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Optimization methods have been broadly applied to two classes of objects viz. (i) modeling and description of data and (ii) the determination of the stationary points of functions. Here, a theoretical basis is developed that optimizes an…

Independent Component Analysis (ICA) is an algorithm originally developed for finding separate sources in a mixed signal, such as a recording of multiple people in the same room speaking at the same time. Unlike Principal Component Analysis…

Often in real-world datasets, especially in high dimensional data, some feature values are missing. Since most data analysis and statistical methods do not handle gracefully missing values, the first step in the analysis requires the…

This paper introduces a novel statistical framework for independent component analysis (ICA) of multivariate data. We propose methodology for estimating and testing the existence of mutually independent components for a given dataset, and a…

Large-scale eigenvalue problems arise in various fields of science and engineering and demand computationally efficient solutions. In this study, we investigate the subspace approximation for parametric linear eigenvalue problems, aiming to…

The widespread deployment of surveillance cameras for facial recognition gives rise to many privacy concerns. This study proposes a privacy-friendly alternative to large scale facial recognition. While there are multiple techniques to…

Here, a separation theorem about Independent Subspace Analysis (ISA), a generalization of Independent Component Analysis (ICA) is proven. According to the theorem, ISA estimation can be executed in two steps under certain conditions. In the…

This thesis develops a system for automatically analyzing and improving dynamic programs, such as those that have driven progress in natural language processing and computer science, more generally, for decades. Finding a correct program…

Active subspace analysis uses the leading eigenspace of the gradient's second moment to conduct supervised dimension reduction. In this article, we extend this methodology to real-valued functionals on Hilbert space. We define an operator…

Independent component analysis (ICA) is popular in many applications, including cognitive neuroscience and signal processing. Due to computational constraints, principal component analysis is used for dimension reduction prior to ICA…

Computer algebra algorithms are developed for evaluating the coefficients in Airy-type asymptotic expansions that are obtained from integrals with a large parameter. The coefficients are defined from recursive schemes obtained from…

Machine Learning algorithms have had a profound impact on the field of computer science over the past few decades. These algorithms performance is greatly influenced by the representations that are derived from the data in the learning…

The unsupervised anomaly localization task faces the challenge of missing anomaly sample training, detecting multiple types of anomalies, and dealing with the proportion of the area of multiple anomalies. A separate teacher-student feature…

We consider problems of dimensionality reduction and learning data representations for continuous spaces with two or more independent degrees of freedom. Such problems occur, for example, when observing shapes with several components that…

This paper proposes a novel face recognition algorithm based on large-scale supervised hierarchical feature learning. The approach consists of two parts: hierarchical feature learning and large-scale model learning. The hierarchical feature…

Minimally invasive image guided treatment procedures often employ advanced image processing algorithms. The recent developments of artificial intelligence algorithms harbor potential to further enhance this domain. In this article we…

The literature on differential privacy almost invariably assumes that the data to be analyzed are fully observed. In most practical applications this is an unrealistic assumption. A popular strategy to address this problem is imputation, in…

We propose a system for differentiating through solutions to geometry processing problems. Our system differentiates a broad class of geometric algorithms, exploiting existing fast problem-specific schemes common to geometry processing,…

We discuss an automated computational methodology for computing two-dimensional spectral submanifolds (SSMs) in autonomous nonlinear mechanical systems of arbitrary degrees of freedom. In our algorithm, SSMs, the smoothest nonlinear…

Independent component analysis (ICA) is a powerful method for blind source separation based on the assumption that sources are statistically independent. Though ICA has proven useful and has been employed in many applications, complete…