Related papers: Nonparametric posterior learning for emission tomo…

This paper addresses Bayesian inference related to partial differential equations (PDEs), particularly nonparametric regression constrained by PDEs. To effectively encode prior information, we propose a novel framework that learns a…

Obtaining high certainty in predictive models is crucial for making informed and trustworthy decisions in many scientific and engineering domains. However, extensive experimentation required for model accuracy can be both costly and…

We consider amortized Bayesian inference for nonlinear inverse problems in settings where only samples from the joint distribution of parameters and observations are available. Classical methods such as Markov chain Monte Carlo require…

We present a Bayesian nonparametric Poisson factorization model for modeling network data with an unknown and potentially growing number of overlapping communities. The construction is based on completely random measures and allows the…

Bayesian methods have been very successful in quantifying uncertainty in physics-based problems in parameter estimation and prediction. In these cases, physical measurements y are modeled as the best fit of a physics-based model…

Understanding how adult humans learn non-native speech categories such as tone information has shed novel insights into the mechanisms underlying experience-dependent brain plasticity. Scientists have traditionally examined these questions…

Analysis of observational studies increasingly confronts the challenge of determining which of a possibly high-dimensional set of available covariates are required to satisfy the assumption of ignorable treatment assignment for estimation…

The statistical inverse problem of estimating the probability distribution of an infinite-dimensional unknown given its noisy indirect observation is studied in the Bayesian framework. In practice, one often considers only…

Sampling from the posterior is a key technical problem in Bayesian statistics. Rigorous guarantees are difficult to obtain for Markov Chain Monte Carlo algorithms of common use. In this paper, we study an alternative class of algorithms…

Uncertainty quantification is crucial for the deployment of image restoration models in safety-critical domains, like autonomous driving and biological imaging. To date, methods for uncertainty visualization have mainly focused on per-pixel…

Convolutional sparse coding (CSC) can learn representative shift-invariant patterns from multiple kinds of data. However, existing CSC methods can only model noises from Gaussian distribution, which is restrictive and unrealistic. In this…

Particle filters flexibly represent multiple posterior modes nonparametrically, via a collection of weighted samples, but have classically been applied to tracking problems with known dynamics and observation likelihoods. Such generative…

Bayesian inference allows us to define a posterior distribution over the weights of a generic neural network (NN). Exact posteriors are usually intractable, in which case approximations can be employed. One such approximation - variational…

Calibration of computer models is a key step in making inferences, predictions, and decisions for complex science and engineering systems. We formulate and analyze a nonparametric Bayesian methodology for computer model calibration. This…

This paper presents a structure-preserving Bayesian approach for learning nonseparable Hamiltonian systems using stochastic dynamic models allowing for statistically-dependent, vector-valued additive and multiplicative measurement noise.…

We propose a novel automatic parameter selection strategy for variational imaging problems under Poisson noise corruption. The selection of a suitable regularization parameter, whose value is crucial in order to achieve high quality…

The missing data problem pervasively exists in statistical applications. Even as simple as the count data in mortality projections, it may not be available for certain age-and-year groups due to the budget limitations or difficulties in…

A nonparametric Bayes approach is proposed for the problem of estimating a sparse sequence based on Gaussian random variables. We adopt the popular two-group prior with one component being a point mass at zero, and the other component being…

We propose a method to facilitate exploration and analysis of new large data sets. In particular, we give an unsupervised deep learning approach to learning a latent representation that captures semantic similarity in the data set. The core…

spectral-based subspace learning is a common data preprocessing step in many machine learning pipelines. The main aim is to learn a meaningful low dimensional embedding of the data. However, most subspace learning methods do not take into…