A new method for sparse PCA using orthogonal rotations and soft-thresholding.
problem Sparse PCA with a new basis using orthogonal rotations.
method Initialize with leading principal components, apply kimesk orthogonal rotation, and soft-threshold the rotated components. result The proposed method is more stable and explains more variance compared to alternatives.
A neural network model tackles high-dimensional data with latent structures.
problem Modeling high-dimensional data with latent low-dimensional structures.
method Integrates PCA and Soft PCA layers into neural network architecture for factor modeling and non-linear transformations.
result Demonstrates improved performance in forecasting and nowcasting with real-world data.
We study the effectiveness of various approaches that defend against adversarial attacks on deep networks via manipulations based on basis function representations of images. Specifically, we experiment with low-pass filtering, PCA, JPEG compression, low resolution wavelet approximation, and soft-thresholding. We evalu…
ALPCAH improves PCA for noisy data samples.
problem Heteroscedastic data with varying noise levels.
method Subspace learning method estimating sample-wise noise variances.
result Improves subspace basis for low-rank data.
Unified diffusion framework enhances generative models flexibility.
problem Improving generative models' design freedom and efficiency.
method Unified framework incorporating choice of representation, prior distribution, and noise scheduling.
result Enhanced flexibility leading to more efficient training and data generation.
New algorithm for robust mean estimation in high dimensions with nearly-PCA time complexity.
problem Robust mean estimation in high-dimensional data with a minority of contaminated data.
method List-decodable mean estimation algorithm using a novel soft downweighting method, SIFT, and a Ky Fan matrix multiplicative weights procedure.
result Optimal sample complexity and error rate for list-decodable mean estimation with runtime nearly matching PCA.
Paper proposes a new descriptor for early trajectory characterization in matrix iterations.
problem Comparing early behavior of high-dimensional trajectories in nonlinear matrix iterations.
method Develops a two-channel fuzzy coordinate system using F-transform for compact representation.
result The descriptor achieves high R^2 values (mean = 0.6480) in approximating convergence lengths.
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.
Design rule check is a critical step in the physical design of integrated circuits to ensure manufacturability. However, it can be done only after a time-consuming detailed routing procedure, which adds drastically to the time of design iterations. With advanced technology nodes, the outcomes of global routing and deta…
Employers actively look for talents having not only specific hard skills but also various soft skills. To analyze the soft skill demands on the job market, it is important to be able to detect soft skill phrases from job advertisements automatically. However, a naive matching of soft skill phrases can lead to false pos…
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.
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.
Soft labeling impacts OOD detection in neural networks.
problem Impact of soft labeling on OOD detection in deep neural networks.
method Empirical analysis of how soft labeling affects OOD detection performance.
result Soft labeling can either improve or deteriorate OOD detection performance.
Developed a new thresholding method that connects soft and hard thresholding.
problem Connecting soft and hard thresholding methods in data analysis.
method Scaled soft thresholding method with empirical scaling values.
result Found two sources of over-fitting in the scaled soft thresholding method.
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…
Soft cells fill space without gaps, derived from minimal surfaces and deformed using edge bending.
problem Creating space-filling shapes without sharp corners.
method Edge bending algorithm to deform polyhedral tilings into soft tilings.
result Soft tilings derived from minimal surfaces can be continuously transformed into one another.
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.
A new method for fair PCA ensures balanced error across groups.
problem Balancing approximation error across different groups in multi-group data.
method Iterative method to compute fair principal components minimizing max group-wise reconstruction error.
result Preserves the containment property of standard PCA and reduces to standard PCA for single-group data.
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.
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.
Proposes σ-PCA to learn identifiable linear transformations without whitening.
problem Cannot identify axes with equal variances in PCA.
method Unified model for linear and nonlinear PCA, introducing a missing piece to eliminate rotational indeterminacy.
result Eliminates subspace rotational indeterminacy in PCA.
Solution to sparse PCA tuning problem using Empirical Bayes.
problem Sparse PCA multiple tuning problem (MTP).
method Empirical Bayes covariance decomposition for penalized PCA.
result Empirical Bayes approach efficiently solves MTP in sparse PCA.
PCA++ improves robustness to background noise in contrastive learning.
problem Recovering shared signal subspaces from positive pairs in high-dimensional data with structured background noise.
method PCA++ uses hard uniformity-constrained contrastive learning to enforce identity covariance on projected features.
result PCA++ outperforms standard PCA and alignment-only PCA+ in simulations and real-world datasets.
ASBART accelerates Soft BART for faster Bayesian regression.
problem Slow computation in Soft BART.
method Proposed ASBART, a variant of Soft BART.
result ASBART is about 10 times faster than Soft BART with similar accuracy.
Maximum entropy deep reinforcement learning (RL) methods have been demonstrated on a range of challenging continuous tasks. However, existing methods either suffer from severe instability when training on large off-policy data or cannot scale to tasks with very high state and action dimensionality such as 3D humanoid l…
New method improves stability of soft FQI for offline RL.
problem Stability issues in soft FQI under function approximation.
method Stationary reweighting to align operator norms.
result Local linear convergence proved under certain conditions.
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.
New analysis improves black-box k-PCA algorithms, reducing parameter loss.
problem Designing efficient k-PCA algorithms with black-box access to a 1-PCA oracle. method Black-box deflation methods, analyzing ePCA and cPCA approximations.
result Deflation methods suffer no asymptotic parameter loss for k-cPCA in feasible regimes. Derives kernel PCA with Nyström method for scalability.
problem Scalability of kernel PCA.
method Nyström method for kernel PCA.
result Provides scalable alternative to full kernel PCA.
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.
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 Tℓ1-norm outperforms existing methods.
problem Outliers and noise sensitivity in classical PCA.
method PCA based on Tℓ1-norm maximization. result The method outperforms PCA-ℓp, ℓpSPCA, and PCA in numerical experiments. Generalizes soft noncommutative schemes to flag varieties.
problem Applying soft noncommutative schemes to flag varieties.
method Generalization via toric geometry and distinguished affine charts.
result Soft noncommutative schemes can be applied to flag varieties.
Paper proposes a new loss function for conditional models using soft targets.
problem Improving generalization performance of deep neural networks on supervised classification tasks.
method Introduces a new loss function compatible with soft targets, based on noise contrastive estimation.
result Soft target InfoNCE loss performs on par with cross-entropy baselines and outperforms other losses.
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.
PCA-Guided Quantile Sampling preserves data structure in large datasets.
problem Preserving data structure in large-scale subsampling.
method PCA QS uses leading principal components to guide stratified sampling.
result PCA QS maintains statistical and geometric structure without distorting semantics.
A method to remove mean-shift noise from PCA using knockoffs.
problem High sensitivity of PCA to mean-shift contamination in high-dimensional data.
method Introducing knockoff mean-shift perturbation to separate and remove mean-shift components from PCA.
result The mean-shift spikes are spectrally separable from stable eigenvalues, allowing for robust PCA.
AgFlow speeds up model selection in penalized PCA.
problem Efficient model selection in penalized PCA for HDLSS settings.
method Implicit regularization effect of gradient flow to reduce computation complexity.
result AgFlow achieves the complete solution path of L2-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…
Introduces Soft-SVM for binary classification bridging logistic and SVM.
problem Data separability issues in binary classification.
method Soft-SVM regression using convex relaxation of hinge loss with softness and class-separation parameters.
result Soft-SVM performs well in classification and prediction errors.
Deep model learns from labeled and unlabeled data for industrial soft sensing.
problem Lack of data limits soft sensor development in industrial processes.
method Hierarchical, generative deep latent variable model for semi-supervised multi-unit soft sensing.
result Model outperforms current methods for soft sensing in industrial processes.
GT-PCA improves PCA for image and time series data.
problem Lack of robustness to transformations in PCA.
method GT-PCA is a neural network that estimates components invariant to specific transformations.
result GT-PCA outperforms alternative methods in synthetic and real data experiments.
This paper introduces TNTK to study infinite soft tree ensembles.
problem Understanding the behavior of infinite soft tree ensembles.
method Introduced Tree Neural Tangent Kernel (TNTK) to analyze infinite soft tree ensembles.
result Identified several non-trivial properties of infinite soft tree ensembles.
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.
PCA-Net combines PCA and neural networks for operator approximation, with new bounds on complexity.
problem Developing approximation theory for PCA-Net architecture.
method Combines PCA and neural networks, derives universal approximation results and lower bounds on complexity.
result PCA-Net can overcome the curse of parametric complexity for specific operators.