Related papers: Asymptotically Scale-invariant Multi-resolution Qu…

Quantizers take part in nearly every digital signal processing system which operates on physical signals. They are commonly designed to accurately represent the underlying signal, regardless of the specific task to be performed on the…

The distortion-rate performance of certain randomly-designed scalar quantizers is determined. The central results are the mean-squared error distortion and output entropy for quantizing a uniform random variable with thresholds drawn…

Communication of quantized information is frequently followed by a computation. We consider situations of \emph{distributed functional scalar quantization}: distributed scalar quantization of (possibly correlated) sources followed by…

Scalar quantization is the most practical and straightforward approach to signal quantization. However, it has been shown that scalar quantization of oversampled or Compressively Sensed signals can be inefficient in terms of the…

We develop a multiscale scanning method to find anomalies in a $d$-dimensional random field in the presence of nuisance parameters. This covers the common situation that either the baseline-level or additional parameters such as the…

Quantile regression is a method to estimate the quantiles of the conditional distribution of a response variable, and as such it permits a much more accurate portrayal of the relationship between the response variable and observed…

The success of machine learning has resulted from its structured representation of data. Similar data have close internal representations as compressed codes for classification or emerged labels for clustering. We observe that the frequency…

We propose novel scale-invariant error estimators for the Monte Carlo and multilevel Monte Carlo estimation of mean and variance. For any linear transformation of the distribution of the quantity of interest, the computation cost across…

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…

Invariant coordinate selection is an unsupervised multivariate data transformation useful in many contexts such as outlier detection or clustering. It is based on the simultaneous diagonalization of two affine equivariant and positive…

One of the goals in scaling sequential machine learning methods pertains to dealing with high-dimensional data spaces. A key related challenge is that many methods heavily depend on obtaining the inverse covariance matrix of the data. It is…

We consider the problem of multi-agent consensus where some agents are subject to faults/attacks and might make updates arbitrarily. The network consists of agents taking integer-valued (i.e., quantized) states under directed communication…

We propose using a coordinate network decoder for the task of super-resolution in MRI. The continuous signal representation of coordinate networks enables this approach to be scale-agnostic, i.e. one can train over a continuous range of…

With an ever-expanding ecosystem of noisy and intermediate-scale quantum devices, exploring their possible applications is a rapidly growing field of quantum information science. In this work, we demonstrate that variational quantum…

Adaptive Molecular Resolution approaches in Molecular Dynamics are becoming relevant tools for the analysis of molecular liquids characterized by the interplay of different physical scales. The essential difference among these methods is in…

Subsampling is one of the popular methods to balance statistical efficiency and computational efficiency in the big data era. Most approaches aim at selecting informative or representative sample points to achieve good overall information…

This paper considers inference for conditional moment inequality models using a multiscale statistic. We derive the asymptotic distribution of this test statistic and use the result to propose feasible critical values that have a simple…

Various problems in computer vision and medical imaging can be cast as inverse problems. A frequent method for solving inverse problems is the variational approach, which amounts to minimizing an energy composed of a data fidelity term and…

This work is concerned with the estimation of multidimensional regression and the asymptotic behaviour of the test involved in selecting models. The main problem with such models is that we need to know the covariance matrix of the noise to…

Linear systems of equations can be found in various mathematical domains, as well as in the field of machine learning. By employing noisy intermediate-scale quantum devices, variational solvers promise to accelerate finding solutions for…