相关论文: Simultaneous Inference Under the Vacuous Orientati…
The present paper proposes an inf-sup stable divergence free virtual element method and associated a priori, and a posteriori error analysis to approximate the eigenvalues and eigenfunctions of the Stokes spectral problem in one shot. For…
This paper suggests a new interpretation of the Dempster-Shafer theory in terms of probabilistic interpretation of plausibility. A new rule of combination of independent evidence is shown and its preservation of interpretation is…
Over the last decade, a series of applied mathematics papers have explored a type of inverse problem--called by a variety of names including "inverse sensitivity", "pushforward based inference", "consistent Bayesian inference", or…
In this paper, we present an optimal filter for linear time-varying continuous-time stochastic systems that simultaneously estimates the states and unknown inputs in an unbiased minimum-variance sense. We first show that the unknown inputs…
We highlight a striking difference in behavior between two widely used variants of coordinate ascent variational inference: the sequential and parallel algorithms. While such differences were known in the numerical analysis literature in…
An unconventional approach for optimal stopping under model ambiguity is introduced. Besides ambiguity itself, we take into account how ambiguity-averse an agent is. This inclusion of ambiguity attitude, via an $\alpha$-maxmin nonlinear…
The steady-state Bayesian vector autoregression (BVAR) makes it possible to incorporate prior information about the long-run mean of the process. This has been shown in many studies to substantially improve forecasting performance, and the…
Many scientific analyses require simultaneous comparison of multiple functionals of an unknown signal at once, calling for multidimensional confidence regions with guaranteed simultaneous frequentist under structural constraints (e.g.,…
We extend the existing framework of semi-implicit variational inference (SIVI) and introduce doubly semi-implicit variational inference (DSIVI), a way to perform variational inference and learning when both the approximate posterior and the…
We propose simultaneous mean-variance regression for the linear estimation and approximation of conditional mean functions. In the presence of heteroskedasticity of unknown form, our method accounts for varying dispersion in the regression…
Non-parametric inference for functional data over two-dimensional domains entails additional computational and statistical challenges, compared to the one-dimensional case. Separability of the covariance is commonly assumed to address these…
The Variational Autoencoder (VAE) is a powerful framework for learning probabilistic latent variable generative models. However, typical assumptions on the approximate posterior distribution of the encoder and/or the prior, seriously…
We develop and analyse residual-based a posteriori error estimates for the virtual element discretisation of a nonlinear stress-assisted diffusion problem in two and three dimensions. The model problem involves a two-way coupling between…
This paper considers a time-varying vector error-correction model that allows for different time series behaviours (e.g., unit-root and locally stationary processes) to interact with each other to co-exist. From practical perspectives, this…
Causal inference with observational data can be performed under an assumption of no unobserved confounders (unconfoundedness assumption). There is, however, seldom clear subject-matter or empirical evidence for such an assumption. We…
The numerical approximation of convection-dominated problems continues to remain subject of strong interest. Families of stabilization techniques for finite element methods were developed in the past. Adaptive techniques based on a…
We develop a uniform inference theory for high-dimensional slope parameters in threshold regression models, allowing for either cross-sectional or time series data. We first establish oracle inequalities for prediction errors, and L1…
We study counterfactual regression, which aims to map input features to outcomes under hypothetical scenarios that differ from those observed in the data. This is particularly useful for decision-making when adapting to sudden shifts in…
Hierarchical models with gamma hyperpriors provide a flexible, sparse-promoting framework to bridge $L^1$ and $L^2$ regularizations in Bayesian formulations to inverse problems. Despite the Bayesian motivation for these models, existing…
Bayesian models quantify uncertainty and facilitate optimal decision-making in downstream applications. For most models, however, practitioners are forced to use approximate inference techniques that lead to sub-optimal decisions due to…