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.
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…
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.
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.
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.
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…
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…
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.
Adaptive classifier optimizes high-dimensional data with spiked covariance structure.
problem Classification of high-dimensional data with spiked covariance structure.
method Adaptive classifier that whitens data, screens features, and applies Fisher linear discriminant.
result The classifier is Bayes optimal under certain conditions and performs well on real and synthetic data.
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…
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.
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.
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.
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 identifies structural parameters without assuming uncorrelated errors.
problem Identifying structural parameters in simultaneous equation models.
method Exploits higher-order cumulant restrictions, not requiring uncorrelated errors.
result Simple diagonality condition on hth-order cumulants identifies structural parameter matrix. 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.
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…
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.
We propose non-stationary spectral kernels for Gaussian process regression. We propose to model the spectral density of a non-stationary kernel function as a mixture of input-dependent Gaussian process frequency density surfaces. We solve the generalised Fourier transform with such a model, and present a family of non-…
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.
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.
Algorithm improves SVM classification in non-Euclidean spaces.
problem Limitations of traditional SVM in non-Euclidean spaces.
method Covariance-adjusted SVM using Cholesky Decomposition.
result Cholesky-SVM outperforms traditional SVM in non-Euclidean spaces.
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.
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.
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…
Reservoir subspace injection improves online ICA by preserving injected features.
problem Discarding injected features in top-n 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.
Exact recovery method for community detection in Gaussian mixtures with dependent noise.
problem Community detection in Gaussian mixtures with dependent and heterogeneous noise.
method Maximum likelihood estimator (MLE) for constrained quadratic optimization problem, using Σ-whitened separation and local inequalities. result Sharp exact-recovery threshold and no-gap mechanism in the unknown-size setting.
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…
We study the sample complexity of canonical correlation analysis (CCA), \ie, the number of samples needed to estimate the population canonical correlation and directions up to arbitrarily small error. With mild assumptions on the data distribution, we show that in order to achieve ε-suboptimality in a properly define…
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 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.
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.
Kalman filters are routinely used for many data fusion applications including navigation, tracking, and simultaneous localization and mapping problems. However, significant time and effort is frequently required to tune various Kalman filter model parameters, e.g. process noise covariance, pre-whitening filter models f…
Improved multivariate conformal prediction by standardizing residuals.
problem Weak conditional coverage in heteroskedastic multivariate settings.
method Natural extension of univariate normalization to multivariate setting, whitening residuals and standardizing local variance.
result Standardized residuals yield asymptotic conditional coverage under certain distributions.
We address the problem of estimating statistics of hidden units in a neural network using a method of analytic moment propagation. These statistics are useful for approximate whitening of the inputs in front of saturating non-linearities such as a sigmoid function. This is important for initialization of training and f…
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.
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…
Efficiently computes matrix square roots and their inverses for large matrices.
problem Computing matrix square roots and inverses for large matrices efficiently.
method Combines Krylov subspace methods with rational approximation for quadratic-time computation.
result Achieves 4 decimal places of accuracy with fewer than 100 matrix-vector multiplications.
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.
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…
A new model for sequential memory using temporal predictive coding.
problem Forming accurate memory of sequential stimuli in the brain.
method Proposes a novel PC-based model called temporal predictive coding (tPC).
result Shows that tPC models can accurately memorize and retrieve sequential inputs.
HIP-GP improves GP inference for inter-domain observations with millions of inducing points.
problem Inference for Gaussian Processes across different domains.
method Hierarchical inducing point Gaussian process with grid structure and stationary kernel assumption.
result Improved approximation accuracy through increased number of inducing points.
Neural networks can learn kernel machines with a data-dependent kernel.
problem Can neural networks in the rich feature learning regime learn a kernel machine?
method Demonstrated silent alignment effect in neural networks, showing they can learn a kernel machine with a data-dependent kernel.
result Neural networks in the rich feature learning regime can learn a kernel machine with a data-dependent kernel due to silent alignment.
New GLS estimator handles high-dimensional data with autocorrelated errors.
problem High-dimensional regressions with autocorrelated errors.
method LASSO regression, autoregressive model fitting, and whitening.
result The method outperforms unadjusted LASSO in estimating errors driven by autoregressive processes.
We analyze deep neural networks using convex duality to reveal hidden layer structures.
problem Understanding the structure of deep neural networks.
method Introducing a convex analytic framework to characterize hidden layer weights.
result Optimal hidden layer weights align with previous layers via duality.
Proposes DR-ME test for interpretable distributional treatment effects.
problem Detects invisible differences in treatment effects on distributional outcomes.
method Semiparametrically efficient finite-location test using kernel witnesses and orthogonal features.
result DR-ME reveals causal-discrepancy coordinates and has noncentral chi-square local power.
The study explains delayed spikes in batch-normalized models.
problem Delayed spikes in batch-normalized models.
method Analyzing batch-normalized linear models, deriving conditions for delayed onset and waiting time.
result Explicit conditions for delayed-onset and waiting time in whitened square-loss linear regression.