Related papers: Noisy nonlinear information and entropy numbers
We consider the stabilization of an unstable discrete-time linear system that is observed over a channel corrupted by continuous multiplicative noise. Our main result shows that if the system growth is large enough, then the system cannot…
We investigate recovery of nonnegative vectors from non-adaptive compressive measurements in the presence of noise of unknown power. In the absence of noise, existing results in the literature identify properties of the measurement that…
A noisy underdetermined system of linear equations is considered in which a sparse vector (a vector with a few nonzero elements) is subject to measurement. The measurement matrix elements are drawn from a Gaussian distribution. We study the…
We consider the linear regression model with observation error in the design. In this setting, we allow the number of covariates to be much larger than the sample size. Several new estimation methods have been recently introduced for this…
In this paper, online linear regression in environments corrupted by non-Gaussian noise (especially heavy-tailed noise) is addressed. In such environments, the error between the system output and the label also does not follow a Gaussian…
We consider the problem of sparse signal recovery from noisy measurements. Many of frequently used recovery methods rely on some sort of tuning depending on either noise or signal parameters. If no estimates for either of them are…
We revisit the classical problem of inverting dimension-reducing linear mappings using the maximum entropy (MaxEnt) criterion. In the literature, solutions are problem-dependent, inconsistent, and use different entropy measures. We propose…
Compressed Sensing decoding algorithms can efficiently recover an N dimensional real-valued vector x to within a factor of its best k-term approximation by taking m = 2klog(N/k) measurements y = Phi x. If the sparsity or approximate…
Estimation of a deterministic quantity observed in non-Gaussian additive noise is explored via order statistics approach. More specifically, we study the estimation problem when measurement noises either have positive supports or follow a…
Heisenberg's uncertainty principle has recently led to general measurement uncertainty relations for quantum systems: incompatible observables can be measured jointly or in sequence only with some unavoidable approximation, which can be…
This paper proposes a new algorithm for linear system identification from noisy measurements. The proposed algorithm balances a data fidelity term with a norm induced by the set of single pole filters. We pose a convex optimization problem…
In this paper, we propose two algorithms for solving linear inverse problems when the observations are corrupted by Poisson noise. A proper data fidelity term (log-likelihood) is introduced to reflect the Poisson statistics of the noise. On…
In experiments, the dynamical behavior of systems is reflected in time series. Due to the finiteness of the observational data set it is not possible to reconstruct the invariant measure up to arbitrary fine resolution and arbitrary high…
A new approach to nonlinear modelling is presented which, by incorporating the global behaviour of the model, lifts shortcomings of both least squares and total least squares parameter estimates. Although ubiquitous in practice, a least…
We consider the problem of recovering linear image of unknown signal belonging to a given convex compact signal set from noisy observation of another linear image of the signal. We develop a simple generic efficiently computable nonlinear…
Compressed Sensing suggests that the required number of samples for reconstructing a signal can be greatly reduced if it is sparse in a known discrete basis, yet many real-world signals are sparse in a continuous dictionary. One example is…
This work proposes a new loss function targeting classification problems, utilizing a source of information overlooked by cross entropy loss. First, we derive a series of the tightest upper and lower bounds for the probability of a random…
In this work, we consider the problem of recovering analysis-sparse signals from under-sampled measurements when some prior information about the support is available. We incorporate such information in the recovery stage by suitably tuning…
In this paper, we study the number of measurements required to recover a sparse signal in ${\mathbb C}^M$ with $L$ non-zero coefficients from compressed samples in the presence of noise. For a number of different recovery criteria, we prove…
Information-theoretic definitions for the noise associated with a quantum measurement and the corresponding disturbance to the state of the system have recently been introduced [F. Buscemi et al., Phys. Rev. Lett. 112, 050401 (2014)]. These…