In this article we present a natural generalization of Newton's Second Law valid in field theory, i.e., when the parameterized curves are replaced by parameterized submanifolds of higher dimension. For it we introduce what we have called the geodesic -vector field, analogous to the ordinary geodesic field and which …
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48 results for “Newton procedure”
Stochastic quasi-Newton tackles noisy gradients in optimization.
problem Optimizing with noisy data in stochastic settings.
method Extends quasi-Newton methods to handle stochastic gradients through flexible Hessian modeling and line-search regularization.
result Demonstrates superior performance in maximum likelihood estimation for complex models.
Paper develops efficient methods for estimating Hessian inverses in stochastic optimization.
problem Estimating the inverse Hessian for convex function minimization.
method Robbins-Monro procedure for recursive estimation of the inverse Hessian.
result Develops universal stochastic Newton methods with improved efficiency.
Paper proposes an efficient online Newton method with Nesterov's acceleration for streaming data.
problem Efficient inference of online Newton methods with robustness to noise and ill-conditioning.
method Online Newton method with Hessian averaging and Nesterov's accelerated sketch-and-project solver.
result Global almost-sure convergence and asymptotic normality of the last iterate with non-asymptotic convergence guarantees.
Paper describes links of mixed polynomials with specific properties.
problem Understanding the links of mixed polynomials with nice Newton boundaries.
method Analyzes links constructed from sequences of links associated with compact 1-faces of the Newton boundary.
result Links of singularities of inner non-degenerate mixed polynomials can be described using a specific procedure.
New interior-point method tackles Wasserstein barycenter problem efficiently.
problem Computing Wasserstein barycenter for large support measures.
method Adapted interior-point method exploiting problem's matrix structure.
result Achieves a well-balanced tradeoff between accuracy and speed.
We propose an algorithmic framework for convex minimization problems of a composite function with two terms: a self-concordant function and a possibly nonsmooth regularization term. Our method is a new proximal Newton algorithm that features a local quadratic convergence rate. As a specific instance of our framework, w…
Bayesian coresets improved with random sampling and quasi-Newton optimization.
problem Efficiently approximate Bayesian posterior distributions for computationally expensive inference.
method Randomly select a subset of data points, then optimize weights using quasi-Newton method.
result First algorithm with high-probability KL divergence bound on coreset quality.
Efficient algorithms compute lambda quantiles for robust portfolio optimization.
problem Computing lambda quantiles efficiently and robustly.
method Λ-Newton-Bis algorithm combining Newton's method and bisection, interval analysis for multiple roots.
result Demonstrated computational efficiency and practical relevance in portfolio optimization.
A parallel optimization method for convex functions using Hessian sketching and debiasing.
problem Massively parallel optimization of convex functions with limited communication.
method Newton method with Hessian sketching and debiasing by workers, server averages descent directions.
result Approximation of Newton step with low-complexity adaptive sketching scheme.
Estimates MoE models with feature selection for high-dimensional data.
problem Estimation and feature selection in Mixtures-of-Experts models with high-dimensional predictors.
method Regularized maximum likelihood estimation with proximal-Newton EM algorithm.
result Good performance in recovering sparse solutions, parameter estimation, and clustering of heterogeneous data.
New method approximates CV for model assessment and selection.
problem Efficient model assessment and selection with large number of folds.
method Approximates expensive refitting with a single Newton step warm-started from full training set optimizer.
result Uniform non-asymptotic, deterministic model assessment guarantees for approximate CV.
Paper proposes a new method for efficient second-order neural network training.
problem Infeasibility of Hessian calculation and noisy second-order information in deep learning.
method Adopting complex-step directional derivative (CSFD) for accurate Hessian computation and designing an effective Newton Krylov procedure.
result Our method outperforms existing methods and often converges one-order faster.
A new multivariate stochastic volatility estimation procedure for financial time series is proposed. A Wishart autoregressive process is considered for the volatility precision covariance matrix, for the estimation of which a two step procedure is adopted. The first step is the conditional inference on the autoregressi…
New method speeds up change-point detection in data sequences.
problem Efficiently detecting change-points in long data sequences.
method Sequential Gradient Descent and Quasi-Newton's Method.
result New method can be orders of magnitude faster than existing methods.
A new sequential method estimates Poisson means in streaming data, achieving optimality and efficiency.
problem Estimating Poisson means in a streaming, or online, framework.
method A quasi-Bayesian approach based on Newton's algorithm for a sequential estimate.
result Established frequentist guarantees including consistency and asymptotic optimality.
A new method for optimization in probability space using Newton's flows.
problem Optimization in probability space with information metrics.
method Information Newton's flows, including Fisher-Rao and Wasserstein-2 metrics, with Newton's Langevin dynamics and variational methods.
result Effective numerical implementation and convergence results for the proposed method.
New method estimates marginal likelihood for deep learning models using training data alone.
problem Estimation difficulties in marginal likelihood for model selection in deep learning.
method Scalable marginal likelihood estimation based on Laplace's method and Gauss-Newton approximations.
result Estimate outperforms cross-validation and manual tuning on various datasets.
We describe stochastic Newton and stochastic quasi-Newton approaches to efficiently solve large linear least-squares problems where the very large data sets present a significant computational burden (e.g., the size may exceed computer memory or data are collected in real-time). In our proposed framework, stochasticity…
This paper studies distributed estimation and inference for a general statistical problem with a convex loss that could be non-differentiable. For the purpose of efficient computation, we restrict ourselves to stochastic first-order optimization, which enjoys low per-iteration complexity. To motivate the proposed metho…
Newton's method solves variational problems on manifolds.
problem Solving variational equations on manifolds.
method Newton's method with affine covariant damping strategy.
result Numerical results for variational problems demonstrated.
Muon with Newton-Schulz converges to the same stationary point as SVD-polar, up to a constant factor.
problem Improving the convergence rate of Muon optimizer.
method Using Newton-Schulz steps for momentum orthogonalization, proving convergence rate and constant factor.
result Muon with Newton-Schulz converges to the same stationary point as SVD-polar, up to a constant factor.
We study deformations of Riemannian metrics on a given manifold equipped with a codimension-one foliation subject to quantities expressed in terms of its second fundamental form. We prove the local existence and uniqueness theorem and estimate the existence time of solutions for some particular cases. The key step of t…
In this note, we introduce a new algorithm to deal with finite dimensional clustering with errors in variables. The design of this algorithm is based on recent theoretical advances (see Loustau (2013a,b)) in statistical learning with errors in variables. As the previous mentioned papers, the algorithm mixes different t…
Simple stochastic Newton and cubic Newton methods with fast convergence.
problem Minimizing large numbers of smooth and strongly convex functions.
method Stochastic Newton and cubic Newton methods with simple local linear-quadratic rates.
result Local linear-quadratic convergence results with fast adaptation to problem's curvature.
Modified Newton step for online learning reduces matrix size for large datasets.
problem Handling large multi-class datasets efficiently in online learning.
method Element-wise multiplication to reduce matrix size of second order matrices.
result Proposed method achieves similar mistake rates to popular methods but with faster computations.
Solving Newton's Equations of Motion with Large Timesteps using Recurrent Neural Networks based Operatorsphysics.comp-ph
RNN operators solve Newton's equations with large timesteps for molecular dynamics.
problem Solving Newton's equations of motion with large timesteps for molecular dynamics simulations.
method Recurrent Neural Networks (RNN) operators to solve Newton's equations using past trajectory data.
result Significant speedup in molecular dynamics simulations with timesteps up to 4000 times larger.
New algorithm improves convergence of gradient boosting trees.
problem Global convergence of Newton boosting in tabular machine learning.
method Introduces Gradient Regularized Newton Descent for GBDTs, proving linear convergence for smooth, strongly convex losses and rate for general convex losses.
result Achieves globally convergent second-order GBDT algorithm with rate matching first-order boosting.
We generalize Newton-type methods for minimizing smooth functions to handle a sum of two convex functions: a smooth function and a nonsmooth function with a simple proximal mapping. We show that the resulting proximal Newton-type methods inherit the desirable convergence behavior of Newton-type methods for minimizing s…
Boosting algorithms are frequently used in applied data science and in research. To date, the distinction between boosting with either gradient descent or second-order Newton updates is often not made in both applied and methodological research, and it is thus implicitly assumed that the difference is irrelevant. The g…
Newton's method tackles nonlinear mappings into vector bundles with connections and retractions.
problem Finding zeros of mappings from a manifold into a vector bundle.
method Local convergence using differentiability concepts, Banach space Riemannian distance, and affine covariant damping strategy.
result Illustrated application to generalized non-symmetric eigenvalue problems.
Study uses Newton polytopes to distinguish Lagrangian fillings of Legendrian submanifolds.
problem Distinguishing Lagrangian fillings of Legendrian submanifolds.
method Utilizes Newton polytopes associated with augmented values of Reeb chords.
result Newton polytopes can distinguish infinitely many distinct Lagrangian fillings.
Unified approach to Bayesian inference with guarantees on covariance matrices.
problem Approximate Bayesian inference with PSD guarantees.
method Bayes-Newton methods extending Newton's method for optimisation.
result Novel algorithms with PSD covariance matrices.
Approximating Full Conformal Prediction for Neural Network Regression with Gauss-Newton Influencecs.LG
This work approximates full conformal prediction for neural networks without sample splitting.
problem Uncertainty quantification for neural network regression models.
method Approximating full conformal prediction using Gauss-Newton influence for post-hoc uncertainty estimation.
result Locally-adaptive and often tighter prediction intervals compared to split-CP.
Paper proposes an online covariance estimator for sketched Newton methods.
problem Estimating the limiting covariance matrix of sketched Newton methods.
method Proposes a fully online covariance matrix estimator from Newton iterates.
result Establishes the consistency and convergence rate of the proposed estimator.
New Q-Newton's method avoids saddle points and converges quadratically.
problem Optimizing functions with saddle points and ensuring convergence guarantees.
method Modified New Q-Newton's method with Backtracking line search.
result Theorem for Morse functions: quadratic convergence to local minima.
A new optimization method improves deep learning accuracy without hyper-parameter tuning.
problem Computational demands and convergence behavior in deep learning training.
method Stochastic quasi-Gauss-Newton (SQGN) optimization method combining stochastic quasi-Newton, Gauss-Newton, and variance reduction.
result SQGN provides excellent accuracy without hyper-parameter experimentation, improving convergence and computational performance.
Proposes a Quasi-Newton trust region method for policy optimization in reinforcement learning.
problem Lack of stepsize selection criterion and slow convergence in gradient descent for policy optimization.
method Uses a trust region method with Quasi-Newton approximation for the Hessian.
result Demonstrates improved performance and efficiency in continuous control tasks.
This thesis disentangles Gauss-Newton and variational approximations in Bayesian deep learning.
problem Understanding the interplay between the Gauss-Newton method and variational approximations in Bayesian deep learning.
method Analysis of the Gauss-Newton method and Laplace/Gaussian variational approximations for neural networks.
result The combination of the Gauss-Newton method with approximate inference can be cast as inference in a linear or Gaussian process model.
Proposes a faster second-order method for MDPs.
problem Slow convergence of first-order value iteration methods in MDPs.
method Applies Newton-Raphson method to successive relaxation value iteration scheme.
result Second-order convergence and faster convergence to optimal solution.
SVRN accelerates Newton methods by reducing variance and improving performance.
problem Improving the efficiency of Newton methods for large-scale optimization problems.
method Stochastic Variance-Reduced Newton (SVRN) algorithm that accelerates Subsampled Newton and Iterative Hessian Sketch algorithms.
result SVRN accelerates Newton methods by reducing the number of passes over the data, achieving a significant improvement in performance.
Deep learning involves a difficult non-convex optimization problem, which is often solved by stochastic gradient (SG) methods. While SG is usually effective, it may not be robust in some situations. Recently, Newton methods have been investigated as an alternative optimization technique, but nearly all existing studies…
Study of measured laminations on surfaces using Newton polytopes and Poisson brackets.
problem Understanding the space of measured laminations on surfaces from a valuative perspective.
method Introducing Newton polytopes for character variety functions, defining tangent spaces, and identifying symplectic structures.
result Trace functions have unit coefficients at the extremal points of their Newton polytopes.
Approximate Newton methods are a standard optimization tool which aim to maintain the benefits of Newton's method, such as a fast rate of convergence, whilst alleviating its drawbacks, such as computationally expensive calculation or estimation of the inverse Hessian. In this work we investigate approximate Newton meth…
Newton-LESS sparsifies Gaussian sketching for faster optimization.
problem Computing the Hessian matrix in optimization is computationally expensive.
method Uses a sparsified version of a dense Gaussian sketching matrix.
result Achieves nearly the same convergence rate as dense Gaussian embeddings without the computational cost.
New quasi-Newton method guarantees global superlinear convergence.
problem Global convergence and superlinear convergence of quasi-Newton methods.
method Hybrid proximal extragradient method with online learning for Hessian approximation.
result First globally convergent quasi-Newton method with explicit superlinear convergence rate.
Usually, in the Black-Scholes pricing theory the volatility is a positive real parameter. Here we explore what happens if it is allowed to be a complex number. The function for pricing a European option with a complex volatility has essential singularities at zero and infinity. The singularity at zero reflects the put-…
Paper develops a robust PP distributed quasi-Newton estimation for Byzantine machines.
problem Byzantine machines in distributed computing under Privacy Protection constraints.
method Robust PP distributed quasi-Newton estimation method that transmits only five vectors.
result Reduces privacy budgeting and transmission cost compared to gradient descent and Newton iteration.