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Reconstructing a complete object from its parts is a fundamental problem in many scientific domains. The purpose of this article is to provide a systematic survey on this topic. The reassembly problem requires understanding the attributes…
Super-resolution theory aims to estimate the discrete components lying in a continuous space that constitute a sparse signal with optimal precision. This work investigates the potential of recent super-resolution techniques for spectral…
Mixed packing and covering problems are problems that can be formulated as linear programs using only non-negative coefficients. Examples include multicommodity network flow, the Held-Karp lower bound on TSP, fractional relaxations of set…
Quantum information processing has been effectively demonstrated on a small number of qubits by nuclear magnetic resonance. An important subroutine in any computing is the readout of the output. ``Spectral implementation'' originally…
We give an efficient algorithm which can obtain a relative error approximation to the spectral norm of a matrix, combining the power iteration method with some techniques from matrix reconstruction which use random sampling.
Principal component analysis (PCA) requires the computation of a low-rank approximation to a matrix containing the data being analyzed. In many applications of PCA, the best possible accuracy of any rank-deficient approximation is at most a…
Conformal Prediction methods have finite-sample distribution-free marginal coverage guarantees. However, they generally do not offer conditional coverage guarantees, which can be important for high-stakes decisions. In this paper, we…
Plotting the residuals is a recommended procedure to diagnose deviations from linear model assumptions, such as non-linearity, heteroscedasticity, and non-normality. The presence of structure in residual plots can be tested using the lineup…
Linear spectral unmixing under nonnegativity and sum-to-one constraints is a convex optimization problem for which many algorithms were proposed. In practice, especially for supervised unmixing (i.e., with a large dictionary), solutions…
An efficient decoding algorithm named `divided decoder' is proposed in this paper. Divided decoding can be combined with any decoder using QR-decomposition and offers different pairs of performance and complexity. Divided decoding provides…
Linear principal component analysis (PCA) can be extended to a nonlinear PCA by using artificial neural networks. But the benefit of curved components requires a careful control of the model complexity. Moreover, standard techniques for…
In the vicinity of a solution of a nonlinear programming problem at which both strict complementarity and linear independence of the active constraints may fail to hold, we describe a technique for distinguishing weakly active from strongly…
The partial least squares algorithm for dependent data realisations is considered. Consequences of ignoring the dependence for the algorithm performance are studied both theoretically and in simulations. It is shown that ignoring certain…
Classical methods such as Principal Component Analysis (PCA) and Canonical Correlation Analysis (CCA) are ubiquitous in statistics. However, these techniques are only able to reveal linear relationships in data. Although nonlinear variants…
In the past years, software reverse engineering dealt with source code understanding. Nowadays, it is levered to software requirements abstract level, supported by feature model notations, language independent, and simpler than the source…
Reed-Muller (RM) codes exhibit good performance under maximum-likelihood (ML) decoding due to their highly-symmetric structure. In this paper, we explore the question of whether the code symmetry of RM codes can also be exploited to achieve…
We propose new quantum algorithms for estimating spectral sums of positive semi-definite (PSD) matrices. The spectral sum of an PSD matrix $A$, for a function $f$, is defined as $ \text{Tr}[f(A)] = \sum_j f(\lambda_j)$, where $\lambda_j$…
We describe a general approach for computing generators for elimination ideals associated with matrix and hypermatrix spectral decomposition constraints. We derive from these generators iterative procedures for approximating the spectral…
We present a spectral approach to design approximation algorithms for network design problems. We observe that the underlying mathematical questions are the spectral rounding problems, which were studied in spectral sparsification and in…
Signal decomposition and multiscale signal analysis provide many useful tools for time-frequency analysis. We proposed a random feature method for analyzing time-series data by constructing a sparse approximation to the spectrogram. The…