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.
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48 results for “optimal PCA”
Robust PCA has drawn significant attention in the last decade due to its success in numerous application domains, ranging from bio-informatics, statistics, and machine learning to image and video processing in computer vision. Robust PCA and its variants such as sparse PCA and stable PCA can be formulated as optimizati…
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.
We develop efficient algorithms for robust PCA that handle outliers.
problem Finding principal components in datasets with outliers.
method Nearly-linear time and streaming algorithms for robust PCA.
result Near-optimal error guarantees for robust PCA with nearly-linear time and memory usage.
Paper optimizes PCA for fairness using MMD and Stiefel manifold optimization.
problem Fair principal component analysis (PCA) to minimize MMD between protected classes.
method Formulates fair PCA as non-convex optimization over Stiefel manifold, solves using REPMS with theoretical guarantees.
result Our approach outperforms prior work in fairness, explained variance, and runtime.
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…
Develops an ℓ_p theory for PCA and spectral clustering.
problem Lack of precise characterizations of PCA scores for low-dimensional embedding.
method An ℓ_p perturbation theory for PCA in Hilbert spaces, analyzing eigenvectors and Gram matrix.
result Optimal recovery results for Gaussian mixture and stochastic block models.
We found hidden convexity in FPCA and developed a faster algorithm.
problem Bias in PCA leading to unequal subgroup outcomes.
method Convex optimization via eigenvalue optimization.
result Faster and fairer PCA algorithm.
Linear principal component analysis (PCA) can be extended to a nonlinear PCA by using artificial neural networks. But the benefit of curved components requires a careful control of the model complexity. Moreover, standard techniques for model selection, including cross-validation and more generally the use of an indepe…
A fair PCA method using JEVD ensures balanced data representation.
problem PCA's bias in data with demographic characteristics.
method Joint Eigenvalue Decomposition (JEVD) for fair PCA.
result JEVD optimally balances fairness and PCA's data structure.
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 samples.
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.
A central problem of random matrix theory is to understand the eigenvalues of spiked random matrix models, introduced by Johnstone, in which a prominent eigenvector (or "spike") is planted into a random matrix. These distributions form natural statistical models for principal component analysis (PCA) problems throughou…
We study Principal Component Analysis (PCA) in a setting where a part of the corrupting noise is data-dependent and, as a result, the noise and the true data are correlated. Under a bounded-ness assumption on the true data and the noise, and a simple assumption on data-noise correlation, we obtain a nearly optimal samp…
Revisits PCA with new formulations and insights.
problem Improving PCA formulations and understanding.
method Difference-of-convex (DC) framework, kernelizability, out-of-sample applicability, simultaneous iteration, DCA perspective.
result PCA-like problems are kernelizable and have new optimization perspectives.
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.
Principal components analysis (PCA) is the optimal linear auto-encoder of data, and it is often used to construct features. Enforcing sparsity on the principal components can promote better generalization, while improving the interpretability of the features. We study the problem of constructing optimal sparse linear a…
The CUR decomposition provides an approximation of a matrix that has low reconstruction error and that is sparse in the sense that the resulting approximation lies in the span of only a few columns of . In this regard, it appears to be similar to many sparse PCA methods. However, CUR takes a randomized algorithm…
The paper studies PCA of probability measures with varying sample sizes and finds optimal convergence rates.
problem PCA of multiple probability measures with varying sample sizes.
method Double asymptotic regime analysis with convergence rates for empirical covariance and PCA risk.
result Optimal convergence rates for empirical covariance and PCA risk in the dense regime are proven.
RieCUR improves Robust PCA by combining Riemannian optimization and CUR decompositions.
problem Robust Principal Component Analysis (PCA) to recover low-rank and sparse matrices from their sum.
method Riemannian CUR (RieCUR) algorithm that combines Riemannian optimization and robust CUR decompositions.
result RieCUR achieves state-of-the-art performance in Robust PCA with improved robustness to outliers and comparable computational complexity.
Generative Adversarial Networks (GANs) have become a powerful framework to learn generative models that arise across a wide variety of domains. While there has been a recent surge in the development of numerous GAN architectures with distinct optimization metrics, we are still lacking in our understanding on how far aw…
The paper optimizes portfolios by selecting financial ratios via PCA for better value investment.
problem Embedding value investment in portfolio optimization models.
method Principal Component Analysis (PCA) to filter out dominant financial ratios, then applying portfolio optimization model with second-order stochastic dominance criteria.
result PCA-SPO(B) strategy outperforms other models in terms of downside deviation, CVaR, VaR, Sortino, Rachev, and STARR ratios.
Unified framework for structured principal subspace estimation with bounds and rates.
problem Structured principal subspace estimation problems.
method Unified framework, minimax lower and upper bounds, information-geometric complexity.
result Minimax rates of convergence for specific settings, including optimal rates for non-negative PCA/SVD.
Principal component analysis (PCA) has been a prominent tool for high-dimensional data analysis. Online algorithms that estimate the principal component by processing streaming data are of tremendous practical and theoretical interests. Despite its rich applications, theoretical convergence analysis remains largely ope…
We study PCA as a stochastic optimization problem and propose a novel stochastic approximation algorithm which we refer to as "Matrix Stochastic Gradient" (MSG), as well as a practical variant, Capped MSG. We study the method both theoretically and empirically.
Principal Component Analysis (PCA) has wide applications in machine learning, text mining and computer vision. Classical PCA based on a Gaussian noise model is fragile to noise of large magnitude. Laplace noise assumption based PCA methods cannot deal with dense noise effectively. In this paper, we propose Cauchy Princ…
EB-PCA reduces noise in high-dimensional PCA by estimating a joint prior distribution.
problem High-dimensional PCA noise in samples comparable to or larger than data.
method Empirical Bayes PCA using Kiefer-Wolfowitz MLE, random matrix theory, and AMP algorithm.
result EB-PCA achieves Bayes-optimal accuracy in spiked models and significantly improves over PCA in simulations and real data.
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.
Sparse Generalized Principal Component Analysis for Large-scale Applications beyond Gaussianitystat.CO
Principal Component Analysis (PCA) is a dimension reduction technique. It produces inconsistent estimators when the dimensionality is moderate to high, which is often the problem in modern large-scale applications where algorithm scalability and model interpretability are difficult to achieve, not to mention the preval…
Combines PCA and AMP for better signal estimation in noisy data.
problem Estimating a rank-1 signal in rotationally invariant noise.
method Combines PCA and AMP, with PCA initialization at the start of AMP.
result Rigorous asymptotic characterization of the new estimator's performance.
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.
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.
A new dynamical formulation of log-PCA captures local principal modes of geodesic variations.
problem Learning principal variations of random probability measures under Wasserstein geometry.
method Introducing a new dynamical formulation of log-PCA as a variational approach.
result Deriving a general statistical convergence rate for empirical WT-PCA.
We present and analyze a simple, two-step algorithm to approximate the optimal solution of the sparse PCA problem. Our approach first solves a L1 penalized version of the NP-hard sparse PCA optimization problem and then uses a randomized rounding strategy to sparsify the resulting dense solution. Our main theoretical r…
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.
QPCA improves PCA for cyclostationary data.
problem Improving PCA for cyclostationary data.
method Formulated as an optimization problem, QPCA decomposes into frequency-domain PCA problems.
result Optimized basis for cyclostationary data.
New fair PCA method using streaming algorithms with statistical guarantees.
problem Perform PCA while ensuring fair projected distributions.
method Formulated new notion PAFO learnability, proposed fair noisy power method (FNPM) for memory efficiency.
result First statistical guarantee for fair PCA in streaming setting.
It is well known that Principal Component Analysis (PCA) is strongly affected by outliers and a lot of effort has been put into robustification of PCA. In this paper we present a new algorithm for robust PCA minimizing the trimmed reconstruction error. By directly minimizing over the Stiefel manifold, we avoid deflatio…
Principal Component Analysis (PCA) is a popular tool for dimensionality reduction and feature extraction in data analysis. There is a probabilistic version of PCA, known as Probabilistic PCA (PPCA). However, standard PCA and PPCA are not robust, as they are sensitive to outliers. To alleviate this problem, this paper i…
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.
New method optimizes PCA for better prediction and variance.
problem Improve PCA for better prediction and variance.
method Jointly optimize prediction error and variance explained.
result Our method outperforms existing approaches in both prediction and variance.
Paper improves robust PCA for noisy, outlier, and missing data.
problem Robust PCA with noise, outliers, and missing data.
method Bridging convex and nonconvex optimization.
result Near-optimal statistical accuracy for robust PCA.
This paper investigates the generalization of Principal Component Analysis (PCA) to Riemannian manifolds. We first propose a new and general type of family of subspaces in manifolds that we call barycentric subspaces. They are implicitly defined as the locus of points which are weighted means of reference points.…
A central problem of random matrix theory is to understand the eigenvalues of spiked random matrix models, in which a prominent eigenvector is planted into a random matrix. These distributions form natural statistical models for principal component analysis (PCA) problems throughout the sciences. Baik, Ben Arous and Pé…
This work obtains novel finite sample guarantees for Principal Component Analysis (PCA). These hold even when the corrupting noise is non-isotropic, and a part (or all of it) is data-dependent. Because of the latter, in general, the noise and the true data are correlated. The results in this work are a significant impr…
Robust PCA is a widely used statistical procedure to recover a underlying low-rank matrix with grossly corrupted observations. This work considers the problem of robust PCA as a nonconvex optimization problem on the manifold of low-rank matrices, and proposes two algorithms (for two versions of retractions) based on ma…
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.
Generalized principal component analysis (GLM-PCA) facilitates dimension reduction of non-normally distributed data. We provide a detailed derivation of GLM-PCA with a focus on optimization. We also demonstrate how to incorporate covariates, and suggest post-processing transformations to improve interpretability of lat…