems by considering non-zero initial conditions. On the base of these conditions, the…
The Iterative Filtering method is a technique developed recently for the decomposition and analysis of non-stationary and non-linear signals. In this work we propose two alternative formulations of the original algorithm which allows to…
The kinematics of many nonlinear control systems, especially in the robotics field, admit a transitive Lie-group symmetry, which is useful in high performance observer design. The recently proposed equivariant filter (EqF) exploits…