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Regularization method and Bayesian inverse method are two dominating ways for solving inverse problems generated from various fields, e.g., seismic exploration and medical imaging. The two methods are related with each other by the MAP…

Classic Bayesian methods with complex models are frequently infeasible due to an intractable likelihood. Simulation-based inference methods, such as Approximate Bayesian Computing (ABC), calculate posteriors without accessing a likelihood…

Principal component regression (PCR) is a popular technique for fixed-design error-in-variables regression, a generalization of the linear regression setting in which the observed covariates are corrupted with random noise. We provide the…

The first-order binomial autoregressive (BAR(1)) model is the most frequently used tool to analyze the bounded count time series. The BAR(1) model is stationary and assumes process parameters to remain constant throughout the time period,…

Additive principal components (APCs for short) are a nonlinear generalization of linear principal components. We focus on smallest APCs to describe additive nonlinear constraints that are approximately satisfied by the data. Thus APCs fit…

Probabilistic model checking for systems with large or unbounded state space is a challenging computational problem in formal modelling and its applications. Numerical algorithms require an explicit representation of the state space, while…

Amortized meta-learning methods based on pre-training have propelled fields like natural language processing and vision. Transformer-based neural processes and their variants are leading models for probabilistic meta-learning with a…

Periodic autoregressive (PAR) time series with finite variance is considered as one of the most common models of second-order cyclostationary processes. However, in the real applications, the signals with periodic characteristics may be…

Reliable uncertainty quantification is of critical importance in time series forecasting, yet traditional methods often rely on restrictive distributional assumptions. Conformal prediction (CP) has emerged as a promising distribution-free…

With the advancement of deep learning techniques, the performance of Automatic Program Repair(APR) techniques has reached a new level. Previous deep learning-based APR techniques essentially modified program sentences in the…

Modern predictive systems encode beliefs that can act as useful prior information for statistical inference in data-limited settings. Using them for prior construction introduces a tradeoff: an informative prior built from a predictive…

Autoregressive cokriging models have been widely used to emulate multiple computer models with different levels of fidelity. The dependence structures are modeled via Gaussian processes at each level of fidelity, where covariance structures…

Despite extensive progress on image generation, common deep generative model architectures are not easily applied to lossless compression. For example, VAEs suffer from a compression cost overhead due to their latent variables. This…

We introduce a computational efficient data-driven framework suitable for quantifying the uncertainty in physical parameters and model formulation of computer models, represented by differential equations. We construct physics-informed…

Through sequential construction of posteriors on observing data online, Bayes' theorem provides a natural framework for continual learning. We develop Variational Auto-Regressive Gaussian Processes (VAR-GPs), a principled posterior updating…

Longitudinal and high-dimensional measurements have become increasingly common in biomedical research. However, methods to predict survival outcomes using covariates that are both longitudinal and high-dimensional are currently missing. In…

A widely applied approach to causal inference from a non-experimental time series $X$, often referred to as "(linear) Granger causal analysis", is to regress present on past and interpret the regression matrix $\hat{B}$ causally. However,…

In high-dimensional problems, choosing a prior distribution such that the corresponding posterior has desirable practical and theoretical properties can be challenging. This begs the question: can the data be used to help choose a good…

The ongoing replication crisis in science has increased interest in the methodology of replication studies. We propose a novel Bayesian analysis approach using power priors: The likelihood of the original study's data is raised to the power…

In this paper an autoregressive time series model with conditional heteroscedasticity is considered, where both conditional mean and conditional variance function are modeled nonparametrically. A test for the model assumption of…