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Gradient Boosting (GB) is a popular methodology used to solve prediction problems by minimizing a differentiable loss function, $L$. GB performs very well on tabular machine learning (ML) problems; however, as a pure ML solver it lacks the…

Variational inference, as an alternative to Markov chain Monte Carlo sampling, has played a transformative role in enabling scalable computation for complex Bayesian models. Nevertheless, existing approaches often depend on either rigid…

Mixtures of linear mixed models (MLMMs) are useful for clustering grouped data and can be estimated by likelihood maximization through the EM algorithm. The conventional approach to determining a suitable number of components is to compare…

By exploiting the invariance of the molecular Hamiltonian by a unitary transformation of the orbitals it is possible to significantly shorter the depth of the variational circuit in the Variational Quantum Eigensolver (VQE) algorithm by…

Bridge sampling is a powerful Monte Carlo method for estimating ratios of normalizing constants. Various methods have been introduced to improve its efficiency. These methods aim to increase the overlap between the densities by applying…

Variational calculations using Gaussian wave functionals combined with an approximate projection on gauge invariant states are presented. We find that the energy exhibits a minimum for a wave functional centered around a non vanishing…

A variety of lifted inference algorithms, which exploit model symmetry to reduce computational cost, have been proposed to render inference tractable in probabilistic relational models. Most existing lifted inference algorithms operate only…

By combining classical Monte Carlo and Bethe ansatz techniques we devise a numerical method to construct the Truncated Generalized Gibbs Ensemble (TGGE) for the spin-1/2 isotropic Heisenberg ($XXX$) chain. The key idea is to sample the…

The main challenge in Bayesian models is to determine the posterior for the model parameters. Already, in models with only one or few parameters, the analytical posterior can only be determined in special settings. In Bayesian neural…

Scene graph generation is a structured prediction task aiming to explicitly model objects and their relationships via constructing a visually-grounded scene graph for an input image. Currently, the message passing neural network based mean…

We present the marginal unbiased score expansion (MUSE) method, an algorithm for generic high-dimensional hierarchical Bayesian inference. MUSE performs approximate marginalization over arbitrary non-Gaussian latent parameter spaces,…

Motivated by a large ground-level ozone dataset, we propose a new computationally efficient additive approximate Gaussian process. The proposed method incorporates a computational-complexity-reduction method and a separable covariance…

In variational inference (VI), an approximation of the posterior distribution is selected from a family of distributions through numerical optimization. With the most common variational objective function, known as the evidence lower bound…

This article introduces a novel residual-based a posteriori error estimators for the Modified Weak Galerkin (MWG) finite element method applied to the obstacle problem. To the best of the author's knowledge, this work represents the first…

We introduce a new Partition of Unity Method for the numerical homogenization of elliptic partial differential equations with arbitrarily rough coefficients. We do not restrict to a particular ansatz space or the existence of a finite…

A new method called "variational sampling" is proposed to estimate integrals under probability distributions that can be evaluated up to a normalizing constant. The key idea is to fit the target distribution with an exponential family model…

Bayesian calibration of black-box computer models offers an established framework to obtain a posterior distribution over model parameters. Traditional Bayesian calibration involves the emulation of the computer model and an additive model…

Weighted ensemble (WE) is an enhanced path-sampling method that is conceptually simple, widely applicable, and statistically exact. In a WE simulation, an ensemble of trajectories is periodically pruned or replicated to enhance sampling of…

In image processing tasks, spatial priors are essential for robust computations, regularization, algorithmic design and Bayesian inference. In this paper, we introduce weighted mean curvature (WMC) as a novel image prior and present an…

We proposed a simple strategy to improve the postprocessing overhead of evaluating Hamiltonian expectation values in Variational quantum eigensolvers (VQEs). Observing the fact that for a mutually commuting observable group G in a given…