Related papers: Nonlinear Principal Component Analysis with Random…

Principal Component Analysis (PCA) finds a linear mapping and maximizes the variance of the data which makes PCA sensitive to outliers and may cause wrong eigendirection. In this paper, we propose techniques to solve this problem; we use…

The Kernel Polynomial Method (KPM) is a well-established scheme in quantum physics and quantum chemistry to determine the eigenvalue density and spectral properties of large sparse matrices. In this work we demonstrate the high optimization…

Principal component analysis (PCA) is recognised as a quintessential data analysis technique when it comes to describing linear relationships between the features of a dataset. However, the well-known sensitivity of PCA to non-Gaussian…

As the complexity of production processes increases, the diversity of data types drives the development of network monitoring technology. This paper mainly focuses on an online algorithm to detect serially correlated directed networks…

Functional principal component analysis has been shown to be invaluable for revealing variation modes of longitudinal outcomes, which serves as important building blocks for forecasting and model building. Decades of research have advanced…

Several approximate inference methods have been proposed for deep discrete latent variable models. However, non-parametric methods which have previously been successfully employed for classical sparse coding models have largely been…

The task of monitoring for a change in the mean of a sequence of Bernoulli random variables has been widely studied. However most existing approaches make at least one of the following assumptions, which may be violated in many real-world…

Quantum one-class support vector machines leverage the advantage of quantum kernel methods for semi-supervised anomaly detection. However, their quadratic time complexity with respect to data size poses challenges when dealing with large…

To maintain the desired quality of a product or service it is necessary to monitor the process that results in the product or service. This monitoring method is called Statistical Process Management, or Statistical Process Control. It is in…

Dimension reduction for high-dimensional compositional data plays an important role in many fields, where the principal component analysis of the basis covariance matrix is of scientific interest. In practice, however, the basis variables…

This paper presents a kernelized offset-free data-driven predictive control scheme for nonlinear systems. Traditional model-based and data-driven predictive controllers often struggle with inaccurate predictors or persistent disturbances,…

We consider the problem of estimating the parameters of a multivariate Bernoulli process with auto-regressive feedback in the high-dimensional setting where the number of samples available is much less than the number of parameters. This…

Despite decades of research and recent progress in adaptive control and reinforcement learning, there remains a fundamental lack of understanding in designing controllers that provide robustness to inherent non-asymptotic uncertainties…

One of the distinguishing characteristics of modern deep learning systems is that they typically employ neural network architectures that utilize enormous numbers of parameters, often in the millions and sometimes even in the billions.…

The tensorial principal component analysis is a generalization of ordinary principal component analysis, focusing on data which are suitably described by tensors rather than matrices. This paper aims at giving the nonperturbative…

Reachable set computation is an important technique for the verification of safety properties of dynamical systems. In this paper, we investigate reachable set computation for discrete nonlinear systems based on parallelotope bundles. The…

Learning and forecasting stochastic time series is essential in various scientific fields. However, despite the proposals of nonlinear filters and deep-learning methods, it remains challenging to capture nonlinear dynamics from a few noisy…

Kernel methods are fundamental tools in machine learning that allow detection of non-linear dependencies between data without explicitly constructing feature vectors in high dimensional spaces. A major disadvantage of kernel methods is…

We propose kernel-based approaches for the construction of a single-step and multi-step predictor of the velocity form of nonlinear (NL) systems, which describes the time-difference dynamics of the corresponding NL system and admits a…

The high performance of denoising diffusion models for image generation has paved the way for their application in unsupervised medical anomaly detection. As diffusion-based methods require a lot of GPU memory and have long sampling times,…