Paper proposes an integrated M&D approach for large multistream data.
problem Inability to progress in monitoring and diagnostics due to high-dimensionality and volume of multistream data.
method Adaptive Principal Component monitoring (APC) and Principal Component Signal Recovery (PCSR).
result The integrated M&D approach enables early detection and streamlined SPC.
Principal component analysis (PCA) is largely adopted for chemical process monitoring and numerous PCA-based systems have been developed to solve various fault detection and diagnosis problems. Since PCA-based methods assume that the monitored process is linear, nonlinear PCA models, such as autoencoder models and kern…
A new method for efficient nonlinear process monitoring using random Bernoulli features.
problem High computational demands and real-time responsiveness in online monitoring systems.
method Random Bernoulli principal component analysis to capture nonlinear patterns efficiently.
result The proposed methods offer excellent scalability and reduced computational complexity.
PCHAL and PCHAR use principal components to speed up HAL and HAR methods.
problem Computational infeasibility in high dimensions for HAL and HAR.
method Outcome-blind principal component reduction of HAL basis.
result Empirical performance comparable to HAL and HAR, with computational gains.
Adaptive probabilistic PCA adapts complexity with varying subspaces.
problem Adaptive probabilistic PCA models varying complexity in data.
method Relaxed linear Gaussian model with discrete latent variables, Bayesian nonparametric approach.
result Proposes locally adaptive probabilistic PCA (A-PPCA) for varying subspaces.
Principal component regression (PCR) is a two-stage procedure that selects some principal components and then constructs a regression model regarding them as new explanatory variables. Note that the principal components are obtained from only explanatory variables and not considered with the response variable. To addre…
New method for robust PCA with exponential family distributions.
problem Recovering low-rank structure from data matrices with outliers.
method Alternating Direction Method of Multipliers for eextRPCA. result Demonstrated effectiveness in steel sheet defect detection and crime activity monitoring.
The dynamic nature of air quality chemistry and transport makes it difficult to identify the mixture of air pollutants for a region. In this study of air quality in the Houston metropolitan area we apply dynamic principal component analysis (DPCA) to a normalized multivariate time series of daily concentration measurem…
Adaptive PCA algorithms for changing environments.
problem Static adversarial regret is not suitable for changing environments.
method Online adaptive algorithms for PCA and variance minimization with sub-linear adaptive regret guarantees.
result The proposed algorithms adapt to changing environments.
SP-SPCA improves sparse PCA by adaptively adjusting variable penalties, enhancing interpretability and stability.
problem Poor interpretability and variable redundancy in PCA for high-dimensional data.
method Introduces a single equilibrium parameter to adaptively adjust variable penalties in the L2 regularization framework.
result Consistently outperforms standard sparse PCA methods in identifying sparse loading patterns and preserving cumulative variance.
Paper presents a faster classical algorithm for principal component regression.
problem Efficiently solving principal component regression problems.
method Uses quantum-inspired linear algebra techniques.
result Achieves polylogarithmic runtime, significantly faster than state-of-the-art.
In the current context of data explosion, online techniques that do not require storing all data in memory are indispensable to routinely perform tasks like principal component analysis (PCA). Recursive algorithms that update the PCA with each new observation have been studied in various fields of research and found wi…
Novel prior for orthogonal functions improves functional component estimation.
problem Improving orthogonality in functional principal component analysis.
method Sequential adaptive priors for orthogonal functions using hierarchical conditionally normal distributions.
result Proposed prior leads to nearly orthogonal posterior estimates.
Adaptive PCR improves panel data analysis with uniform guarantees.
problem Adaptive data collection in panel data settings.
method Adapting PCR to online settings using martingale concentration.
result Time-uniform guarantees for adaptive PCR in panel data.
Algorithm estimates principal eigenvector with adaptive sensing, improving over non-adaptive methods.
problem Estimating principal eigenvector with limited scalar measurements.
method Compressed variant of Oja's algorithm using two adaptive measurements per sample.
result Convergence rate of O(λ1λ2d2/(Δ2t)) after t iterations, matching information-theoretic lower bound. A novel online framework for analyzing multidimensional functional data.
problem Analysis of multidimensional functional data streams poses significant challenges.
method Online functional principal component analysis using tensor product splines on a Stiefel manifold with Riemannian stochastic gradient descent.
result Efficient and scalable modeling of multidimensional functional data.
New method uses deep learning for better monitoring of industrial processes.
problem Monitoring high-dimensional, nonlinear profiles in industrial systems.
method Variational Autoencoders (VAEs) for modeling nonlinear manifolds.
result Deep probabilistic models outperform traditional methods in residual-space.
Modified PCA algorithm with continual learning preserves features of previous modes for multimode process monitoring.
problem Catastrophic forgetting of previous modes in monitoring models for successive modes.
method Modified PCA algorithm with elastic weight consolidation (EWC) to preserve features of previous modes.
result PCA-EWC algorithm effectively monitors multimode processes without performance decrease.
This paper solves tensor robust principal component analysis via scaled gradient descent.
problem Extracting useful information from tensor data robust to corruptions and ill-conditioning.
method Directly recovers low-rank tensor factors via scaled gradient descent with adaptive thresholding.
result The proposed algorithm converges linearly to the true low-rank tensor at a constant rate independent of the condition number.
R-PCA extends PCA to Riemannian manifolds for structured data.
problem Applying PCA to data on Riemannian manifolds without vector space operations.
method Adapting PCA to Riemannian manifolds by equipping data with local metrics.
result Unified approach for dimensionality reduction and statistical analysis on manifolds.
SPPCSO addresses multicollinearity in high-dimensional data, improving model stability and predictive accuracy.
problem Multicollinearity in high-dimensional data leads to unstable estimation and reduced predictive accuracy.
method SPPCSO integrates principal component regression and L1 regularization to adaptively adjust shrinkage factors.
result SPPCSO achieves stable and reliable estimation in high-noise settings, distinguishing signal variables from noise.
Robust principal component analysis (RPCA) can recover low-rank matrices when they are corrupted by sparse noises. In practice, many matrices are, however, of high-rank and hence cannot be recovered by RPCA. We propose a novel method called robust kernel principal component analysis (RKPCA) to decompose a partially cor…
Adaptive activity monitoring framework for wearable sensors.
problem Efficiently monitor human activities with low power consumption.
method Switching Gaussian process model with block circulant embedding and FFT for inference.
result Optimized trade-off between sensor power consumption and prediction performance.
Adaptive monitoring for AI systems detects and diagnoses shifts in data distribution.
problem Continuous monitoring of AI systems to detect and address unsafe behavior.
method Weighted-conformal martingales (WCTMs) for online monitoring of AI systems.
result Improved performance over state-of-the-art baselines on real-world datasets.
Risk monitoring detects when TTA models degrade at test time.
problem Detecting when TTA models degrade at test time.
method Extended risk monitoring tools based on sequential testing with confidence sequences.
result Demonstrated effectiveness of TTA monitoring framework across various datasets and methods.
New simulations advise caution in choosing principal components for multivariate functional data.
problem Inaccurate selection of principal components in multivariate functional data.
method Extensive simulations investigating the reliability of percentage of variance explained thresholds.
result Conventional threshold methods may fail to accurately explain overall variance in multivariate functional data.
The paper uses conformal prediction to monitor CPS with machine learning components.
problem Ensuring trustworthy CPS with machine learning components.
method Conformal prediction framework for real-time assurance monitoring of CPS with machine learning.
result The method provides well-calibrated confidence and limits the number of alarms.
Generalizes PCA to maximize any convex function of components.
problem Finding a principal vector that maximizes a convex function of components.
method Gradient ascent algorithm for solving the generalized PCA problem; fixed points of neural networks for kernel version.
result Solutions can be obtained as fixed points of simple neural networks.
LOFT separates subspace rotation and transformation for orthogonal fine-tuning.
problem Conflating subspace rotation and transformation in orthogonal fine-tuning.
method LOFT explicitly separates subspace rotation and transformation, using task-aware support selection.
result LOFT recovers principal-subspace orthogonal adaptation and improves efficiency-performance trade-off.
The paper introduces a method for interpretable principal component analysis of high-dimensional time series.
problem Inconsistent and difficult-to-interpret principal component estimates in high-dimensional regimes.
method Localized sparse principal component analysis of spectral density matrices in frequency domain.
result Efficient algorithm for sparse-localized estimates of principal subspaces.
Efficient private matrix analysis algorithms for recent variants.
problem Private analysis of recent matrix updates.
method Identifying sufficient conditions on positive semidefinite matrices.
result First efficient differentially private algorithms for various matrix analysis tasks.
Novel PCA method for high-dimensional inverse problems.
problem Optimizing large-scale random fields with gradient information.
method Gradient-Sensitive Principal Component Analysis (Gradient-SPCA) that modifies PCA using objective function gradients.
result Improvements in encoding quality for objective function minimization and field distribution.
Two new models forecast multiple subpopulations' mortality, outperforming existing methods.
problem Modeling mortality patterns and trajectories in related populations.
method Adapted multivariate functional principal component analysis techniques.
result The second proposed model outperforms existing methods in forecast accuracy.
We show how to efficiently project a vector onto the top principal components of a matrix, without explicitly computing these components. Specifically, we introduce an iterative algorithm that provably computes the projection using few calls to any black-box routine for ridge regression. By avoiding explicit principal …
A new PCR method using SVD with sparse regularization.
problem Lack of response variable information in traditional PCR.
method One-stage SVD approach with two loss functions and sparse regularization.
result Obtains principal component loadings with response variable information.
RSI uses Bayesian inference to monitor compliance in rule-governed domains.
problem Structural obstacles in compliance monitoring, including unlabeled outcomes and selective withholding of evidence.
method Rule-State Inference (RSI) treats formalized rules as Bayesian priors and infers compliance states through mean-field variational inference.
result RSI delivers formal guarantees of adaptability, consistency, and convergence, validated on a synthetic enterprise benchmark.
Essential principal components simplify spectral analysis with minimal training data.
problem Accurate spectral quantification from complex mixtures.
method Identifying essential principal components and using molar extinction coefficients.
result Near one-to-one projection from principal components to mixture constituents.
A new method detects sparse changes in high-dimensional data streams using tailored PCA projections.
problem Detecting sparse changes in high-dimensional data streams.
method Tailored PCA projections for online change detection.
result High efficiency in detecting even very sparse changes in mean, variance, and correlation.
A new model validation framework for agentic AI systems based on POMDPs.
problem Model validation of agentic AI systems.
method A POMDP-based framework for belief-state, forecast, and policy validation.
result The framework decomposes autonomous decision making into information, beliefs, forecasts, actions, and utility.
Paper uses PCA to analyze Chinese sovereign bonds and discusses bond immunization.
problem Analyzing factors affecting Chinese sovereign bond yield changes.
method Applied Principal Component Analysis (PCA) on bond yield data.
result Identified principal factors influencing Chinese sovereign bond yield changes.
In this paper, a similarity-driven cluster merging method is proposed for unsuper-vised fuzzy clustering. The cluster merging method is used to resolve the problem of cluster validation. Starting with an overspecified number of clusters in the data, pairs of similar clusters are merged based on the proposed similarity-…
Principal component regression (PCR) is a widely used two-stage procedure: principal component analysis (PCA), followed by regression in which the selected principal components are regarded as new explanatory variables in the model. Note that PCA is based only on the explanatory variables, so the principal components a…
QAPCA uses quantum annealing for robust PCA.
problem Outliers in data skew L2-norm principal components.
method Quantum annealing for L1-norm optimization.
result QAPCA's reconstruction error is comparable to L1-BF.
New supervised and unsupervised NFLTs for elliptical distributions.
problem Understanding unsupervised No Free Lunch Theorems for elliptical distributions.
method Proved two equally optimal strategies for elliptical distributions, inspired PRIM-based bump-hunting algorithms.
result Optimal strategies for selecting principal components based on variance or volume.
Two new PCA variants improve financial data analysis.
problem Numerical instability and nonstationarity in PCA for finance.
method Iterated and exponentially weighted moving PCA variants using Ogita-Aishima iteration.
result Improved stability and adaptability in financial data analysis.
Improved estimation of multiple principal components using manifold optimization and iterative deflation techniques.
problem Estimating multiple principal components efficiently and orthogonally.
method Extended SFPCA using manifold optimization and iterative deflation techniques.
result Alternative deflation schemes improve signal extraction and component estimation.
CPCR mitigates bias in PCR for overparameterized models.
problem Bias in Principal Component Regression (PCR) for overparameterized models.
method Calibrated Principal Component Regression (CPCR) learns a low-variance prior in the PC subspace and calibrates the model in the original feature space.
result CPCR outperforms standard PCR in overparameterized settings, improving prediction across multiple problems.
This paper analyzes how errors accumulate in PCA's deflation method.
problem Error accumulation in PCA's deflation method.
method Mathematical analysis of inexact Hotelling's deflation method in two scenarios.
result Characterization of error propagation in PCA's deflation method.