Whitening, or sphering, is a common preprocessing step in statistical analysis to transform random variables to orthogonality. However, due to rotational freedom there are infinitely many possible whitening procedures. Consequently, there is a diverse range of sphering methods in use, for example based on principal com…
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48 results for “PCA whitening”
Proposes -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.
Zipfian Whiteningcs.CL
PCA whitening weighted by Zipfian word frequencies improves task performance.
problem Skewed word embedding spaces in neural models.
method PCA whitening weighted by empirical word frequencies following Zipf's law.
result Significantly improves task performance, surpassing baselines.
Unified framework for scale-invariant representation learning using MAPCA.
problem Learning invariant representations in data.
method Metric-Aware Principal Component Analysis (MAPCA) based on generalized eigenproblem.
result MAPCA provides a unified geometric language for various self-supervised learning objectives.
Batch Normalization (BN) is capable of accelerating the training of deep models by centering and scaling activations within mini-batches. In this work, we propose Decorrelated Batch Normalization (DBN), which not just centers and scales activations but whitens them. We explore multiple whitening techniques, and find th…
There are a multitude of methods to perform multi-set correlated component analysis (MCCA), including some that require iterative solutions. The methods differ on the criterion they optimize and the constraints placed on the solutions. This note focuses perhaps on the simplest version, which can be solved in a single s…
New method extracts biological concepts from cell microscopy images.
problem Extracting meaningful concepts from vision foundation models trained on cell microscopy images.
method Sparse dictionary learning (DL) combined with PCA whitening pre-processing.
result Successfully retrieved biologically meaningful concepts like cell types and genetic perturbations.
Finite-size scaling of hetero-associative retrieval in continuous-signal-driven Ising spin systemscond-mat.dis-nn
A bridge between continuous signals and discrete Ising spins for associative memory.
problem Associative memory in continuous-signal-driven Ising spin systems.
method Multilayer Ising framework with PCA whitening and SimHash projection, coupled to pseudo-inverse memory couplings.
result Finite-size scaling of operational storage capacity with , approaching .
New Convolutional Unit improves Batch Whitening performance.
problem Improving the efficiency and effectiveness of Batch Whitening.
method Proposes a new Convolutional Unit that aligns with Batch Whitening theory and empirically analyzes the original Convolutional Unit.
result Significantly improved performance on multiple image classification datasets.
Corrected whitening restores orthogonality in high-dimensional spherical Gaussian mixtures.
problem In high-dimensional data, standard whitening fails to preserve orthogonality of mixture means.
method Derived exact limits for whitened means dot products using random matrix theory, constructed a corrected whitening matrix.
result Corrected whitening allows for improved estimation of spherical Gaussian mixtures in the large-dimensional regime.
We create consistent option surfaces without arbitrage.
problem Constructing consistent option surfaces free of arbitrage across different maturities.
method Combining PCA-Smolyak approximation with chain-consistent diffusion and c-EMOT bridge.
result Computable certificates for strong convexity, solver correctness, and Dupire/Greeks stability.
We present here a new model and algorithm which performs an efficient Natural gradient descent for Multilayer Perceptrons. Natural gradient descent was originally proposed from a point of view of information geometry, and it performs the steepest descent updates on manifolds in a Riemannian space. In particular, we ext…
Proposes group whitening to enhance deep learning models' performance.
problem Improving learning efficiency and representational capacity in deep learning models.
method Group Whitening (GW) combines whitening and group normalization to balance these aspects.
result Group Whitening consistently improves model performance across different architectures and benchmarks.
Eigendecomposition (ED) is widely used in deep networks. However, the backpropagation of its results tends to be numerically unstable, whether using ED directly or approximating it with the Power Iteration method, particularly when dealing with large matrices. While this can be mitigated by partitioning the data in sma…
CW-Gen models improve probabilistic time series forecasting by incorporating prior information.
problem Challenges in probabilistic forecasting of multivariate time series due to non-stationarity, inter-variable dependencies, and distribution shifts.
method CW-Gen framework that incorporates prior information through conditional whitening. JMCE learns conditional mean and covariance, improving sample quality.
result CW-Gen consistently enhances predictive performance, capturing non-stationary dynamics and inter-variable correlations more effectively than prior-free approaches.
A new SSL method using whitening of latent-space features.
problem Efficiency and effectiveness of self-supervised representation learning.
method Proposes a new loss function based on whitening of latent-space features, avoiding the need for negatives and asymmetric networks.
result Improves efficiency and effectiveness of SSL by avoiding the need for negatives and asymmetric networks.
Data whitening and second order optimization harm generalization by reducing access to dataset information.
problem Harmful effects of data whitening and second order optimization on generalization in machine learning.
method Analysis of fully connected models and experimental verification.
result Data whitening and second order optimization reduce or prevent generalization by limiting access to dataset information.
Likelihood-free methods are an established approach for performing approximate Bayesian inference for models with intractable likelihood functions. However, they can be computationally demanding. Bayesian synthetic likelihood (BSL) is a popular such method that approximates the likelihood function of the summary statis…
WS diffusion models handle anisotropic Gaussian noise better than conventional methods.
problem Handling anisotropic Gaussian noise in imaging inverse problems.
method Whitened Score (WS) diffusion models based on stochastic differential equations.
result WS DMs outperform conventional DMs on anisotropic Gaussian noise.
CW normalizes and decorrelates neural network layers for better concept understanding.
problem Challenges in understanding neural network hidden layers.
method Introducing concept whitening (CW) to alter neural network layers.
result CW provides clearer understanding of how networks learn concepts over layers.
Non-Gaussian component analysis (NGCA) is an unsupervised linear dimension reduction method that extracts low-dimensional non-Gaussian "signals" from high-dimensional data contaminated with Gaussian noise. NGCA can be regarded as a generalization of projection pursuit (PP) and independent component analysis (ICA) to mu…
Real-world optimization problems often have expensive objective functions in terms of cost and time. It is desirable to find near-optimal solutions with very few function evaluations. Surrogate-assisted optimizers tend to reduce the required number of function evaluations by replacing the real function with an efficien…
New proof shows coupling-based flows converge linearly to diagonalize data covariance.
problem Understanding convergence of coupling-based normalizing flows to arbitrary data distributions.
method Proved linear convergence rate for whitening of data distribution.
result Coupling-based flows achieve linear convergence to diagonalize data covariance.
Batch Normalization (BN) is a common technique used to speed-up and stabilize training. On the other hand, the learnable parameters of BN are commonly used in conditional Generative Adversarial Networks (cGANs) for representing class-specific information using conditional Batch Normalization (cBN). In this paper we pro…
Improved convergence in deep learning networks via gradient transformation.
problem Reduced convergence speed in deep learning networks.
method Gradient transformation to weight gradients and recursive condition number reduction.
result Improved convergence speed and accuracy in image classification tasks.
Reservoir subspace injection improves online ICA by preserving injected features.
problem Discarding injected features in top- whitening can degrade performance.
method Formalized reservoir subspace injection (RSI) and developed diagnostics (IER, SSO, ρ_x) to identify and mitigate the failure mode.
result RSI controller preserves passthrough retention, improving performance by up to 2.2 dB.
CVAE detects weak complex signals in maritime radar, improving detection over classical methods.
problem Detecting weak complex-valued signals in non-Gaussian, range-varying interference.
method Complex-valued Variational AutoEncoder (CVAE) trained on clutter-plus-noise, whitening, ANMF fusion.
result CVAE yields higher detection probability Pd at matched false-alarm rate Pfa, especially with whitening.
The natural gradient allows for more efficient gradient descent by removing dependencies and biases inherent in a function's parameterization. Several papers present the topic thoroughly and precisely. It remains a very difficult idea to get your head around however. The intent of this note is to provide simple intuiti…
Paper introduces a new cost function to improve deep learning model generalization.
problem Overfitting and poor extrapolation of deep learning models.
method Introduces a 'whitening' cost function based on the Ljung-Box statistic.
result Significant improvement in generalization for RNNs and image autoencoders.
Proposes a flexible feature allocation model for sparse factor analysis.
problem Sparse data and rigid assumptions in traditional exploratory tools.
method Adaptive latent feature sharing with control over feature sparsity.
result Derives a novel adaptive Factor analysis (aFA) and aPPCA for flexible dimensionality reduction.
Interneurons accelerate learning dynamics in recurrent neural networks for statistical adaptationq-bio.NC
Interneurons improve learning in neural networks by accelerating convergence.
problem Rapid adaptation to changing input statistics in neural networks.
method Two mathematically tractable recurrent linear neural networks were compared: one with direct recurrent connections and the other with interneurons that mediate recurrent communication.
result The network with interneurons converges more quickly than the network with direct recurrent connections, scaling logarithmically with initialization spectrum.
Sharp-SSL: Selective high-dimensional axis-aligned random projections for semi-supervised learningstat.ME
Sharp-SSL uses random projections to identify important variables for semi-supervised learning.
problem High-dimensional semi-supervised learning problems.
method Careful aggregation of low-dimensional results from many axis-aligned random projections.
result Sharp-SSL algorithm can recover signal coordinates with high probability.
Novel framework synthesizes stochastic trajectories with anticipated structural breaks.
problem Synthesizing forward-looking, time-evolving stochastic trajectories with anticipated structural breaks.
method Anticipatory Neural Jump-Diffusion (ANJD) flow, AVNSG for dynamic spectral whitening.
result The framework effectively captures non-commutative moments and high-order stochastic texture.
Generalized canonical correlation analysis (GCCA) aims at finding latent low-dimensional common structure from multiple views (feature vectors in different domains) of the same entities. Unlike principal component analysis (PCA) that handles a single view, (G)CCA is able to integrate information from different feature …
After deep generative models were successfully applied to image generation tasks, learning disentangled latent variables of data has become a crucial part of deep generative model research. Many models have been proposed to learn an interpretable and factorized representation of latent variable by modifying their objec…
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.
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.
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…
Anchor PCAstat.ML
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…
One primary focus in multimodal feature extraction is to find the representations of individual modalities that are maximally correlated. As a well-known measure of dependence, the Hirschfeld-Gebelein-Rényi (HGR) maximal correlation becomes an appealing objective because of its operational meaning and desirable propert…
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.
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.