Related papers: TabMGP: Martingale Posterior with TabPFN

When prior information is lacking, the go-to strategy for probabilistic inference is to combine a "default prior" and the likelihood via Bayes's theorem. Objective Bayes, (generalized) fiducial inference, etc. fall under this umbrella. This…

The predictive Bayesian view involves eliciting a sequence of one-step-ahead predictive distributions in lieu of specifying a likelihood function and prior distribution. Recent methods have leveraged predictive distributions which are…

Modelling claim frequency and severity for non-life insurance pricing predominantly relies on generalised linear models, with gradient-boosted machines as the leading machine learning alternative. Tabular foundation models (TFMs) present a…

Bayesian computational strategies for inference can be inefficient in approximating the posterior distribution in models that exhibit some form of periodicity. This is because the probability mass of the marginal posterior distribution of…

The main challenges that arise when adopting Gaussian Process priors in probabilistic modeling are how to carry out exact Bayesian inference and how to account for uncertainty on model parameters when making model-based predictions on…

Gaussian process (GP) regression is a powerful probabilistic modeling technique with built-in uncertainty quantification. When one has access to multiple correlated simulations (tasks), it is common to fit a multitask GP (MTGP) surrogate…

In the usual Bayesian setting, a full probabilistic model is required to link the data and parameters, and the form of this model and the inference and prediction mechanisms are specified via de Finetti's representation. In general, such a…

Bayesian inference promises a framework for principled uncertainty quantification of neural network predictions. Barriers to adoption include the difficulty of fully characterizing posterior distributions on network parameters and the…

In this paper, we approach the problem of uncertainty quantification in deep learning through a predictive framework, which captures uncertainty in model parameters by specifying our assumptions about the predictive distribution of unseen…

Foundation models for tabular data, such as the Tabular Prior-data Fitted Network (TabPFN), are pre-trained on a massive number of synthetic datasets generated by structural causal models (SCM). They leverage in-context learning to offer…

The recently developed Prior-Data Fitted Networks (PFNs) have shown very promising results for applications in low-data regimes. The TabPFN model, a special case of PFNs for tabular data, is able to achieve state-of-the-art performance on a…

We introduce a probabilistic model with implicit norm regularization for learning nonnegative matrix factorization (NMF) that is commonly used for predicting missing values and finding hidden patterns in the data, in which the matrix…

We propose a general method to carry out a valid Bayesian analysis of a finite-dimensional `targeted' parameter in the presence of a finite-dimensional nuisance parameter. We apply our methods to causal inference based on estimating…

Bayesian inference requires specification of a single, precise prior distribution, whereas frequentist inference only accommodates a vacuous prior. Since virtually every real-world application falls somewhere in between these two extremes,…

Sparse variational Gaussian processes (GPs) construct tractable posterior approximations to GP models. At the core of these methods is the assumption that the true posterior distribution over training function values ${\bf f}$ and inducing…

Sparse variational approximations allow for principled and scalable inference in Gaussian Process (GP) models. In settings where several GPs are part of the generative model, theses GPs are a posteriori coupled. For many applications such…

A new algorithm is developed to tackle the issue of sampling non-Gaussian model parameter posterior probability distributions that arise from solutions to Bayesian inverse problems. The algorithm aims to mitigate some of the hurdles faced…

Simulation-based inference (SBI) offers a flexible and general approach to performing Bayesian inference: In SBI, a neural network is trained on synthetic data simulated from a model and used to rapidly infer posterior distributions for…

A partially identified model, where the parameters can not be uniquely identified, often arises during statistical analysis. While researchers frequently use Bayesian inference to analyze the models, when Bayesian inference with an…

Estimating model parameters of a general family of cure models is always a challenging task mainly due to flatness and multimodality of the likelihood function. In this work, we propose a fully Bayesian approach in order to overcome these…