Related papers: Linear Convergence in Hilbert's Projective Metric …
We consider a decision aggregation problem with two experts who each make a binary recommendation after observing a private signal about an unknown binary world state. An agent, who does not know the joint information structure between…
We propose two algorithms that use both models and datasets to estimate angular power spectra from channel covariance matrices in massive MIMO systems. The first algorithm is an iterative fixed-point method that solves a hierarchical…
Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…
In information theory, the channel capacity, which indicates how efficient a given channel is, plays an important role. The best-used algorithm for evaluating the channel capacity is Arimoto algorithm. This paper aims to reveal an…
Quantum information quantities play a substantial role in characterizing operational quantities in various quantum information-theoretic problems. We consider numerical computation of four quantum information quantities: Petz-Augustin…
This paper studies the learning of linear operators between infinite-dimensional Hilbert spaces. The training data comprises pairs of random input vectors in a Hilbert space and their noisy images under an unknown self-adjoint linear…
Optimal dimensionality reduction methods are proposed for the Bayesian inference of a Gaussian linear model with additive noise in presence of overabundant data. Three different optimal projections of the observations are proposed based on…
A new variant of Newton's method for empirical risk minimization is studied, where at each iteration of the optimization algorithm, the gradient and Hessian of the objective function are replaced by robust estimators taken from existing…
We study algorithms for online linear optimization in Hilbert spaces, focusing on the case where the player is unconstrained. We develop a novel characterization of a large class of minimax algorithms, recovering, and even improving,…
We provide another look at the statistical calibration problem in computer models. This viewpoint is inspired by two overarching practical considerations of computer models: (i) many computer models are inadequate for perfectly modeling…
Two fundamental research tasks in science and engineering are forward predictions and data inversion. This article introduces a recent R package RobustCalibration for Bayesian data inversion and model calibration by experiments and field…
Information measures can be constructed from R\'enyi divergences much like mutual information from Kullback-Leibler divergence. One such information measure is known as Sibson $\alpha$-mutual information and has received renewed attention…
We consider centralized and distributed mirror descent algorithms over a finite-dimensional Hilbert space, and prove that the problem variables converge to an optimizer of a possibly nonsmooth function when the step sizes are square…
A new learning algorithm proposed by Brandt and Lin for neural network [1], [2] has been shown to be mathematically equivalent to the conventional back-propagation learning algorithm, but has several advantages over the backpropagation…
We propose an Adagrad-like algorithm for multi-objective unconstrained optimization that relies on the computation of a common descent direction only. Unlike classical local algorithms for multi-objective optimization, our approach does not…
The convergence analysis of a third-order scheme for the highly nonlinear Landau-Lifshitz-Gilbert equation with a non-convex constraint is considered. In this paper, we first present a fully discrete semi-implicit method for solving the…
In this work, we analyze two of the most fundamental algorithms in geodesically convex optimization: Riemannian gradient descent and (possibly inexact) Riemannian proximal point. We quantify their rates of convergence and produce different…
Large scale optimization problems are ubiquitous in machine learning and data analysis and there is a plethora of algorithms for solving such problems. Many of these algorithms employ sub-sampling, as a way to either speed up the…
In this paper we investigate the parallelization of two modular algorithms. In fact, we consider the modular computation of Gr\"obner bases (resp. standard bases) and the modular computation of the associated primes of a zero-dimensional…
In the present paper, we propose and analyze a novel method for estimating a univariate regression function of bounded variation. The underpinning idea is to combine two classical tools in nonparametric statistics, namely isotonic…