Related papers: An introduction to ML(n)BiCGStab

Meta-learning offers a principled framework leveraging \emph{task-invariant} priors from related tasks, with which \emph{task-specific} models can be fine-tuned on downstream tasks, even with limited data records. Gradient-based…

Many recently proposed methods for Neural Architecture Search (NAS) can be formulated as bilevel optimization. For efficient implementation, its solution requires approximations of second-order methods. In this paper, we demonstrate that…

We propose a Bayesian nonparametric model based on Markov Chain Monte Carlo (MCMC) methods for unveiling the structure of the invariant global stable manifold from observed time-series data. The underlying unknown dynamical process is…

We introduce $\pi$-Girsanov, a new method for constructing Markov state models from biased enhanced-sampling molecular dynamics simulations based on Girsanov reweighting. The key idea behind this new method is to separate the reweighting…

This paper presents two new augmented flexible (AF)-Krylov subspace methods, AF-GMRES and AF-LSQR, to compute solutions of large-scale linear discrete ill-posed problems that can be modeled as the sum of two independent random variables,…

Computational modeling of assembly is challenging for many systems because their timescales vastly exceed those accessible to simulations. This article describes the MultiMSM, which is a general framework that uses Markov state models…

Markov chain Monte Carlo (MCMC) methods form one of the algorithmic foundations of Bayesian inverse problems. The recent development of likelihood-informed subspace (LIS) methods offers a viable route to designing efficient MCMC methods for…

In many hierarchical inverse problems, not only do we want to estimate high- or infinite-dimensional model parameters in the parameter-to-observable maps, but we also have to estimate hyperparameters that represent critical assumptions in…

Kernel logistic regression (KLR) is a conventional nonlinear classifier in machine learning. With the explosive growth of data size, the storage and computation of large dense kernel matrices is a major challenge in scaling KLR. Even the…

Bilevel optimization is a popular two-level hierarchical optimization, which has been widely applied to many machine learning tasks such as hyperparameter learning, meta learning and continual learning. Although many bilevel optimization…

Applications of machine learning (ML) techniques to operational settings often face two challenges: i) ML methods mostly provide point predictions whereas many operational problems require distributional information; and ii) They typically…

Markov logic networks (MLNs) reconcile two opposing schools in machine learning and artificial intelligence: causal networks, which account for uncertainty extremely well, and first-order logic, which allows for formal deduction. An MLN is…

The Lattice Boltzmann method (LBM) offers a powerful and versatile approach to simulating diverse hydrodynamic phenomena, spanning microfluidics to aerodynamics. The vast range of spatiotemporal scales inherent in these systems currently…

This article was motivated by the desire to improve Markov chain Monte Carlo methods for spatial survival models in which the locations of individuals in space are known. For a dataset comprising information on n individuals, standard…

Geometric graph neural networks (GNNs) excel at capturing molecular geometry, yet their locality-biased message passing hampers the modeling of long-range interactions. Current solutions have fundamental limitations: extending cutoff radii…

Markov Chain Monte Carlo (MCMC) sampling from a posterior distribution corresponding to a massive data set can be computationally prohibitive since producing one sample requires a number of operations that is linear in the data size. In…

We tackle the general differentiable meta learning problem that is ubiquitous in modern deep learning, including hyperparameter optimization, loss function learning, few-shot learning, invariance learning and more. These problems are often…

We combine machine learning (ML) with Monte Carlo (MC) simulations to study the crystal nucleation process. Using ML, we evaluate the canonical partition function of the system over the range of densities and temperatures spanned during…

Uniform sampling of binary matrix with fixed margins is an important and difficult problem in statistics, computer science, ecology and so on. The well-known swap algorithm would be inefficient when the size of the matrix becomes large or…

This article proposes a biconvex modification to convex biclustering in order to improve its performance in high-dimensional settings. In contrast to heuristics that discard a subset of noisy features a priori, our method jointly learns and…