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.
Proposes FOAGP for efficient orthogonal effect decomposition of black-box computer experiments.
problem Challenges in sensitivity analysis of black-box computer experiments with complex, nonlinear functional outputs.
method Functional-output orthogonal additive Gaussian process (FOAGP) with conditional orthogonality constraint.
result Demonstrates effectiveness in orthogonal effect decomposition and variance decomposition through simulations and real-world application.
We study the Chern-Simons partition function of orthogonal quantum group invariants, and propose a new orthogonal Labastida-Mariño-Ooguri-Vafa conjecture as well as degree conjecture for free energy associated to the orthogonal Chern-Simons partition function. We prove the degree conjecture and some interesting cases o…
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.
Derives new orthogonal coordinates for evolving surfaces and curves.
problem Accounting for geometric effects in boundary layer asymptotics.
method Elementary derivation of orthogonal signed-distance coordinates.
result Provides vector calculus identities for these coordinates.
New algorithms learn sparse set functions in non-orthogonal Fourier bases.
problem Learning sparse set functions in non-orthogonal Fourier bases.
method Novel algorithms using non-orthogonal Fourier transforms.
result At most nk−klog2k+k queries for k non-zero Fourier coefficients. 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.
Paper links set derivatives to its orthogonal projections.
problem Understanding the relationship between set derivatives and projections.
method Derives equations from topological link between Minkowski functional partial derivatives and set boundary.
result System of equations for orthogonal projections derived.
New method relaxes PCA orthogonality constraints using explained variance of correlated components.
problem Difficulty in using PCA for sparse design due to orthogonality constraints and non-differentiable penalty.
method Introduce expvar(Y) to measure variance explained by correlated components, relax orthogonality constraints.
result Two expvar(Y) definitions suitable for block PCA formulations without orthogonality constraints.
The paper finds at least N orthogonal Finsler geodesic chords in a disk-like manifold.
problem Existence and multiplicity of orthogonal Finsler geodesic chords in a disk-like manifold.
method Study of Finsler geodesic chords under reversibility assumption.
result At least N orthogonal Finsler geodesic chords found in a disk-like manifold.
Based on the orthogonal Labastida-Mari{ñ}o-Ooguri-Vafa conjecture made by L. Chen & Q. Chen [5], we derive an infinite product formula for Chern-Simons partition functions, which generalizes the Liu-Peng's [19] recent results to the orthogonal case. Symmetry property of this new infinite product structure is also discu…
Semi-parametric framework for nonlinear system identification
problem Nonlinear system identification
method Orthogonal Gaussian process regression
result Interpretable models from incomplete physics
DONUT improves treatment effect estimation by enforcing orthogonality constraints.
problem Estimating treatment effects from observational data is challenging due to unobserved outcomes.
method DONUT uses a regularization framework that formalizes unconfoundedness as orthogonality, leading to deep orthogonal networks.
result DONUT outperforms state-of-the-art methods in estimating average treatment effects.
Paper shows CR Q-curvature orthogonal to CR pluriharmonic functions.
problem Understanding CR Q-curvature and pluriharmonic functions on CR manifolds. method Obtained a cohomological expression for the integral of CR Q-curvature and pluriharmonic functions. result CR Q-curvature is orthogonal to CR pluriharmonic functions. New method estimates and optimizes policy differences using orthogonal learning.
problem Offline reinforcement learning with safety concerns and cost limitations.
method Dynamic R-learner for estimating and optimizing Qπ(s,1)−Qπ(s,0), leveraging orthogonal estimation. result Consistent policy optimization with improved convergence rates.
Formula for Laplace-Beltrami on orthogonal group in Euclidean coords.
problem Computing Laplace-Beltrami on constrained submanifolds.
method Embedded gradient vector field method, explicit formula derivation.
result Explicit formula for Laplace-Beltrami on orthogonal group.
A machine learning method selects optimal orthonormal bases for functional data analysis.
problem Lack of formal criteria for choosing initial orthonormal bases in functional data methods.
method Proposes a machine learning algorithm to learn and place knots for efficient orthogonal spline bases (splinets).
result Demonstrates efficiency, especially for sparse functional data and complex physical systems.
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 argues for using Neyman orthogonal score for balancing in debiased machine learning.
problem Debiased machine learning requires a proper approach to balance covariates.
method The paper advocates for using Riesz regression with basis functions of X for balancing.
result Covariate balancing is only valid when the score-relevant regression error is a function of covariates alone.
Geodesic flows with diagonalisable integrals are orthogonal.
problem Understanding geodesic flows with specific integrals.
method Analyzing quadratic integrals for geodesic flows.
result Diagonalisable integrals imply orthogonal separation of variables.
Improved Gaussian process models for interpretable predictions.
problem Complex responses require high-dimensional interaction terms in additive Gaussian processes.
method Orthogonal additive kernel (OAK) with orthogonality constraint on additive functions.
result OAK models achieve similar or better predictive performance with fewer terms, retaining interpretability.
The paper solves PDEs from matrices with orthogonal columns, linking them to Hessian metrics and symmetric spaces.
problem Solving third order PDEs for strictly convex smooth functions.
method Geometric methods using Hessian metrics and symmetric spaces.
result Explicit solutions and a family of non-generic solutions with applications in Poisson geometry and Kahler structures.
We show how Ramond free neutral Fermi fields lead to a τ-function theory of BKP type which describes iso-orthogonal deformations of systems of ortogonal curvilinear coordinates. We also provide a vertex operator representation for the classical Ribaucour transformation.
The theory of slice regular functions of a quaternion variable is applied to the study of orthogonal complex structures on domains Ω of R^4. When Ω is a symmetric slice domain, the twistor transform of such a function is a holomorphic curve in the Klein quadric. The case in which Ω is the complement of a parabola is st…
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 l1-norm penalized orthogonal forward regression (l1-POFR) algorithm is proposed based on the concept of leaveone- out mean square error (LOOMSE). Firstly, a new l1-norm penalized cost function is defined in the constructed orthogonal space, and each orthogonal basis is associated with an individually tunable regulari…
New differential geometry perspective on orthogonal RNNs.
problem Mitigating exploding and vanishing gradients in RNNs.
method Using tools from differential geometry, parameterizing vector fields via directional derivatives of scalar functions.
result Our approach achieves comparable or better results on benchmark tasks.
The use of orthogonal projections on high-dimensional input and target data in learning frameworks is studied. First, we investigate the relations between two standard objectives in dimension reduction, preservation of variance and of pairwise relative distances. Investigations of their asymptotic correlation as well a…
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.
We orthogonalize the NSS model to condition and diagnose its ill-conditioned parameters.
problem The ill-conditioning of the NSS model's design matrix.
method Exact orthogonal reparametrization via QR decomposition.
result Orthogonalization isolates the conditioning structure and maintains fit uncertainty.
A method for interpreting SVMs using polynomial kernels, revealing model complexity.
problem Interpreting SVMs built with truncated orthogonal polynomial kernels.
method Orthogonal Representation Contribution Analysis (ORCA) with normalized Orthogonal Kernel Contribution (OKC) indices.
result The method reveals structural aspects of model complexity not captured by predictive accuracy.
Study geodesics on flat tori, focusing on orthogonal lengths and their distribution.
problem Properties of geodesics on flat tori and their lengths.
method Fine study of dynamical correlation function and anisotropic Sobolev spaces.
result Properties of the length distribution and singularities of its Fourier transform.
We define systems of pre-extremals for the energy functional of regular rheonomic Lagrange manifolds and show how they induce well-defined Hamilton orthogonal nets. Such nets have applications in the modelling of e.g. wildfire spread under time- and space-dependent conditions. The time function inherited from such a Ha…
We study the relations between the quaternion H-type group and the boundary of the unit ball on two dimensional quaternionic space. The orthogonal projection of the space of square integrable functions defined on quaternion H-type group into its subspace of boundary values of q-holomorphic functions is consider. …
We present an algorithm for the decomposition of periodic financial return data into orthogonal factors of expected return and "systemic", "productive", and "nonproductive" risk. Generally, when the number of funds does not exceed the number of periods, the expected return of a portfolio is an affine function of its pr…
A new hashing method improves accuracy by learning an orthogonal transform.
problem Improving hashing accuracy for similarity search.
method Procrustean Orthogonal Sparse Hashing (POSH) method.
result POSH outperforms state-of-the-art hashing methods.
This work proves the asymptotic freeness of layerwise Jacobians in MLPs with Haar orthogonal matrices.
problem Proving the asymptotic freeness of layerwise Jacobians in multilayer perceptrons (MLPs).
method Replacing each layer's parameter matrix with itself multiplied by a Haar orthogonal matrix, and using the invariance of the MLP.
result Proves the asymptotic freeness of layerwise Jacobians in MLPs with Haar orthogonal matrices.
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.
OPAA estimates probability densities using functional analysis.
problem Estimating probability density functions efficiently and accurately.
method OPAA uses a parallelizable algorithm based on functional analysis to estimate probability distributions.
result OPAA provides an efficient method to estimate probability density functions and normalizing weights.
In this article we apply a Bochner type formula to show that on a compact conformally flat riemannian manifold (or half-conformally flat in dimension 4) certain types of orthogonal almost-complex structures, if they exist, give the absolute minimum for the energy functional. We give a few examples when such minimizers …
In this paper we prove a gap theorem for Kähler manifolds with nonnegative orthogonal bisectional curvature and nonnegative Ricci curvature, which generalizes an earlier result of the first author. We also prove a Liouville theorem for plurisubharmonic functions on such a manifolds, which generalizes a previous result …
An artificial general intelligence (AGI) might have an instrumental drive to modify its utility function to improve its ability to cooperate, bargain, promise, threaten, and resist and engage in blackmail. Such an AGI would necessarily have a utility function that was at least partially observable and that was influenc…
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 optimization algorithms on orthogonal group for machine learning.
problem Efficient optimization on the orthogonal group for machine learning tasks.
method Stochastic geometric algorithms on Lie groups.
result Strong performance on diverse machine learning tasks.
A new meta-learner improves prediction of individualized outcomes in sequential decisions.
problem Predicting individualized outcomes over long horizons in sequential decision-making.
method Developed a novel meta-learner called DRQ-learner with theoretical guarantees of orthogonality and quasi-oracle efficiency.
result DRQ-learner achieves quasi-oracle efficiency, doubly robustness, and Neyman-orthogonality.
A new optimizer preserves orthogonality constraints on matrices efficiently.
problem Optimization on Stiefel manifold with orthogonality constraints.
method Interplay between continuous and discrete dynamics leading to a gradient-based optimizer with momentum.
result The method optimizes matrices on Stiefel manifold efficiently and accurately.
In the multiple linear regression setting, we propose a general framework, termed weighted orthogonal components regression (WOCR), which encompasses many known methods as special cases, including ridge regression and principal components regression. WOCR makes use of the monotonicity inherent in orthogonal components …
MOBO-OSD optimizes multi-objective functions using orthogonal search directions.
problem Challenging multi-objective optimization problem.
method Solves multiple constrained optimization problems along orthogonal search directions.
result Consistently outperforms state-of-the-art algorithms.