相关论文: A Newton-Like Algorithm for Likelihood Maximizatio…

For latent class models where the class weights depend on individual covariates, we derive a simple expression for computing the score vector and a convenient hybrid between the observed and the expected information matrices which is always…

We propose a continuous-time second-order optimization algorithm for solving unconstrained convex optimization problems with bounded Hessian. We show that this alternative algorithm has a comparable convergence rate to that of the…

Distributional shifts pose a significant challenge to achieving robustness in contemporary machine learning. To overcome this challenge, robust satisficing (RS) seeks a robust solution to an unspecified distributional shift while achieving…

Many randomized approximation algorithms operate by giving a procedure for simulating a random variable $X$ which has mean $\mu$ equal to the target answer, and a relative standard deviation bounded above by a known constant $c$. Examples…

Point sets matching method is very important in computer vision, feature extraction, fingerprint matching, motion estimation and so on. This paper proposes a robust point sets matching method. We present an iterative algorithm that is…

Maximum likelihood estimations for the parameters of extreme value distributions are discussed in this paper using fixed point iteration. The commonly used numerical approach for addressing this problem is the Newton-Raphson approach which…

We propose a Distributionally Robust Optimization (DRO) formulation with a Wasserstein-based uncertainty set for selecting grouped variables under perturbations on the data for both linear regression and classification problems. The…

We address high dimensional covariance estimation for elliptical distributed samples, which are also known as spherically invariant random vectors (SIRV) or compound-Gaussian processes. Specifically we consider shrinkage methods that are…

The initialization of equation-based differential-algebraic system models, and more in general the solution of many engineering and scientific problems, require the solution of systems of nonlinear equations. Newton-Raphson's method is…

Leverage scores have become essential in statistics and machine learning, aiding regression analysis, randomized matrix computations, and various other tasks. This paper delves into the inverse problem, aiming to recover the intrinsic model…

Bayesian neural networks (BNNs) hold great promise as a flexible and principled solution to deal with uncertainty when learning from finite data. Among approaches to realize probabilistic inference in deep neural networks, variational Bayes…

We study the problem of computationally efficient robust estimation of the covariance/scatter matrix of elliptical distributions -- that is, affine transformations of spherically symmetric distributions -- under the strong contamination…

We introduce a new dynamical system, at the interface between second-order dynamics with inertia and Newton's method. This system extends the class of inertial Newton-like dynamics by featuring a time-dependent parameter in front of the…

Variable selection in linear regression has been a central topic in statistical research for decades. Bayesian variable selection methods, which account for uncertainty in both the regression coefficients and the noise variance, have…

In modern deep learning, highly subsampled stochastic approximation (SA) methods are preferred to sample average approximation (SAA) methods because of large data sets as well as generalization properties. Additionally, due to perceived…

In this paper, we first describe a matricial Newton-type algorithm designed to solve the multivariable spectrum approximation problem. We then prove its global convergence. Finally, we apply this approximation procedure to multivariate…

Motivated by machine learning problems over large data sets and distributed optimization over networks, we develop and analyze a new method called incremental Newton method for minimizing the sum of a large number of strongly convex…

We show that, for finite-sum minimization problems, incorporating partial second-order information of the objective function can dramatically improve the robustness to mini-batch size of variance-reduced stochastic gradient methods, making…

Due to the highly non-convex nature of large-scale robust parameter estimation, avoiding poor local minima is challenging in real-world applications where input data is contaminated by a large or unknown fraction of outliers. In this paper,…

The main result characterises the equivalence of the Newton-Raphson algorithm and PDE of conservation of electric charge. Based on this equivalence we analyse the properties of the Fisher-scoring method, a variant of Newton's method…