Efficient CF approach using fast adaptive PCA for recommender systems.
problem Matrix completion problem in recommender systems.
method Fast adaptive randomized singular value decomposition (SVD) and termination mechanism for latent factors.
result The approach achieves near optimal prediction accuracy with high runtime efficiency.
CA-PCA improves manifold dimension estimation by accounting for curvature.
problem Estimating the dimension of manifolds in high-dimensional data.
method Develops CA-PCA, a local PCA method calibrated with a quadratic embedding to account for curvature.
result Improves manifold dimension estimation in various settings.
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.
AdaOja improves Oja's algorithm for streaming PCA with adaptive learning rates.
problem Lack of standardized learning rates in Oja's algorithm for streaming PCA.
method Proposes AdaOja, a novel learning rate scheme for Oja's method.
result AdaOja outperforms common learning rate choices and performs comparably to state-of-the-art algorithms.
We propose algorithms for online principal component analysis (PCA) and variance minimization for adaptive settings. Previous literature has focused on upper bounding the static adversarial regret, whose comparator is the optimal fixed action in hindsight. However, static regret is not an appropriate metric when the un…
SDSPCAAN combines supervised and local data structures for better dimensionality reduction.
problem Preserving both global and local data structures for noisy high-dimensional data.
method Supervised discriminative sparse PCA with adaptive neighbors (SDSPCAAN).
result SDSPCAAN improves classification accuracy on high-dimensional datasets.
New risk factors improve stress testing accuracy.
problem Improving stress testing accuracy with new risk factors.
method Adapted PCA and autoencoders for dimension reduction and interpretation.
result Aggregated risk factors enhance stress testing outcomes.
PCA-Triage optimizes sensor data sampling for IoT networks.
problem Excessive sensor data in IoT networks exceeds available bandwidth.
method PCA-Triage uses streaming incremental PCA loadings to adaptively triage sensor data.
result PCA-Triage achieves high inference performance with minimal bandwidth usage.
Algorithm estimates top k eigenvectors of shared covariance matrices while preserving privacy.
problem Differentially private PCA with adaptive noise for arbitrary k.
method Iterative algorithm with adaptive noise reduction.
result First algorithm for estimating top k eigenvectors with near-optimal statistical error.
In this paper, we present an online adaptive PCA algorithm that is able to compute the full dimensional eigenspace per new time-step of sequential data. The algorithm is based on a one-step update rule that considers all second order correlations between previous samples and the new time-step. Our algorithm has O(n) co…
We present Matrix Krasulina, an algorithm for online k-PCA, by generalizing the classic Krasulina's method (Krasulina, 1969) from vector to matrix case. We show, both theoretically and empirically, that the algorithm naturally adapts to data low-rankness and converges exponentially fast to the ground-truth principal su…
DP-PCA improves privacy in PCA computations with optimal statistical error.
problem Differentially private principal component analysis with sub-linear sample complexity.
method Private minibatch gradient ascent with private mean estimation.
result Achieves optimal statistical error rates for sub-Gaussian data with n = i l d e O ( d ) n= ilde O(d) n = i l d e O ( d ) samples. Paper develops methods for PCA inference with missing data and heteroskedastic noise.
problem Constructing confidence regions for PCA in high dimensions with missing data and heteroskedastic noise.
method Proposes HeteroPCA and develops non-asymptotic distributional guarantees for valid inference.
result Valid inference on principal subspace and spiked covariance matrix with missing data.
Sequential or online dimensional reduction is of interests due to the explosion of streaming data based applications and the requirement of adaptive statistical modeling, in many emerging fields, such as the modeling of energy end-use profile. Principal Component Analysis (PCA), is the classical way of dimensional redu…
Improved online PCA algorithm learns from evolving norm of parameter vector.
problem Discarding evolving norm in online PCA leads to suboptimal learning.
method Implicitly Normalized Online PCA (INO-PCA) removes unit-norm constraint.
result Parameter norm evolution leads to improved learning behavior.
Improved Bandit PCA with optimal regret bound.
problem Minimizing regret in online PCA with bandit feedback.
method Combines online mirror descent and multiscale exploration.
result Minimax optimal regret bound of r d T r\sqrt{dT} r d T . PCA adapted for curved spaces improves data analysis.
problem PCA's limitations in curved spaces.
method Space Form PCA (SFPCA) for Riemannian manifolds.
result SFPCA provides faster and more accurate subspaces estimation.
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…
AdvPCA uses robust optimization to achieve sparse PCA without tuning.
problem Sparse PCA for high-dimensional data with implicit sparsity.
method Adversarial PCA (AdvPCA) using robust optimization.
result AdvPCA achieves effective sparse PCA with a closed-form solution.
PEA improves PCA and k-means for non-linear data and complex clusters.
problem Non-linear dimensionality reduction and clustering challenges.
method Principal Elliptical Analysis (PEA) for efficient non-linear approximation.
result PEA outperforms k-means in complex data clustering.
Unified framework for fast large-scale portfolio optimization.
problem Efficient portfolio optimization for large-scale financial data.
method Incorporates shrinkage and regularization techniques, addressing multiple objectives.
result AP-Trees and PCA-based factor models consistently outperform other approaches in out-of-sample portfolio performance.
Proposes a fair PCA algorithm that balances reconstruction loss and fairness.
problem PCA can be unfair to different groups.
method Adaptive first-order algorithm for Pareto optimality.
result The algorithm finds a fair subspace that minimizes reconstruction loss.
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.
Bayes-optimal limits in PCA with structured noise are determined.
problem Analyzing statistical dependencies in measurement noise for high-dimensional inference.
method Study of spiked matrix model with low-order polynomial orthogonal noise, providing Bayes-optimal limits and proposing a novel AMP.
result A novel AMP algorithm reaches the information-theoretic limits for more general priors.
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.
Proposes a robust portfolio method for large asset universes.
problem Outliers in return data affect traditional portfolio optimizations.
method Robust PCA, shrinkage estimation, and adaptive portfolio weights.
result Superior portfolio performance in numerical and empirical tests.
We introduce a new spatial data structure for high dimensional data called the \emph{approximate principal direction tree} (APD tree) that adapts to the intrinsic dimension of the data. Our algorithm ensures vector-quantization accuracy similar to that of computationally-expensive PCA trees with similar time-complexity…
Federated PCA algorithm uses limited memory and privacy-preserving techniques.
problem Memory-limited federated PCA in an asynchronous setting.
method Incremental streaming updates, differential privacy via input-perturbation, invariant to data permutations.
result Guarantees differential privacy and robustness against stragglers.
Paper proposes efficient methods for clustering and signal recovery in high-dimensional data with block structures.
problem High-dimensional clustering and signal recovery under block signal structures.
method CFA-PCA and MA-PCA methods for sparse and dense block signals.
result Proposed methods achieve computational minimax optimality for clustering and signal recovery.
STVNN models spatiotemporal data using covariance matrices.
problem Challenges in modeling spatiotemporal interactions in multivariate time series.
method Introduces SpatioTemporal coVariance Neural Network (STVNN) that operates on sample covariance matrix and uses joint spatiotemporal convolutions.
result STVNN is stable to online estimation uncertainties and outperforms temporal PCA.
RFPCA improves robustness of FPCA for matrix data.
problem Outliers in matrix data degrade the performance of FPCA.
method RFPCA uses matrix-variate t-distribution and EM algorithm for robust estimation.
result RFPCA outperforms other methods in detecting matrix-valued outliers.
Study uses deep learning for pairs trading in Polish equities, achieving profits in 2017-2019.
problem Statistical arbitrage in Polish equities market using traditional methods.
method Deep learning (LSTMs) for asset replication, PCA for risk factor analysis, Ornstein Uhlenbeck process for residual modeling.
result Deep learning methods, especially LSTMs, show promise for profitable trading in Polish equities.
New insights into SGD and SGD-M in high dimensions.
problem Understanding and comparing SGD and SGD-M in high-dimensional settings.
method Developed high-dimensional scaling limits for SGD-M and online SGD, examining their dynamics and performance.
result SGD-M amplifies high-dimensional effects, potentially degrading performance compared to online SGD.
In many-body physics, renormalization techniques are used to extract aspects of a statistical or quantum state that are relevant at large scale, or for low energy experiments. Recent works have proposed that these features can be formally identified as those perturbations of the states whose distinguishability most res…
Simplifies fair PCA with fast, efficient solution.
problem Learning fair low-rank approximations of data.
method Conceptually simple approach with analytic solution.
result Faster and similar results to existing fair PCA methods.
Botnet, a group of coordinated bots, is becoming the main platform of malicious Internet activities like DDOS, click fraud, web scraping, spam/rumor distribution, etc. This paper focuses on design and experiment of a new approach for botnet detection from streaming web server logs, motivated by its wide applicability, …
KAN-PCA improves asset return analysis by capturing more variance than classical PCA during market crises.
problem Inefficient classical PCA during market crises when correlations between assets change dramatically.
method KAN-PCA uses KAN (Kolmogorov-Arnold Networks) with B-spline functions to learn nonlinear projections.
result KAN-PCA achieves a higher reconstruction R^2 (66.57%) compared to classical PCA (62.99%) on 20 S&P 500 stocks.
We study adaptive data-dependent dimensionality reduction in the context of supervised learning in general metric spaces. Our main statistical contribution is a generalization bound for Lipschitz functions in metric spaces that are doubling, or nearly doubling. On the algorithmic front, we describe an analogue of PCA f…
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.
Explains various PCA and SPCA methods with theory and applications.
problem No specific problem stated; focuses on explaining methods.
method Explains PCA, SPCA, kernel PCA, and kernel SPCA methods with theory and applications.
result Comprehensive coverage of PCA and SPCA methods with theory and applications.
New algorithm solves fair PCA, robust PCA, and sparse PCA problems efficiently.
problem Fair Principal Component Analysis (FPCA) to ensure fairness in PCA solutions.
method Iterative MM algorithm with SDP reformulation to quadratic program.
result Algorithm monotonically improves fairness objectives at each iteration.
Unified framework improves PCA for outliers and distributed data.
problem Outliers and limitations in PCA for large-scale applications.
method φ-PCA framework that retains PCA efficiency and adds robustness.
result HM-PCA achieves optimal robustness and efficiency.
TL-PCA uses transfer learning to improve PCA performance with limited target data.
problem PCA performance is limited with scarce target data.
method Transfer learning approach to PCA (TL-PCA) that combines source task knowledge with target task data.
result Improved PCA representation for dimensionality reduction with limited target data.
Bucketed PCA-NN outperforms DNNs by 96% on MNIST.
problem Benchmarking deep neural networks for supervised classification.
method Applies PCA to individual buckets constructed in two phases, retains neural network architecture, and uses neurons that mirror input signals.
result Bucketed PCA-NN achieves 96% accuracy on MNIST, similar to DNNs.
A new low-dimensional parameterization based on principal component analysis (PCA) and convolutional neural networks (CNN) is developed to represent complex geological models. The CNN-PCA method is inspired by recent developments in computer vision using deep learning. CNN-PCA can be viewed as a generalization of an ex…
Denise learns a function to quickly decompose covariance matrices robustly.
problem Robustly decomposing covariance matrices for feature extraction.
method Deep learning for symmetric positive semidefinite matrices.
result Denise achieves state-of-the-art performance in decomposition quality and speed.
Sparse principal component analysis (PCA) involves nonconvex optimization for which the global solution is hard to obtain. To address this issue, one popular approach is convex relaxation. However, such an approach may produce suboptimal estimators due to the relaxation effect. To optimally estimate sparse principal su…
Anchor PCA improves robustness in multi-domain PCA.
problem PCA on pooled data can focus on spurious directions.
method Anchor PCA focuses on shared directions of variation.
result Anchor PCA outperforms pooling and worst-case alternatives.