Improves statistical learning bounds with self-concordant losses.
problem Statistical prediction with nuisance components.
method Orthogonal statistical learning with self-concordant loss.
result Non-asymptotic bounds on excess risk improved by a dimension factor.
New convergence guarantees for learning with unknown nuisance parameters.
problem Learning problems with unknown nuisance parameters.
method Stochastic gradient optimization with Neyman orthogonality and approximately orthogonalized updates.
result Stochastic gradient algorithms can converge under conditions of nuisance parameters.
Novel prior for orthogonal functions improves functional component estimation.
problem Improving orthogonality in functional principal component analysis.
method Sequential adaptive priors for orthogonal functions using hierarchical conditionally normal distributions.
result Proposed prior leads to nearly orthogonal posterior estimates.
Decomposing tensors into orthogonal factors is a well-known task in statistics, machine learning, and signal processing. We study orthogonal outer product decompositions where the factors in the summands in the decomposition are required to be orthogonal across summands, by relating this orthogonal decomposition to the…
Equivalent tests for SGD batch size selection found.
problem Finding equivalent tests for adaptive batch size selection in SGD.
method Norm and inner product/orthogonality tests equivalence demonstration.
result Norm and inner product/orthogonality tests are equivalent under specific conditions.
Orthogonal matching pursuit (OMP) is a widely used algorithm for recovering sparse high dimensional vectors in linear regression models. The optimal performance of OMP requires \textit{a priori} knowledge of either the sparsity of regression vector or noise statistics. Both these statistics are rarely known \textit{a p…
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.
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 $(1+o(1)) rac{σ^2 d(d-1)}{2np}$.
Study removes bias from chest X-ray embeddings using orthogonalization.
problem Reduces bias in chest X-ray embeddings due to protected features.
method Orthogonalization technique to remove protected feature effects.
result Orthogonalization removes bias and makes predictions of protected attributes infeasible.
Improves model predictability by mixing forecasts and orthogonalizing models.
problem Redundant models contaminate model space and degrade predictive performance.
method Principal Component Analysis for model orthogonalization in Bayesian forecast mixing.
result Better prediction accuracy and excellent uncertainty quantification.
Many modern big data applications feature large scale in both numbers of responses and predictors. Better statistical efficiency and scientific insights can be enabled by understanding the large-scale response-predictor association network structures via layers of sparse latent factors ranked by importance. Yet sparsit…
This paper concerns dictionary learning, i.e., sparse coding, a fundamental representation learning problem. We show that a subgradient descent algorithm, with random initialization, can provably recover orthogonal dictionaries on a natural nonsmooth, nonconvex ℓ1 minimization formulation of the problem, under mi…
Study smooth linear statistics on random covers of hyperbolic surfaces, showing central limit and variance results.
problem Analyzing fluctuations and energy variance of random covers of compact hyperbolic surfaces.
method Examining fluctuations in a small energy window around a fixed energy level, considering the variance of a typical surface, using a double limit where n and L go to infinity. result Distribution of fluctuations tends to a Gaussian with variance of GOE/GUE, and energy variance of a typical random n-cover is that of GOE/GUE. Transformers learn to recall with non-orthogonal embeddings in realistic settings.
problem Understanding how transformers store and retrieve knowledge in practical scenarios.
method Analyzing a single-layer transformer with random embeddings trained on a token-retrieval task.
result Explicit formulas for the model's storage capacity reveal a multiplicative dependence on sample size, embedding dimension, and sequence length.
Proposes a new method for analyzing multimodal neuroimaging data.
problem Combining interpretability and flexibility in multimodal data analysis.
method Orthogonalized kernel debiased machine learning approach.
result Established consistency and asymptotic normality of the estimated primary parameter.
Revisits CP tensor decomposition for noisy, non-orthogonal data.
problem Statistical optimality and convergence of ALS in noisy, non-orthogonal, higher-rank settings.
method Statistical analysis and TASD method for initialization.
result ALS with TASD achieves optimal error in rank-one setting within one or two iterations.
Study finds Calabi-Yau models' operator spectra match random matrix theory.
problem Understanding spectra of Calabi-Yau sigma models.
method Numerical methods for Ricci-flat metrics, averaging over complex structure moduli space.
result Spectrum matches Gaussian orthogonal ensemble of random matrix theory.
Deterministic bounds for tensor singular values and vectors, differing from matrix cases.
problem Spectral learning of higher-order orthogonally decomposable tensors.
method Deterministic perturbation bounds for singular values and vectors of orthogonally decomposable tensors.
result Perturbation affects each essential singular value/vector in isolation, independent of multiplicity and distance from other singular values.
TGCCA analyzes higher-order tensors using orthogonal rank-R CP decomposition.
problem Handling higher-order structures in multi-block data analysis.
method Tensor Generalized Canonical Correlation Analysis (TGCCA) with orthogonal rank-R CP decomposition.
result TGCCA outperforms state-of-the-art methods on simulated and real data.
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.
ICCNLS models complex relationships as convex and concave components.
problem Complex input-output relationships with affine ambiguity.
method Sub-gradient constrained affine functions, global orthogonality constraints, L1, L2, and elastic net regularisation.
result Improved predictive accuracy and model simplicity compared to conventional methods.
Unified approach to tensor PCA and related problems using tensor cumulants.
problem Statistical inference on invariant distributions, particularly tensor PCA.
method Definition and analysis of tensor cumulants to unify and extend previous results.
result Unified explanation of hardness and subexponential-time algorithms for tensor PCA.
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.
This paper presents a unified geometric framework for the statistical analysis of a general ill-posed linear inverse model which includes as special cases noisy compressed sensing, sign vector recovery, trace regression, orthogonal matrix estimation, and noisy matrix completion. We propose computationally feasible conv…
OrthoGrad improves neural calibration by constraining gradient updates orthogonally.
problem Overconfidence in neural networks, leading to poor uncertainty estimates.
method Orthogonal gradient updates to optimize for decision boundaries and reduce overconfidence.
result Significant improvements in test loss, predictive entropy, and confidence measures.
Extends deep learning with interpretable additive models.
problem Identifiability issues between neural networks and additive models.
method Orthogonalization cell to separate deep neural network and structured model parts.
result Stable estimation and interpretability of structured model parts.
We propose the orthogonal random forest, an algorithm that combines Neyman-orthogonality to reduce sensitivity with respect to estimation error of nuisance parameters with generalized random forests (Athey et al., 2017)--a flexible non-parametric method for statistical estimation of conditional moment models using rand…
Information geometry offers new tools for statistical analysis.
problem Statistical analysis of probability distributions.
method Geometric perspective on statistical manifolds.
result New applications in radar sensing, signal processing, etc.
Unified analysis of multilabel Fisher discriminants with improved dimensionality and robustness.
problem Improving discriminant analysis for multilabel classification with enhanced dimensionality and robustness.
method Unified theoretical analysis of multilabel Fisher discriminants with algebraic and statistical guarantees.
result Unified characterization of multilabel Fisher objectives and their equivalence under orthogonality constraints.
Random Matrix Theory explains loss surface Hessians in neural networks.
problem Understanding the loss surfaces of neural networks.
method Investigation of local spectral statistics of neural network Hessians.
result Excellent agreement with Gaussian Orthogonal Ensemble statistics.
Unified analysis of multilabel Fisher discriminants with improved dimensionality and robustness.
problem Improving discriminant analysis for multilabel classification with enhanced dimensionality and robustness.
method Unified algebraic and statistical analysis of multilabel Fisher discriminants with Stiefel orthogonality constraints.
result Equivalence of four Fisher objectives under the Stiefel constraint and improved discriminant dimensionality.
A fast feature selection method using OLS and SOCC for classification.
problem Feature selection for linear classification.
method Orthogonal Least Squares (OLS) with Squared Orthogonal Correlation Coefficient (SOCC).
result The proposed method outperforms other feature selection methods in speed and accuracy.
IMA addresses non-identifiability in nonlinear ICA by assuming orthogonal Jacobian columns.
problem Non-identifiability in nonlinear ICA.
method IMA assumes orthogonal Jacobian columns and extends to manifold settings.
result IMA circumvents non-identifiability issues and can be beneficial for higher-dimensional observations.
The paper tackles learning symmetries in data without expert knowledge.
problem Learning symmetries in data from raw data without prior knowledge.
method Develops methods to select eigenvectors for orthogonal symmetries and compares their effectiveness.
result The problem of learning symmetries is as hard as the graph automorphism problem in the worst case, but can be simplified with certain restrictions.
This paper introduces SS-MAMP to address convergence issues in AMP algorithms.
problem Convergence issues in AMP algorithms for signal reconstruction.
method Proposes SS-MAMP algorithm framework for right-unitarily invariant sensing matrices and Lipschitz-continuous local processors.
result Covariance matrices of SS-MAMP are L-banded and convergent, ensuring optimal convergence.
New PHO formula improves SSNs performance.
problem Suboptimal network estimation and degenerated predictions in SSNs.
method Non-invasive post-hoc orthogonalization (PHO) to identify model components.
result Better estimation and prediction quality in SSNs.
Solves a fundamental problem in statistics and imaging with new methods.
problem Generalized Orthogonal Procrustes Problem (GOPP)
method Semidefinite relaxation (SDR) and generalized power method (GPM)
result GPM converges linearly to the global minimizer under large signal-to-noise ratio.
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.
The paper develops statistical inference methods for SHAP values.
problem Lack of statistical inference for SHAP values in model-agnostic feature importance.
method Semi-parametric approach using U-statistics and Neyman orthogonal scores for functionals of nested regressions.
result Asymptotically normal estimates of the pth powers of SHAP values for various p.
New CVs preserve transition rates in molecular dynamics.
problem Designing CVs that accurately capture rare events in high-dimensional systems.
method Integrating manifold learning and group-invariant featurization to construct neural network-based CVs that satisfy orthogonality conditions.
result Achieved a CV for butane that reproduces the anti-gauche transition rate with less than ten percent relative error.
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.
The study extends Jacobi-orthogonality to indefinite scalar product spaces.
problem Generalizing Jacobi-orthogonality to indefinite scalar product spaces.
method Comparing principles, investigating tensor relations, proving properties.
result Every quasi-Clifford tensor is Jacobi-orthogonal; certain tensors are Jacobi-dual or Osserman.
We provide non-asymptotic excess risk guarantees for statistical learning in a setting where the population risk with respect to which we evaluate the target parameter depends on an unknown nuisance parameter that must be estimated from data. We analyze a two-stage sample splitting meta-algorithm that takes as input ar…
Paper studies statistical manifolds with logarithmic divergences.
problem Understanding statistical manifolds induced by logarithmic divergences.
method Constructs dual foliation of the statistical manifold.
result Extends dual foliation of a dually flat manifold.
New characterization of Osserman tensors using Jacobi-orthogonality.
problem Characterizing Osserman tensors.
method Introducing Jacobi-orthogonality as a new potential characterization.
result Jacobi-orthogonal tensors are Osserman, and all known Osserman tensors are Jacobi-orthogonal.
Study isotropy groups for complex orthogonal and skew-symmetric matrices.
problem Understanding isotropy subgroups of orthogonal similarity transformations.
method Analysis of group structure of nonsingular block matrices.
result Group structure of isotropy subgroups related to block Toeplitz matrices.
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.
GRRT recovers sparse signals without prior sparsity or noise variance knowledge.
problem Recovering sparse signals without prior sparsity or noise variance knowledge.
method Generalized residual ratio thresholding (GRRT) for SOMP and BOMP.
result Finite sample and finite SNR guarantees for exact support recovery.