This paper studies iteration convergence of Kronecker graphical lasso (KGLasso) algorithms for estimating the covariance of an i.i.d. Gaussian random sample under a sparse Kronecker-product covariance model and MSE convergence rates. The KGlasso model, originally called the transposable regularized covariance model by …
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48 results for “Kronecker covariance factorization”
Extended wMEM approach for MEG inverse problem using wavelet and spatial filters.
problem Infer brain activity from full space-time data in MEG.
method Wavelet decomposition, spatial filters, Kronecker product modeling, numerical optimization.
result Smooth numerical optimization problem solved with reasonable dimensionality.
Optimization algorithms that leverage gradient covariance information, such as variants of natural gradient descent (Amari, 1998), offer the prospect of yielding more effective descent directions. For models with many parameters, the covariance matrix they are based on becomes gigantic, making them inapplicable in thei…
EiGLasso speeds up sparse Kronecker-sum covariance estimation.
problem Sparse Kronecker-sum inverse covariance estimation challenges in scalability and parameter identification.
method Newton's method combined with eigendecomposition of sample and feature graphs, approximating Hessian for speed.
result Two to three orders-of-magnitude speed-up on simulated and real-world data.
In this paper we consider the use of the space vs. time Kronecker product decomposition in the estimation of covariance matrices for spatio-temporal data. This decomposition imposes lower dimensional structure on the estimated covariance matrix, thus reducing the number of samples required for estimation. To allow a sm…
A new method for learning Bayesian neural networks using layerwise inference.
problem Learning Bayesian neural networks efficiently and accurately.
method Bayesian layerwise inference, treating neural networks as stacked Bayesian linear models, with pseudo-targets defined by backpropagated gradients.
result The method converges quickly and performs well on various benchmarks.
This paper presents a new method for estimating high dimensional covariance matrices. The method, permuted rank-penalized least-squares (PRLS), is based on a Kronecker product series expansion of the true covariance matrix. Assuming an i.i.d. Gaussian random sample, we establish high dimensional rates of convergence to…
Nonsingular estimation of high dimensional covariance matrices is an important step in many statistical procedures like classification, clustering, variable selection an future extraction. After a review of the essential background material, this paper introduces a technique we call slicing for obtaining a nonsingular …
GLSKF improves tensor completion by capturing both global and local variations.
problem Tensor completion with missing entries, especially in data with spatial or temporal side information.
method Integrates smoothness-constrained low-rank factorization with a locally correlated residual process.
result GLSKF achieves superior performance and scalability on real-world datasets.
A new method for optimizing deep neural networks using TKFAC.
problem Optimizing deep neural networks with second-order methods.
method Proposes Trace-restricted Kronecker-factored Approximate Curvature (TKFAC) for Fisher information matrix approximation.
result TKFAC improves performance on deep network architectures compared to state-of-the-art algorithms.
In this work we consider the problem of detecting anomalous spatio-temporal behavior in videos. Our approach is to learn the normative multiframe pixel joint distribution and detect deviations from it using a likelihood based approach. Due to the extreme lack of available training samples relative to the dimension of t…
New algorithm estimates matrix-valued regression parameters efficiently.
problem High-dimensional matrix regression with limited sample size.
method KRO-PRO-FAC algorithm using Kronecker product factorization.
result Algorithm provides accurate parameter estimates without covariance estimation.
EigenDamage reduces neural network size and FLOPs with structured pruning in the Kronecker-Factored Eigenbasis.
problem Reducing neural network size and FLOPs while maintaining accuracy for resource-constrained devices.
method Kronecker-Factored Eigenbasis reparameterization and Hessian-based structured pruning.
result Empirically validated improvements in model size and FLOPs with negligible accuracy loss.
KF-LAX uses KFAC to improve sample efficiency in reinforcement learning.
problem Sample efficiency and low variance in gradient-based optimization methods.
method Kronecker-factored curvature estimation (KFAC) applied to RELAX gradient estimator.
result Improved performance on synthetic and Atari games.
Adaptive regularization improves neural network performance on small datasets.
problem Improving neural network performance on limited data.
method Adaptive regularization using a matrix-variate normal prior with a Kronecker product structure.
result The method leads to networks with smaller stable ranks and spectral norms, suggesting better generalization.
MCCA extracts shared structure from multiple tensor datasets.
problem Extracting shared structure from multiple tensor datasets.
method Multilinear common component analysis (MCCA) using Kronecker products of mode-wise covariance matrices.
result MCCA constructs a common basis that retains information from multiple tensor datasets.
New methods use Kronecker-factored approximations for faster deep learning optimization.
problem Optimizing deep learning models with rich curvature information.
method Approximate Hessian using Kronecker products for efficient quasi-Newton methods.
result New methods outperform first-order methods and perform comparably to second-order methods.
SINGD improves KFAC for memory-efficiency and stability in low-precision training.
problem Memory inefficiency and numerical instability of KFAC in low-precision training.
method Formulated inverse-free KFAC update and imposed structures in Kronecker factors.
result SINGD is memory-efficient and numerically robust, often outperforming AdamW in half precision.
New methods estimate covariance for matrix data without assuming fixed size or specific distributions.
problem Estimating covariance for high-dimensional matrix data without distributional assumptions.
method Unified framework for bandable covariance estimation with rank one approximation, robust to heavy-tailed data.
result Proposed estimators are rate-optimal and perform well in simulations and real applications.
Second-order optimization methods such as natural gradient descent have the potential to speed up training of neural networks by correcting for the curvature of the loss function. Unfortunately, the exact natural gradient is impractical to compute for large models, and most approximations either require an expensive it…
Efficiently models learning curves using Gaussian processes with latent Kronecker structure.
problem Joint modeling of machine learning model performance across hyper-parameters and training progress.
method Imposes latent Kronecker structure to leverage efficient product kernels and handle missing values.
result Matches the performance of a Transformer on a learning curve prediction task.
KrADagrad: Kronecker Approximation-Domination Gradient Preconditioned Stochastic Optimizationstat.ML
A new optimization method reduces memory and compute requirements for deep learning.
problem Memory and compute constraints in second-order stochastic optimizers for deep learning.
method Proposes KrAD, a novel factorization to approximate inverse Fisher matrix without inversion, leading to KrADagrad.
result Improves performance over Shampoo for 32-bit precision and comparable/generalization on real datasets.
A new iterative K-FAC algorithm reduces training time and memory usage.
problem Training deep learning models efficiently.
method Uses conjugate gradient to approximate Fisher information matrix without generating the matrix or factors.
result Time and memory complexity of iterative CG-FAC is less than standard K-FAC.
Shampoo optimizes preconditioners for faster convergence in machine learning.
problem Improving convergence speed in machine learning optimization.
method Explicit connection between Shampoo's Kronecker product approximation and optimal matrix approximations.
result The square of Shampoo's approximation is equivalent to a single power iteration step for optimal Kronecker product approximation.
We introduce the Kronecker factored online Laplace approximation for overcoming catastrophic forgetting in neural networks. The method is grounded in a Bayesian online learning framework, where we recursively approximate the posterior after every task with a Gaussian, leading to a quadratic penalty on changes to the we…
Develops efficient quasi-Newton methods for training deep neural networks.
problem Training deep neural networks with large-scale Hessian matrices.
method Approximates Hessian as block-diagonal Kronecker product of smaller matrices, applies damping.
result Outperforms or matches state-of-the-art methods in autoencoder models.
This paper investigates Shampoo's heuristics and decouples preconditioner updates.
problem Improving Shampoo's heuristics for training neural networks.
method Decomposing preconditioner updates, correcting eigenvalues, and adapting eigenbasis computation frequency.
result Principled techniques to remove Shampoo's heuristics and improve training algorithms.
Improved continual learning for neural networks with BN layers using K-FAC extension.
problem Continual learning challenges in neural networks with BN layers.
method Extended K-FAC method to account for inter-example relations, weight merging, and reparameterization for BN layers; proposed weight merging and reparameterization for BN layers; proposed method to select hyperparameters without source task data.
result Better performance in continual learning tasks with BN layers compared to baselines.
A Kronecker product model is the set of visible marginal probability distributions of an exponential family whose sufficient statistics matrix factorizes as a Kronecker product of two matrices, one for the visible variables and one for the hidden variables. We estimate the dimension of these models by the maximum rank …
This paper improves compression of large NLP models using doped Kronecker Products.
problem Accuracy loss when compressing large NLP tasks with Kronecker Products.
method Doping Kronecker Products with an overlay matrix to recover accuracy, and a new regularization scheme called co matrix dropout regularization (CMR).
result Compression of a large language model with LSTM layers of size 25 MB by 25x with 1.4% loss in perplexity score.
Extends multivariate regression for tensor-variate data, identifying brain regions and facial characteristics.
problem Challenges in fitting regression models with multivariate responses and covariates.
method Low-rank tensor formats on regression coefficients and tensor-variate normal distribution for errors.
result Maximum likelihood estimators for tensor-on-tensor regression via block-relaxation algorithms.
Improved neural network inference with eigenvalue correction.
problem Inference of flexible variational posteriors is computationally expensive.
method Eigenvalue correction to matrix-variate Gaussian posterior.
result Empirically, the method outperforms existing algorithms.
This paper speeds up K-FAC for deep learning by focusing on only a few eigen-modes.
problem Time-consuming computation of Kronecker factors in K-FAC for large layers.
method Theoretical analysis and randomized numerical linear algebra to approximate eigen-spectrum decay.
result Reduces time complexity from cubic to quadratic in layer width, improving efficiency.
We propose an efficient method for approximating natural gradient descent in neural networks which we call Kronecker-Factored Approximate Curvature (K-FAC). K-FAC is based on an efficiently invertible approximation of a neural network's Fisher information matrix which is neither diagonal nor low-rank, and in some cases…
This paper compresses RNNs for IoT devices by 15-38x using Kronecker products.
problem Resource constraints on IoT devices make RNNs difficult to deploy.
method Kronecker product (KP) for compressing RNN layers by 15-38x with minimal accuracy loss.
result Kronecker product can compress RNNs by 50x when quantized to 8-bits.
Improved GCRF model for multi-scale networks with reduced computation time.
problem Scaling issues in GCRF for large networks.
method Factor graph decomposition using Kronecker product, new Laplacian eigenvalue estimations.
result High prediction accuracy with improved computational complexity.
K-FAC speeds up training of modern neural networks with linear weight-sharing.
problem Efficiently training modern neural networks with linear weight-sharing layers.
method Kronecker-Factored Approximate Curvature (K-FAC) applied to linear weight-sharing layers.
result K-FAC-reduce is generally faster than K-FAC-expand for deep linear networks.
Enhances Deep Hedging with K-FAC for financial data.
problem High computational burden in training neural networks for financial applications.
method Integrates Kronecker-Factored Approximate Curvature (K-FAC) optimization with LSTM networks.
result Significant improvements in convergence and hedging efficacy, reducing transaction costs and P&L variance.
Researchers solve the realization of Jordan-Kronecker invariants in Lie algebras.
problem Identifying which Jordan-Kronecker invariants can be realized by Lie algebras.
method Analyzing the Kronecker and Jordan cases, proving impossibility for certain invariants, and describing realizability for others.
result Complete solution for Jordan and Kronecker cases, partial answers for others.
New methods improve Fisher Matrix approximations for neural networks at low cost.
problem High cost of solving Fisher Information Matrix (FIM) in neural networks.
method Direct minimization via Kronecker product singular value decomposition.
result Improved approximations to FIM provide more accurate and faster optimization.
Jointly models cause-of-death mortality rates across multiple countries and genders.
problem Modeling cause-of-death mortality rates in a multinational setting.
method Multi-Output Gaussian Processes (MOGP) with Kronecker-structured kernels and latent factors.
result Efficiently captures heterogeneity and dependence across different factor inputs.
We introduce a framework and early results for massively scalable Gaussian processes (MSGP), significantly extending the KISS-GP approach of Wilson and Nickisch (2015). The MSGP framework enables the use of Gaussian processes (GPs) on billions of datapoints, without requiring distributed inference, or severe assumption…
Despite all the impressive advances of recurrent neural networks, sequential data is still in need of better modelling. Truncated backpropagation through time (TBPTT), the learning algorithm most widely used in practice, suffers from the truncation bias, which drastically limits its ability to learn long-term dependenc…
Paper compresses RNNs for resource-constrained devices.
problem Difficulty deploying RNNs on resource-constrained devices.
method Uses Kronecker product (KP) to compress RNN layers.
result KP compresses RNN layers by 16-38x with minimal accuracy loss.
Study on rotational hypersurfaces with constant Gauss-Kronecker curvature.
problem Exploring hypersurfaces with constant Gauss-Kronecker curvature.
method Solving ODE for generating curves and analyzing geometric properties.
result Discovery of non-compact rotational hypersurfaces with negative Gauss-Kronecker curvature and finite volume.
Sketchy reduces memory and compute requirements for adaptive regularization in deep learning.
problem Prohibitive memory and running time for adaptive regularization methods in deep learning.
method Low-rank sketching approach using Frequent Directions (FD) to reduce memory and compute requirements.
result Efficient interpolation between resource requirements and degradation in regret guarantees with rank .
Machine learning predicts Kronecker coefficients with high accuracy.
problem Predicting Kronecker coefficients from tensor products of symmetric group representations.
method Training machine learning models (NN, CNN, GBDT) to classify Kronecker coefficients as zero or non-zero.
result Trained models achieve high accuracy () in classifying Kronecker coefficients.
SyGlasso models tensor data dependencies using Sylvester equations.
problem Capturing multiway dependencies in tensor-valued data.
method Based on Sylvester equation, uses nodewise regression for estimation.
result Demonstrates simultaneous estimation of brain connectivity and temporal dependencies.