arXiv research

Meta-learning bandits by reducing dimensionality with PCA.

Improved Bandit PCA with optimal regret bound.

High-dimensional representations often have a lower dimensional underlying structure. This is particularly the case in many decision making settings. For example, when the representation of actions is generated from a deep neural network, it is reasonable to expect a low-rank structure whereas conventional structures l…

When confronted with massive data streams, summarizing data with dimension reduction methods such as PCA raises theoretical and algorithmic pitfalls. Principal curves act as a nonlinear generalization of PCA and the present paper proposes a novel algorithm to automatically and sequentially learn principal curves from d…

We consider a partial-feedback variant of the well-studied online PCA problem where a learner attempts to predict a sequence of $d$-dimensional vectors in terms of a quadratic loss, while only having limited feedback about the environment's choices. We focus on a natural notion of bandit feedback where the learner only…

Simplifies fair PCA with fast, efficient solution.

KAN-PCA improves asset return analysis by capturing more variance than classical PCA during market crises.

New algorithm solves fair PCA, robust PCA, and sparse PCA problems efficiently.

Unified framework improves PCA for outliers and distributed data.

TL-PCA uses transfer learning to improve PCA performance with limited target data.

Bucketed PCA-NN outperforms DNNs by 96% on MNIST.

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…

Anchor PCA improves robustness in multi-domain PCA.

A new method for fair PCA ensures balanced error across groups.

This is a detailed tutorial paper which explains the Principal Component Analysis (PCA), Supervised PCA (SPCA), kernel PCA, and kernel SPCA. We start with projection, PCA with eigen-decomposition, PCA with one and multiple projection directions, properties of the projection matrix, reconstruction error minimization, an…

Revisits PCA with new formulations and insights.

Proposes $σ$-PCA to learn identifiable linear transformations without whitening.

Solution to sparse PCA tuning problem using Empirical Bayes.

PCA++ improves robustness to background noise in contrastive learning.

EB-PCA reduces noise in high-dimensional PCA by estimating a joint prior distribution.

New analysis improves black-box $k$-PCA algorithms, reducing parameter loss.

Derives kernel PCA with Nyström method for scalability.

We develop efficient algorithms for robust PCA that handle outliers.

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…

A new PCA method using T$\ell_1$-norm outperforms existing methods.

New fair PCA method using streaming algorithms with statistical guarantees.

PCA-Guided Quantile Sampling preserves data structure in large datasets.

A method to remove mean-shift noise from PCA using knockoffs.

AgFlow speeds up model selection in penalized PCA.

One technique to visualize the training of neural networks is to perform PCA on the parameters over the course of training and to project to the subspace spanned by the first few PCA components. In this paper we compare this technique to the PCA of a high dimensional random walk. We compute the eigenvalues and eigenvec…

GT-PCA improves PCA for image and time series data.

Modified PCA algorithm with continual learning preserves features of previous modes for multimode process monitoring.

PCA-Net combines PCA and neural networks for operator approximation, with new bounds on complexity.

A new dynamical formulation of log-PCA captures local principal modes of geodesic variations.

We performed an empirical comparison of ICA and PCA algorithms by applying them on two simulated noisy time series with varying distribution parameters and level of noise. In general, ICA shows better results than PCA because it takes into account higher moments of data distribution. On the other hand, PCA remains quit…

Generative Kernel PCA explores latent spaces for data interpretation and novelty detection.

Principal Component Analysis (PCA) has been used to study the pathogenesis of diseases. To enhance the interpretability of classical PCA, various improved PCA methods have been proposed to date. Among these, a typical method is the so-called sparse PCA, which focuses on seeking sparse loadings. However, the performance…

A fair PCA method using JEVD ensures balanced data representation.

Two new PCA variants improve financial data analysis.

One-shot algorithm for feature-distributed kernel PCA reduces communication costs.

EigenGame reinterprets PCA as a game to find eigenvectors.

CA-PCA improves manifold dimension estimation by accounting for curvature.

pPCA speeds up PCA by priming initial estimates for faster, more accurate results.

PCA-Triage optimizes sensor data sampling for IoT networks.

The paper studies PCA of probability measures with varying sample sizes and finds optimal convergence rates.

Deep-RLS uses deep learning to improve PCA for better source separation.

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…

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…