We propose an efficient algorithm for solving orthogonal canonical correlation analysis (OCCA) in the form of trace-fractional structure and orthogonal linear projections. Even though orthogonality has been widely used and proved to be a useful criterion for pattern recognition and feature extraction, existing methods …
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
168,742 papers · 148 categories
Trend · papers per month
48 results for “orthogonal iteration”
New method for curve comparison using iterated integrals and moving frames.
problem Comparing curves robustly to noise and transformations.
method Moving frame method paired with log-signature transform.
result Algorithmic construction of invariants for curve equivalence under rigid motions.
AuON is a linear-time optimizer that improves upon Muon's performance without approximate orthogonal matrices.
problem High memory and computational costs of orthogonal momentum updates.
method AuON uses normalized nonlinear scaling and a 'emergency brake' to handle exploding attention logits.
result AuON achieves strong performance without approximate orthogonal matrices, preserving structural alignment and reconditioning.
Study optimizes estimation of orthogonal and rotation matrices from noisy data.
problem Estimating orthogonal and rotation matrices from noisy data.
method Iterative polar decomposition algorithm initialized by spectral methods.
result Algorithm achieves optimal error rate of $(1+o(1)) rac{σ^2 d(d-1)}{2np}$.
We consider the problem of sampling from posterior distributions for Bayesian models where some parameters are restricted to be orthogonal matrices. Such matrices are sometimes used in neural networks models for reasons of regularization and stabilization of training procedures, and also can parameterize matrices of bo…
Predictive models are increasingly deployed for the purpose of determining access to services such as credit, insurance, and employment. Despite potential gains in productivity and efficiency, several potential problems have yet to be addressed, particularly the potential for unintentional discrimination. We present an…
Novel tensor perturbation bounds for orthogonal iteration methods.
problem Developing robust bounds for tensor reconstruction and subspace estimation.
method Blockwise tensor perturbation bounds for high-order orthogonal iteration (HOOI).
result Upper bounds for singular subspace estimation converge linearly and tensor reconstruction error bound is characterized by a simple quantity.
A Support-Set Algorithm for Optimization Problems with Nonnegative and Orthogonal Constraintsmath.OC
An algorithm simplifies optimization with nonnegative and orthogonal constraints.
problem Optimization problems with nonnegative and orthogonal constraints.
method Support-set algorithm exploiting structural sparsity.
result Global convergence to first-order stationary point with iteration complexity .
New algorithms improve tensor CP decomposition under mild conditions.
problem Improving tensor CP decomposition with theoretical guarantees under mild incoherence conditions.
method Composite PCA and Concurrent Orthogonalization algorithms.
result Theoretical guarantees and practical superiority over existing methods.
DFSOS improves sparse discriminant analysis for high-dimensional data.
problem Sparse discriminant analysis in high-dimensional settings with feature selection.
method Deflation-Free Sparse Optimal Scoring (DFSOS) using Bregman iteration and orthogonality-constrained optimization.
result DFSOS achieves comparable or better classification accuracy than deflation-based methods.
NS-RGS improves orthogonal group synchronization with faster convergence.
problem Orthogonal group synchronization from pairwise measurements.
method Newton-Schulz iteration for Riemannian gradient optimization.
result NS-RGS achieves linear convergence and near-optimal accuracy.
Batch normalization makes deep neural networks' representations increasingly orthogonal.
problem Orthogonality of deep neural network representations.
method Random linear transformations in successive batch-normalizations.
result Orthogonality of representations improves SGD performance.
New algorithms reduce orthogonality constraint enforcement time in machine learning.
problem Efficiently solving orthogonality constraints in machine learning.
method Extending the landing algorithm to Stiefel manifold, incorporating stochastic and variance reduction techniques.
result All proposed methods achieve the same convergence rate as Riemannian counterparts enforcing constraints.
Multi-Rank Sparse and Functional PCA: Manifold Optimization and Iterative Deflation Techniquesstat.ML
We consider the problem of estimating multiple principal components using the recently-proposed Sparse and Functional Principal Components Analysis (SFPCA) estimator. We first propose an extension of SFPCA which estimates several principal components simultaneously using manifold optimization techniques to enforce orth…
Muon optimizer simplifies matrix optimization with spectral orthogonalization.
problem Matrix optimization challenges, especially with large condition numbers.
method Simplified Muon optimizer using spectral orthogonalization of gradients.
result Simplified Muon converges linearly with independent scalar sequences, outperforming gradient descent and Adam.
Effective features can improve the performance of a model, which can thus help us understand the characteristics and underlying structure of complex data. Previous feature selection methods usually cannot keep more local structure information. To address the defects previously mentioned, we propose a novel supervised o…
Study uses random matrix theory to improve tensor approximation accuracy.
problem Improving tensor approximation accuracy in the presence of noise.
method Random matrix theory applied to tensor unfoldings.
result Characterizes spectral behavior of tensor unfoldings and predicts reconstruction performance.
Guaranteed Simultaneous Asymmetric Tensor Decomposition via Orthogonalized Alternating Least Squaresstat.ML
Tensor CANDECOMP/PARAFAC (CP) decomposition is an important tool that solves a wide class of machine learning problems. Existing popular approaches recover components one by one, not necessarily in the order of larger components first. Recently developed simultaneous power method obtains only a high probability recover…
New method for robust policy evaluation in offline reinforcement learning with sequentially exogenous unobserved confounders.
problem Offline reinforcement learning in domains with unobserved confounders.
method Orthogonalized robust fitted-Q-iteration with closed-form solutions and bias-correction.
result Effective in simulations and real-world data, improving robustness and computational ease.
New algorithm for signal estimation in noisy matrix models.
problem Signal estimation in rectangular spiked matrix models with rotationally invariant noise.
method Orthogonal Approximate Message Passing (OAMP) algorithm for signal estimation.
result Optimal OAMP algorithm minimizes mean-squared error and achieves Bayes-optimal performance.
Unified framework for multi-view learning with orthogonal projections.
problem Learning individual orthogonal projections for multiple views.
method Successive approximations via eigenvectors, iterative Krylov subspace method.
result Consistently competitive and often better than existing methods.
Study spectral learning for odeco tensors, addressing initialization bottlenecks.
problem Recovering orthogonally decomposable tensors under noise.
method Investigates perturbation bounds, non-convex optimization, and initialization strategies.
result Initialization is the main bottleneck for efficient algorithms.
The paper approximates financial derivatives using neural networks and iterated integrals.
problem Approximating -integrable financial derivatives.
method Using iterated Stratonovich integrals and neural networks.
result Approximate solutions to the -hedging problem.
A new algorithm avoids retractions to optimize orthogonal matrices efficiently.
problem Optimizing functions over the manifold of orthogonal matrices efficiently.
method Landing algorithm that avoids retractions using potential energy.
result The landing algorithm is faster and less prone to numerical errors than retraction-based methods.
We consider the Orthogonal Least-Squares (OLS) algorithm for the recovery of a -dimensional -sparse signal from a low number of noisy linear measurements. The Exact Recovery Condition (ERC) in bounded noisy scenario is established for OLS under certain condition on nonzero elements of the signal. The new result a…
Orthogonalization of data via Gromov-Wasserstein type feedback for clustering and visualizationstat.ML
Adaptive orthogonalization of data for clustering and visualization.
problem Clustering and visualization of data with high specificity.
method Adaptive orthogonalization process using Gromov-Wasserstein feedback.
result Method refines orthogonality of data to achieve high specificity clustering.
Efficient Optimization with Orthogonality Constraint: a Randomized Riemannian Submanifold Methodmath.OC
A new method reduces complexity for optimizing large-scale problems with orthogonality constraints.
problem Optimizing large-scale problems with orthogonality constraints.
method Randomized Riemannian submanifold method that restricts updates to random submanifolds.
result Significantly reduces per-iteration complexity for large-scale problems.
New algorithm finds sparse matrices on Stiefel manifold for optimisation.
problem Finding sparse matrices on Stiefel manifold for optimisation.
method Modified Orthogonal Iteration algorithm for sparse global optimality.
result Proposed method finds globally optimal sparse Stiefel matrices.
Sparse Subspace Clustering (SSC) is one of the most popular methods for clustering data points into their underlying subspaces. However, SSC may suffer from heavy computational burden. Orthogonal Matching Pursuit applied on SSC accelerates the computation but the trade-off is the loss of clustering accuracy. In this pa…
Optimal spectral estimators and AMP combine for efficient weak recovery in orthogonally invariant GLMs.
problem Parameter estimation from generalized linear models with complex correlation structures.
method Spectral initialization and approximate message passing (AMP) algorithm.
result Established rigorous performance guarantees for spectral initialization and AMP.
Orthogonal Matching Pursuit (OMP) has long been considered a powerful heuristic for attacking compressive sensing problems; however, its theoretical development is, unfortunately, somewhat lacking. This paper presents an improved Restricted Isometry Property (RIP) based performance guarantee for T-sparse signal reconst…
New method solves sparse PCA for multiple components efficiently.
problem Sparse PCA for multiple orthogonal components.
method Reformulates orthogonality as rank constraints, uses semidefinite relaxations and bounds.
result Exact solutions with near-optimal variance explained and orthogonality.
In this paper, we consider the problem of compressed sensing where the goal is to recover almost all the sparse vectors using a small number of fixed linear measurements. For this problem, we propose a novel partial hard-thresholding operator that leads to a general family of iterative algorithms. While one extreme of …
EigenVI uses orthogonal function expansions for efficient variational inference.
problem Efficiently approximate complex distributions in variational inference.
method EigenVI constructs variational approximations using orthogonal function expansions, minimizing Fisher divergence.
result EigenVI provides more accurate approximations than existing methods for Gaussian BBVI.
New method speeds up solving orthogonality constrained problems.
problem Solving orthogonality constrained problems efficiently.
method Riemannian optimization and Riemannian preconditioning.
result Preconditioning improves computational costs and convergence.
A Double Tracking Method for Optimization with Decentralized Generalized Orthogonality Constraintsmath.OC
New algorithm tackles optimization with distributed constraints.
problem Optimization problems with generalized orthogonality constraints in a decentralized setting.
method Introduced a novel algorithm that tracks gradients and Jacobians simultaneously.
result Global convergence with an iteration complexity established.
In this paper, we propose an efficient and scalable low rank matrix completion algorithm. The key idea is to extend orthogonal matching pursuit method from the vector case to the matrix case. We further propose an economic version of our algorithm by introducing a novel weight updating rule to reduce the time and stora…
A new method solves optimization problems on the generalized Stiefel manifold using random estimates of B.
problem Optimization over the generalized Stiefel manifold in applications like CCA, ICA, and GEVP.
method Cheap stochastic iterative method that converges to critical points on the manifold.
result The method achieves the same convergence rates as Riemannian optimization but with lower per-iteration cost.
New method for sampling on constrained domains using orthogonal-space gradient flow.
problem Sampling on manifolds defined by constraints is challenging.
method Orthogonal-Space Variational Gradient Descent (O-Gradient)
result O-Gradient converges to the target constrained distribution efficiently.
Duality of subanalytic setsmath.DG
We study the link between a compact hypersurface in and the set of all its tangent planes. In this context, we identify to the set of linear subspaces of codimension one by orthogonal complementarity. This gives rise to a kind of duality which has already been studied Bruce and Romerro-Fuster, and r…
ParK efficiently solves kernel ridge regression for large datasets.
problem Large-scale kernel ridge regression efficiency and accuracy.
method Partitioning feature space with random projections and iterative optimization.
result Provably maintains statistical accuracy with reduced space and time complexity.
SINF models transform arbitrary PDFs to target PDFs using 1D slices.
problem Transforming arbitrary probability distributions to target distributions efficiently.
method Iterative Optimal Transport of 1D slices, maximizing Wasserstein distance.
result SINF models generate high-quality samples and competitive density estimates.
A new algorithm reduces communication in distributed SVD by factors.
problem Efficiently compute SVD in distributed systems.
method LocalPower algorithm with weighted aggregation and periodic decay of iterations.
result Reduces communication cost by a factor of .
A new gradient boosting method improves interpretability of probabilistic models.
problem Learning interpretable yet accurate probabilistic models with limited rule complexity.
method A new objective function that measures the angle between risk gradient and condition output vector projection.
result Significantly improves comprehensibility/accuracy trade-off of fitted ensemble.
This paper considers the fundamental problem of learning a complete (orthogonal) dictionary from samples of sparsely generated signals. Most existing methods solve the dictionary (and sparse representations) based on heuristic algorithms, usually without theoretical guarantees for either optimality or complexity. The r…
CP-factorization for high-dimensional tensor time series and double projection iterations
problem Identifying and estimating factor loadings in CP decomposition for high-dimensional tensor time series
method One-pass estimation procedure using standard eigen-analysis for matrix constructed based on serial dependence
result Asymptotic properties established under general settings, adapt to sparsity, accommodates weak factors
We propose a novel application of the Simultaneous Orthogonal Matching Pursuit (S-OMP) procedure for sparsistant variable selection in ultra-high dimensional multi-task regression problems. Screening of variables, as introduced in \cite{fan08sis}, is an efficient and highly scalable way to remove many irrelevant variab…
Multivariate Analysis (MVA) comprises a family of well-known methods for feature extraction that exploit correlations among input variables of the data representation. One important property that is enjoyed by most such methods is uncorrelation among the extracted features. Recently, regularized versions of MVA methods…