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Uncertainty quantification in automated image analysis is highly desired in many applications. Typically, machine learning models in classification or segmentation are only developed to provide binary answers; however, quantifying the…

This work introduces a novel nonlinear optimal filtering method, termed the Ensemble Schr{\"o}dinger Bridge nonlinear filter. The proposed filter combines the standard prediction step with a diffusion-generative-modeling-based analysis…

The iterative ensemble Kalman filter (IEnKF) is widely used in inverse problems to estimate system parameters from limited observations. However, the IEnKF, when applied to nonlinear systems, can be plagued by poor convergence. Here we…

Spectral clustering refers to a family of unsupervised learning algorithms that compute a spectral embedding of the original data based on the eigenvectors of a similarity graph. This non-linear transformation of the data is both the key of…

The ensemble Kalman filter (EnKF) is an efficient algorithm for many data assimilation problems. In certain circumstances, however, divergence of the EnKF might be spotted. In previous studies, the authors proposed an…

Deep Learning methods are known to suffer from calibration issues: they typically produce over-confident estimates. These problems are exacerbated in the low data regime. Although the calibration of probabilistic models is well studied,…

On noisy intermediate-scale quantum (NISQ) devices, expectation values of many observables are obtained through sampling-based approximations to trace-like quantities. A central limitation of this approach is destructive cancellation under…

Statistical learning algorithms provide a generally-applicable framework to sidestep time-consuming experiments, or accurate physics-based modeling, but they introduce a further source of error on top of the intrinsic limitations of the…

Boltzmann sampling based on Metropolis algorithm has been extensively used for simulating a canonical ensemble. An estimate of a mechanical property, like energy, of an equilibrium system, can be made by averaging over a large number…

Despite increasing popularity in empirical studies, the integration of machine learning generated variables into regression models for statistical inference suffers from the measurement error problem, which can bias estimation and threaten…

Implicit samplers are algorithms for producing independent, weighted samples from multi-variate probability distributions. These are often applied in Bayesian data assimilation algorithms. We use Laplace asymptotic expansions to analyze two…

In order to reach the sensitivity required to detect gravitational waves, pulsar timing array experiments need to mitigate as much noise as possible in timing data. A dominant amount of noise is likely due to variations in the dispersion…

In the strong-constraint formulation of the history-matching problem, we assume that all the model errors relate to a selection of uncertain model input parameters. One does not account for additional model errors that could result from,…

In this paper, we propose a new framework for solving state estimation problems with an additional sparsity-promoting $L_1$-regularizer term. We first formulate such problems as minimization of the sum of linear or nonlinear quadratic error…

Ensembling is a simple and popular technique for boosting evaluation performance by training multiple models (e.g., with different initializations) and aggregating their predictions. This approach is commonly reserved for the largest…

Ensembles improve prediction performance and allow uncertainty quantification by aggregating predictions from multiple models. In deep ensembling, the individual models are usually black box neural networks, or recently, partially…

Sampling experiments provide a viable route to show quantum advantages of quantum devices over classical computers in well-defined computational tasks. However, quantum devices such as boson samplers are susceptible to various errors,…

For objects in the low Earth orbit region, uncertainty in atmospheric density estimation is an important source of orbit prediction error, which is critical for space situational awareness activities such as the satellite conjunction…

The random demodulator is a recent compressive sensing architecture providing efficient sub-Nyquist sampling of sparse band-limited signals. The compressive sensing paradigm requires an accurate model of the analog front-end to enable…

In recent years, several ensemble-based filtering methods have been proposed and studied. The main challenge in such procedures is the updating of a prior ensemble to a posterior ensemble at every step of the filtering recursions. In the…