Paper improves Monte Carlo sampling with new theoretical insights and methods.
problem Improving Monte Carlo sampling for variance reduction.
method Theoretical analysis of negatively dependent random variables and novel extensions using number theory and particle algorithms.
result Near-Orthogonal Monte Carlo (NOMC) consistently outperforms Orthogonal Monte Carlo (OMC) in various applications.
VRSGT algorithm reduces orthogonality constraints in decentralized optimization.
problem Decentralized optimization with orthogonality constraints.
method VRSGT algorithm with variance reduction and orthogonal techniques.
result VRSGT achieves convergence rate of O(1 / k) for orthogonality constraints.
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…
SpecNet2 improves spectral embedding without orthogonalization, achieving better performance and efficiency.
problem Improving spectral embedding methods for better performance and efficiency.
method Optimizes an equivalent objective of the eigen-problem without orthogonalization, allowing separate row and column sampling.
result Local and global convergence of the new objective using batch-based gradient descent is proven, and improved performance and efficiency are demonstrated on simulated and image datasets.
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.
A new method reduces bootstrap simulation cost and improves accuracy.
problem Efficiently simulating input uncertainty with large sample sizes.
method Orthogonal Bootstrap: Decomposes into Infinitesimal Jackknife and orthogonal parts.
result Significantly reduces computational cost and maintains accuracy.
OOMP selects features online for sparse linear regression.
problem Feature selection in high-dimensional sparse linear models.
method Online algorithm that alternates between feature selection and coefficient estimation.
result Theoretical guarantees and computational complexity analysis of OOMP.
New LT-O-learners improve HLTE estimation with low overlap.
problem Challenges in estimating heterogeneous long-term treatment effects due to limited overlap.
method Introduces LT-O-learners that use custom overlap weights to downweight low-overlap samples.
result LT-O-learners provide robust HLTE estimates with lower variance in low-overlap regimes.
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.
New algorithm identifies best arm in semiparametric bandits with near optimal efficiency.
problem Fixed-confidence Best Arm Identification in semiparametric bandits with unknown baseline shift.
method Phase-elimination algorithm based on orthogonalized regression design.
result Nearly optimal high-probability sample-complexity upper bound established.
This work improves SGD minibatch sampling using determinantal point processes based on orthogonal polynomials.
problem Improving variance reduction in stochastic gradient descent (SGD) for large datasets.
method Orthogonal polynomial-based determinantal point processes for sampling minibatches in SGD.
result DPP minibatches lead to a smaller mean square approximation error than uniform minibatches.
Paper improves feature selection accuracy using transfer learning.
problem Improving feature selection accuracy in information criteria-based methods.
method Proposes TLCp, a transfer learning procedure based on Mallows' Cp.
result TLCp outperforms conventional Cp in accuracy and stability.
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.
Wasserstein distances are increasingly used in a wide variety of applications in machine learning. Sliced Wasserstein distances form an important subclass which may be estimated efficiently through one-dimensional sorting operations. In this paper, we propose a new variant of sliced Wasserstein distance, study the use …
Study shows RFRR's effectiveness with nearly orthogonal data in overparameterized settings.
problem Understanding the effectiveness of random feature regression with nearly orthogonal data.
method Investigates RFRR with nearly orthogonal deterministic unit-length input data vectors in the overparameterized regime.
result Shows high-probability non-asymptotic concentration results for RFRR's training, cross-validation, and generalization errors.
A common method of generalizing binary to multi-class classification is the error correcting code (ECC). ECCs may be optimized in a number of ways, for instance by making them orthogonal. Here we test two types of orthogonal ECCs on seven different datasets using three types of binary classifier and compare them with t…
TreeHFD algorithm explains tree ensemble models through hierarchical orthogonality.
problem Difficulty in explaining black-box tree ensemble models.
method TreeHFD algorithm using hierarchical orthogonality constraints.
result TreeHFD estimates Hoeffding decomposition from data samples.
A new method tests Expected Shortfall by analyzing both duration and severity of VaR violations.
problem Lack of separate testing for frequency and severity in ES backtesting.
method Uses bivariate orthogonal polynomials to derive moment conditions for durations and severities.
result Proposes a Wald test for identifying mis-specified components in ES models.
P-OCS detects OOD samples in a low-dimensional subspace, outperforming existing methods.
problem Efficient OOD detection for deep learning models in open-world environments.
method P-OCS operates in the orthogonal complement of the principal subspace, applying a single projected perturbation.
result P-OCS achieves state-of-the-art OOD detection with negligible computational cost and without requiring model retraining.
We study the distribution of the adaptive LASSO estimator (Zou (2006)) in finite samples as well as in the large-sample limit. The large-sample distributions are derived both for the case where the adaptive LASSO estimator is tuned to perform conservative model selection as well as for the case where the tuning results…
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…
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.
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.
In this paper we derive a series expansion for the price of a continuously sampled arithmetic Asian option in the Black-Scholes setting. The expansion is based on polynomials that are orthogonal with respect to the log-normal distribution. All terms in the series are fully explicit and no numerical integration nor any …
The study reveals how adversarial perturbations can include class features for generalization.
problem Understanding why adversarial examples deceive neural networks and transfer between networks.
method A one-hidden-layer network trained on mutually orthogonal samples.
result Adversarial perturbations, even of a few pixels, contain sufficient class features for generalization.
We study the problem of inferring a sparse vector from random linear combinations of its components. We propose the Accelerated Orthogonal Least-Squares (AOLS) algorithm that improves performance of the well-known Orthogonal Least-Squares (OLS) algorithm while requiring significantly lower computational costs. While OL…
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…
Bayesian method maps high-dimensional inputs to lower dimensions for efficient multi-fidelity Gaussian Process modeling.
problem Efficiently modeling high-dimensional inputs with low-dimensional latent variables for multi-fidelity Gaussian Processes.
method Bayesian approach with orthonormal projection matrix inference using Markov Chain Monte Carlo (MCMC) and Geodesic Monte Carlo sampling.
result Optimal transformations identified that improve computational efficiency in multi-fidelity Gaussian Process modeling.
The paper develops methods for causal function estimation and inference with multiway clustered data.
problem Estimation and inference for causal functions under multiway clustering.
method Two-step procedure using machine learning for nuisance parameters and projection onto basis functions.
result Rejects the null hypothesis of uniformly zero effects and reveals heterogeneous treatment effects.
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…
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.
The paper proposes a new model for predicting and analyzing economic variables.
problem Predicting and analyzing economic variables in developed regions.
method Time-varying parameter global vector autoregressive (TVP-GVAR) framework combined with machine learning models.
result The proposed model provides high precision out-of-sample predictions and novel insights into economic variable connectedness.
Convolutional nets require fewer samples than fully-connected nets for image classification.
problem Understanding why convolutional nets are more sample-efficient than fully-connected nets.
method Construction of a natural distribution and target function to demonstrate a sample complexity gap.
result Convolutional nets require O(1) samples for a single target function, while fully-connected nets require Ω(d2) samples. The study examines how shallow neural nets converge to training samples or manifold points during diffusion.
problem Understanding when and how shallow neural nets converge to training samples or manifold points during diffusion.
method Analysis of shallow ReLU neural network denoisers trained with minimal ℓ2 norm, comparing score flow and diffusion flow. result Probability flow converges to training points, sums of training points, or manifold points, depending on the diffusion time scheduler.
The paper develops methods to estimate treatment effects in sample selection models.
problem Evaluation of treatments when outcomes are only observed for a subpopulation due to sample selection or attrition.
method Combines selection-on-observables and instrumental variable assumptions with double machine learning for treatment evaluation.
result Proposed estimators are asymptotically normal and root-n consistent.
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.
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.
This paper considers the recovery of a rank r positive semidefinite matrix XXT∈Rn×n from m scalar measurements of the form yi:=aiTXXTai (i.e., quadratic measurements of X). Such problems arise in a variety of applications, including covariance sketching of high-dimensional data…
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.
GOPO optimizes large models in Hilbert space, avoiding Kullback-Leibler's curvature.
problem Optimizing large language models with Kullback-Leibler divergence's curvature issues.
method GOPO uses Hilbert space L2(pi_k) with orthogonality constraints and a work-dissipation functional.
result GOPO achieves competitive generalization with stable gradient dynamics and entropy preservation.
New findings on Kähler manifolds restrict orthogonal coordinates existence.
problem Existence of orthogonal coordinates on Kähler manifolds.
method Algebraic and geometric techniques applied to Kähler manifolds.
result No nontrivial self-dual Kähler 4-manifolds or Ricci-flat Kähler 4-manifolds support orthogonal coordinates.
Efficient diffusion model for symmetric manifolds reduces training and computation costs.
problem Heat kernel computations for manifold diffusion models are computationally expensive and infeasible.
method Spatially-varying covariance diffusion model, efficient objective derived via Ito's Lemma.
result Our model reduces training time and arithmetic operations by orders of magnitude.
Constructs orthogonal coordinates in curved spaces.
problem Separating variables in curved spaces.
method Explicit construction of orthogonal coordinates and transformations.
result Explicit formulas for Killing tensors and Stäckel matrices.
OPT framework improves neural network generalization by learning an orthogonal transformation.
problem Improving neural network generalization.
method Orthogonal over-parameterized training (OPT) framework that minimizes hyperspherical energy.
result OPT framework provably minimizes hyperspherical energy and improves empirical generalization.
The paper studies surfaces in a bounded domain with orthogonal boundaries and proves curvature estimates.
problem Estimating the area of surfaces with orthogonal boundaries in a bounded domain.
method Weak formulation of orthogonality for curvature varifolds, classification of vanishing curvature varifolds.
result Existence of an orthogonal 2-varifold that minimizes L2 curvature in the integer rectifiable class. Paper proposes a KGE framework that reduces training time and carbon footprint.
problem Efficient KGE learning with reduced computational cost and environmental impact.
method Full batch learning, Orthogonal Procrustes Analysis, non-negative-sampling training.
result Significant reduction in training time and carbon footprint compared to state-of-the-art approaches.
Orthogonal random features approximate a Bessel kernel, offering sharper bounds than random Fourier features.
problem Approximating Gaussian kernel efficiently for large datasets.
method Use of Haar orthogonal matrices to construct orthogonal random features and analyze their bias and variance.
result Orthogonal random features approximate a Bessel kernel, not the Gaussian kernel, with sharper bounds.
We consider two stage estimation with a non-parametric first stage and a generalized method of moments second stage, in a simpler setting than (Chernozhukov et al. 2016). We give an alternative proof of the theorem given in (Chernozhukov et al. 2016) that orthogonal second stage moments, sample splitting and n1/4-…