Related papers: Bayesian alignment using hierarchical models, with…

A common task in inverse problems and imaging is finding a solution that is sparse, in the sense that most of its components vanish. In the framework of compressed sensing, general results guaranteeing exact recovery have been proven. In…

The problem of validating or criticising models for georeferenced data is challenging, since the conclusions can vary significantly depending on the locations of the validation set. This work proposes the use of cross-validation techniques…

When related learning tasks are naturally arranged in a hierarchy, an appealing approach for coping with scarcity of instances is that of transfer learning using a hierarchical Bayes framework. As fully Bayesian computations can be…

This paper analyzes hierarchical Bayesian inverse problems using techniques from high-dimensional statistics. Our analysis leverages a property of hierarchical Bayesian regularizers that we call approximate decomposability to obtain…

Sequences of nucleotides (for DNA and RNA) or amino acids (for proteins) are central objects in biology. Among the most important computational problems is that of sequence alignment, i.e. arranging sequences from different organisms in…

Identifying disease-indicative genes is critical for deciphering disease mechanisms and has attracted significant interest in biomedical research. Spatial transcriptomics offers unprecedented insights for the detection of disease-specific…

Virtually any model we use in machine learning to make predictions does not perfectly represent reality. So, most of the learning happens under model misspecification. In this work, we present a novel analysis of the generalization…

Well-established methods for the solution of stochastic partial differential equations (SPDEs) typically struggle in problems with high-dimensional inputs/outputs. Such difficulties are only amplified in large-scale applications where even…

It is often of interest to combine available estimates of a similar quantity from multiple data sources. When the corresponding variances of each estimate are also available, a model should take into account the uncertainty of the estimates…

Spatially misaligned data can be fused by using a Bayesian melding model that assumes that underlying all observations there is a spatially continuous Gaussian random field process. This model can be used, for example, to predict air…

Proteins play crucial roles in every cellular process by interacting with each other, with nucleic acids, metabolites, and other molecules. The resulting assemblies can be very large and intricate and pose challenges to experimental…

Unsupervised clustering of curves according to their shapes is an important problem with broad scientific applications. The existing model-based clustering techniques either rely on simple probability models (e.g., Gaussian) that are not…

Mathematical models are routinely applied to interpret biological data, with common goals that include both prediction and parameter estimation. A challenge in mathematical biology, in particular, is that models are often complex and…

One of the goals of computer-aided surgery is to match intraoperative data to preoperative images of the anatomy and add complementary information that can facilitate the task of surgical navigation. In this context, mechanical palpation…

Identification of local structure in intensive data -- such as time series, images, and higher dimensional processes -- is an important problem in astronomy. Since the data are typically generated by an inhomogeneous Poisson process, an…

With the growing capabilities of Geographic Information Systems (GIS) and user-friendly software, statisticians today routinely encounter geographically referenced data containing observations from a large number of spatial locations and…

We present a Bayesian approach to machine learning with probabilistic programs. In our approach, training on available data is implemented as inference on a hierarchical model. The posterior distribution of model parameters is then used to…

Resolving the structural variability of proteins is often key to understanding the structure-function relationship of those macromolecular machines. Single particle analysis using Cryogenic electron microscopy (CryoEM), combined with…

A widely used method to create a continuous representation of a discrete data-set is regression analysis. When the regression model is not based on a mathematical description of the physics underlying the data, heuristic techniques play a…

Bayesian inference methods are applied within a Bayesian hierarchical modelling framework to the problems of joint state and parameter estimation, and of state forecasting. We explore and demonstrate the ideas in the context of a simple…