Related papers: Extreme Value Statistics and Error Correcting Code…
Quantum error correction protects quantum information against environmental noise. When using qubits, a measure of quality of a code is the maximum number of errors that it is able to correct. We show that a suitable notion of ``number of…
Self-synchronization under the presence of additive noise can be achieved by allocating a certain number of bits of each codeword as markers for synchronization. Difference systems of sets are combinatorial designs which specify the…
Neural networks can efficiently encode the probability distribution of errors in an error correcting code. Moreover, these distributions can be conditioned on the syndromes of the corresponding errors. This paves a path forward for a…
The inverse problem methodology is a commonly-used framework in the sciences for parameter estimation and inference. It is typically performed by fitting a mathematical model to noisy experimental data. There are two significant sources of…
We propose a new optimization framework for aleatoric uncertainty estimation in regression problems. Existing methods can quantify the error in the target estimation, but they tend to underestimate it. To obtain the predictive uncertainty…
A computer model can be used for predicting an output only after specifying the values of some unknown physical constants known as calibration parameters. The unknown calibration parameters can be estimated from real data by conducting…
Accuracy-driven computation is a strategy widely used in exact-decisions number types for robust geometric algorithms. This work provides an overview on the usage of error bounds in accuracy-driven computation, compares different approaches…
Using a maximum-likelihood criterion, we derive optimal correlation strategies for signals with and without digitization. We assume that the signals are drawn from zero-mean Gaussian distributions, as is expected in radio-astronomical…
In risk management, often the probability must be estimated that a random vector falls into an extreme failure set. In the framework of bivariate extreme value theory, we construct an estimator for such failure probabilities and analyze its…
A geometric method is described to characterize the different kinds of extremals in optimal control theory. This comes from the use of a presymplectic constraint algorithm starting from the necessary conditions given by Pontryagin's Maximum…
Quantile estimation in deconvolution problems is studied comprehensively. In particular, the more realistic setup of unknown error distributions is covered. Our plug-in method is based on a deconvolution density estimator and is minimax…
Building a scalable machine learning system for unsupervised anomaly detection via representation learning is highly desirable. One of the prevalent methods is using a reconstruction error from variational autoencoder (VAE) via maximizing…
Understanding the effect of uncertainty and noise in data on machine learning models (MLM) is crucial in developing trust and measuring performance. In this paper, a new model is proposed to quantify uncertainties and noise in data on MLMs.…
Signal-to-noise ratios (SNR) play a crucial role in various statistical models, with important applications in tasks such as estimating heritability in genomics. The method-of-moments estimator is a widely used approach for estimating SNR,…
The Extreme Learning Machine (ELM) technique is a machine learning approach for constructing feed-forward neural networks with a single hidden layer and their models. The ELM model can be constructed while being trained by concurrently…
Rate distortion theory was developed for optimizing lossy compression of data, but it also has a lot of applications in statistics. In this paper we will see how rate distortion theory can be used to analyze a complicated data set involving…
Multi-class classification is mandatory for real world problems and one of promising techniques for multi-class classification is Error Correcting Output Code. We propose a method for constructing the Error Correcting Output Code to obtain…
We show that a large class of Estimation of Distribution Algorithms, including, but not limited to, Covariance Matrix Adaption, can be written as a Monte Carlo Expectation-Maximization algorithm, and as exact EM in the limit of infinite…
This paper investigates the use of extreme value theory for modelling the distribution of demand-net-of-wind for capacity adequacy assessment. Extreme value theory approaches are well-established and mathematically justified methods for…
Denoising is of utmost importance for the visualization and processing of images featuring low signal-to-noise ratio. Total variation methods are among the most popular techniques to perform this task improving the signal-to-noise ratio…