Related papers: Determining the Dimension of the Improper Signal S…

Based on weak measurement technology, we propose the first three-observer dimension witness protocol in a prepare-and-measure setup. By applying the dimension witness inequality based on the quantum random access code and the nonlinear…

Penalized likelihood models are widely used to simultaneously select variables and estimate model parameters. However, the existence of weak signals can lead to inaccurate variable selection, biased parameter estimation, and invalid…

Multidimensional scaling is an important dimension reduction tool in statistics and machine learning. Yet few theoretical results characterizing its statistical performance exist, not to mention any in high dimensions. By considering a…

Remote sensing hyperspectral sensors collect large volumes of high dimensional spectral and spatial data. However, due to spectral and spatial redundancy the true hyperspectral signal lies on a subspace of much lower dimension than the…

The existence of observables that are incompatible or not jointly measurable is a characteristic feature of quantum mechanics, which lies at the root of a number of nonclassical phenomena, such as uncertainty relations, wave--particle dual…

The one-dimensional phase retrieval problem consists in the recovery of a complex-valued signal from its Fourier intensity. Due to the well-known ambiguousness of this problem, the determination of the original signal within the extensive…

Pairwise comparisons are widely used in decision analysis, preference modeling, and evaluation problems. In many practical situations, the observed comparison matrix is not reciprocal. This lack of reciprocity is often treated as a defect…

Model-Based Diagnosis deals with the identification of the real cause of a system's malfunction based on a formal system model and observations of the system behavior. When a malfunction is detected, there is usually not enough information…

The goal of dimension reduction tools is to construct a low-dimensional representation of high-dimensional data. These tools are employed for a variety of reasons such as noise reduction, visualization, and to lower computational costs.…

Physics-based and first-principles models pervade the engineering and physical sciences, allowing for the ability to model the dynamics of complex systems with a prescribed accuracy. The approximations used in deriving governing equations…

This work considers an estimation task in compressive sensing, where the goal is to estimate an unknown signal from compressive measurements that are corrupted by additive pre-measurement noise (interference, or clutter) as well as…

This article reports on a new approach to properly analyze time series of dynamical systems which are spoilt by the simultaneous presence of dynamical noise and measurement noise. It is shown that even strong external measurement noise as…

This paper studies the classical problem of detecting the locations of signal occurrences in a one-dimensional noisy measurement. Assuming the signal occurrences do not overlap, we formulate the detection task as a constrained likelihood…

Estimating intrinsic dimensionality of data is a classic problem in pattern recognition and statistics. Principal Component Analysis (PCA) is a powerful tool in discovering dimensionality of data sets with a linear structure; it, however,…

The degrees of freedom of MIMO interference networks with constant channel coefficients are not known in general. Determining the feasibility of a linear interference alignment solution is a key step toward solving this open problem. Our…

In NMR spectroscopy, undersampling in the indirect dimensions causes reconstruction artifacts whose size can be bounded using the so-called {\it coherence}. In experiments with multiple indirect dimensions, new undersampling approaches were…

We study the problem of parameter estimation for time-series possessing two, widely separated, characteristic time scales. The aim is to understand situations where it is desirable to fit a homogenized singlescale model to such multiscale…

Nonlinearity in many systems is heavily dependent on component variation and environmental factors such as temperature. This is often overcome by keeping signals close enough to the device's operating point that it appears approximately…

Traditional methods for matching in causal inference are impractical for high-dimensional datasets. They suffer from the curse of dimensionality: exact matching and coarsened exact matching find exponentially fewer matches as the input…

This paper describes how a priori information about the signal parameters can influence the accuracy of estimating the number of these signals. This study considers sinusoidal signals and it is supposed that the parameters (amplitudes,…