Related papers: Constructive subsampling of finite frames with app…
Low-rank matrix factorizations arise in a wide variety of applications -- including recommendation systems, topic models, and source separation, to name just a few. In these and many other applications, it has been widely noted that by…
A compressed sensing method consists of a rectangular measurement matrix, $M \in \mathbbm{R}^{m \times N}$ with $m \ll N$, together with an associated recovery algorithm, $\mathcal{A}: \mathbbm{R}^m \rightarrow \mathbbm{R}^N$. Compressed…
Snapshot compressive imaging (SCI) refers to compressive imaging systems where multiple frames are mapped into a single measurement, with video compressive imaging and hyperspectral compressive imaging as two representative applications.…
In this paper we show error bounds for randomly subsampled rank-1 lattices. We pay particular attention to the ratio of the size of the subset to the size of the initial lattice, which is decisive for the computational complexity. In the…
Reconstructing an infinite-dimensional signal from a finite set of measurements is a fundamental problem in approximation theory and signal processing. While the generalized sampling (GS) framework provides a robust methodology for…
The technique of subsampling has been extensively employed to address the challenges posed by limited computing resources and meet the needs for expedite data analysis. Various subsampling methods have been developed to meet the challenges…
We present a sampling theory for a class of binary images with finite rate of innovation (FRI). Every image in our model is the restriction of $\mathds{1}_{\{p\leq0\}}$ to the image plane, where $\mathds{1}$ denotes the indicator function…
An efficient computational approach for optimal reconstruction of binary-type images suitable for models in various applications including biomedical imaging is developed and validated. The methodology includes derivative-free optimization…
Sampling-based methods for motion planning, which capture the structure of the robot's free space via (typically random) sampling, have gained popularity due to their scalability, simplicity, and for offering global guarantees, such as…
Answering counterfactual queries has important applications such as explainability, robustness, and fairness but is challenging when the causal variables are unobserved and the observations are non-linear mixtures of these latent variables,…
Suppose that we observe entries or, more generally, linear combinations of entries of an unknown $m\times T$-matrix $A$ corrupted by noise. We are particularly interested in the high-dimensional setting where the number $mT$ of unknown…
We present a practical and powerful new framework for both unconstrained and constrained submodular function optimization based on discrete semidifferentials (sub- and super-differentials). The resulting algorithms, which repeatedly compute…
Models with fewer parameters are often easier to interpret and more robust. Parsimony can be achieved through optimizing objectives like the AIC or BIC, which are functions of the the number of free parameters in the model. Optimizing this…
We propose a general framework for reconstructing and denoising single entries of incomplete and noisy entries. We describe: effective algorithms for deciding if and entry can be reconstructed and, if so, for reconstructing and denoising…
This paper studies the matrix completion problem under arbitrary sampling schemes. We propose a new estimator incorporating both max-norm and nuclear-norm regularization, based on which we can conduct efficient low-rank matrix recovery…
We consider stochastic zero-order optimization problems, which arise in settings from simulation optimization to reinforcement learning. We propose an adaptive sampling quasi-Newton method where we estimate the gradients of a stochastic…
In this work, we consider the approximate reconstruction of high-dimensional periodic functions based on sampling values. As sampling schemes, we utilize so-called reconstructing multiple rank-1 lattices, which combine several preferable…
This paper addresses the problem of approximating an unknown function from point evaluations. When obtaining these point evaluations is costly, minimising the required sample size becomes crucial, and it is unreasonable to reserve a…
The recently introduced and characterized scalable frames can be considered as those frames which allow for perfect preconditioning in the sense that the frame vectors can be rescaled to yield a tight frame. In this paper we define…
We consider the estimation of a structural function which models a non-parametric relationship between a response and an endogenous regressor given an instrument in presence of dependence in the data generating process. Assuming an…