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Dimensionality reduction algorithms like principal component analysis (PCA) are workhorses of machine learning and neuroscience, but each has well-known limitations. Variants of PCA are simple and interpretable, but not flexible enough to…

In many applications, particularly in the natural sciences, the available high-dimensional set of features may contain variables that are not correlated with the response under consideration. Such irrelevant features can, in certain cases,…

Using observation data to estimate unknown parameters in computational models is broadly important. This task is often challenging because solutions are non-unique due to the complexity of the model and limited observation data. However,…

We develop a new principal components analysis (PCA) type dimension reduction method for binary data. Different from the standard PCA which is defined on the observed data, the proposed PCA is defined on the logit transform of the success…

In the maintenance of complex systems, fault trees are used to locate problems and provide targeted solutions. To enable fault trees stored as images to be directly processed by large language models, which can assist in tracking and…

This paper delivers improved theoretical guarantees for the convex programming approach in low-rank matrix estimation, in the presence of (1) random noise, (2) gross sparse outliers, and (3) missing data. This problem, often dubbed as…

For large-scale simulation codes with huge and complex code bases, where bit-for-bit comparisons are too restrictive, finding the source of statistically significant discrepancies (e.g., from a previous version, alternative hardware or…

Localizing the root cause of network faults is crucial to network operation and maintenance. However, due to the complicated network architectures and wireless environments, as well as limited labeled data, accurately localizing the true…

In this paper, we propose an efficient semidefinite programming (SDP) approach to worst-case linear discriminant analysis (WLDA). Compared with the traditional LDA, WLDA considers the dimensionality reduction problem from the worst-case…

Energy increasingly constrains modern computer hardware, yet protecting computations and data against errors costs energy. This holds at all scales, but especially for the largest parallel computers being built and planned today. As…

The mutations of a complex systemic disease like cancer can be modeled as stuck-at faults in the Boolean system paradigm. For a class of multiple faults, the fault identification is exceptionally significant under the incomplete access of…

In this paper, we study a fault-tolerant control for systems consisting of multiple homogeneous components such as parallel processing machines. This type of system is often more robust to uncertainty compared to those with a single…

Reasoning about causes and effects naturally arises in the engineering of safety-critical systems. A classical example is Fault Tree Analysis, a deductive technique used for system safety assessment, whereby an undesired state is reduced to…

Robust Principal Component Analysis (RPCA) is a fundamental technique for decomposing data into low-rank and sparse components, which plays a critical role for applications such as image processing and anomaly detection. Traditional RPCA…

A learning task, understood as the problem of fitting a parametric model from supervised data, fundamentally requires the dataset to be large enough to be representative of the underlying distribution of the source. When data is limited,…

In this paper, we study the problem of computing a Principal Component Analysis of data affected by Poisson noise. We assume samples are drawn from independent Poisson distributions. We want to estimate principle components of a fixed…

In order to improve the fault diagnosis capability of multivariate statistical methods, this article introduces a fault isolation framework based on structured sparsity modeling. The developed method relies on the reconstruction based…

Principal component analysis (PCA) is a classical dimension reduction method which projects data onto the principal subspace spanned by the leading eigenvectors of the covariance matrix. However, it behaves poorly when the number of…

In multitemporal InSAR, phase linking (PL) refers to the estimation of a single-reference interferometric phase history for distributed scatterers (DS) from the information contained in the sample coherence matrix. Because the phase…

One of the most significant obstacles in bearing fault diagnosis is a lack of labeled data for various fault types. Also, sensor-acquired data frequently lack labels and have a large amount of missing data. This paper tackles these issues…