Related papers: An adaptive augmented regularization method and it…
This paper introduces and studies a new model of computation called an Alternating Automatic Register Machine (AARM). An AARM possesses the basic features of a conventional register machine and an alternating Turing machine, but can carry…
The autoregressive (AR) models are used to represent the time-varying random process in which output depends linearly on previous terms and a stochastic term (the innovation). In the classical version, the AR models are based on normal…
The estimation of normalizing constants is a fundamental step in probabilistic model comparison. Sequential Monte Carlo methods may be used for this task and have the advantage of being inherently parallelizable. However, the standard…
Multiplicative noise arises in inverse problems when, for example, uncertainty on measurements is proportional to the size of the measurement itself. The likelihood that arises is hence more complicated than that from additive noise. We…
We introduce a novel adaptive Gaussian Process Regression (GPR) methodology for efficient construction of surrogate models for Bayesian inverse problems with expensive forward model evaluations. An adaptive design strategy focuses on…
Adaptive cubic regularization methods have emerged as a credible alternative to linesearch and trust-region for smooth nonconvex optimization, with optimal complexity amongst second-order methods. Here we consider a general/new class of…
Re-randomization has gained popularity as a tool for experiment-based causal inference due to its superior covariate balance and statistical efficiency compared to classic randomized experiments. However, the basic re-randomization method,…
The need to blend observational data and mathematical models arises in many applications and leads naturally to inverse problems. Parameters appearing in the model, such as constitutive tensors, initial conditions, boundary conditions, and…
A reciprocal LASSO (rLASSO) regularization employs a decreasing penalty function as opposed to conventional penalization approaches that use increasing penalties on the coefficients, leading to stronger parsimony and superior model…
Due to their uncertainty quantification, Bayesian solutions to inverse problems are the framework of choice in applications that are risk averse. These benefits come at the cost of computations that are in general, intractable. New advances…
This paper introduces a dual-regularized ADMM approach to distributed, time-varying optimization. The proposed algorithm is designed in a prediction-correction framework, in which the computing nodes predict the future local costs based on…
This work proposes ensemble Kalman randomized maximum likelihood estimation, a new derivative-free method for performing randomized maximum likelihood estimation, which is a method that can be used to generate approximate samples from…
Most recently, He and Yuan [arXiv:2108.08554, 2021] have proposed a balanced augmented Lagrangian method (ALM) for the canonical convex programming problem with linear constraints, which advances the original ALM by balancing its…
Posterior sampling for high-dimensional Bayesian inverse problems is a common challenge in real-world applications. Randomized Maximum Likelihood (RML) is an optimization based methodology that gives samples from an approximation to the…
Generalized additive models (GAMs) provide a way to blend parametric and non-parametric (function approximation) techniques together, making them flexible tools suitable for many modeling problems. For instance, GAMs can be used to…
Efficient topology optimization based on the adaptive auxiliary reduced model reanalysis (AARMR) is proposed to improve computational efficiency and scale. In this method, a projection auxiliary reduced model (PARM) is integrated into the…
Bayesian inference for high-dimensional inverse problems is computationally costly and requires selecting a suitable prior distribution. Amortized variational inference addresses these challenges via a neural network that approximates the…
Model-assisted estimation with complex survey data is an important practical problem in survey sampling. When there are many auxiliary variables, selecting significant variables associated with the study variable would be necessary to…
To infer the parameters of mechanistic models with intractable likelihoods, techniques such as approximate Bayesian computation (ABC) are increasingly being adopted. One of the main disadvantages of ABC in practical situations, however, is…
Inverse scattering problems have many important applications. In this paper, given limited aperture data, we propose a Bayesian method for the inverse acoustic scattering to reconstruct the shape of an obstacle. The inverse problem is…