The paper introduces a method for training sparse Bayesian neural networks by integrating spike-and-slab priors into sticky piecewise deterministic Markov processes (PDMPs). It demonstrates that these modern Monte Carlo techniques can sample posterior distributions of Bayesian neural networks exactly, provided numerical rate bounds are satisfied. Experiments show that the resulting sparse models not only converge well but also exhibit greater robustness to input noise compared to their dense counterparts.
arXiv:2610.09886v1 Announce Type: cross Abstract: Bayesian neural networks need not be fully stochastic to be universal conditional density approximators, but it remains open which parameters should...
arXiv:2610.19074v1 Announce Type: new Abstract: Reliable uncertainty quantification remains an important challenge in AI. Hierarchical Bayesian methods provide a principled framework for this by repr...
arXiv:2608. 08644v1 Announce Type: new Abstract: We consider the problem of sampling compositional and discrete objects from a given unnormalized posterior distribution.
arXiv:2601. 07944v2 Announce Type: replace-cross Abstract: Since the turn of the century, approximate Bayesian inference has steadily evolved as new computational techniques have been incorporated to handle increasingly complex, large-scale predictive problems.
The paper introduces a method that uses confidence sequences to adaptively determine the number of Monte Carlo samples needed for Bayesian neural network predictions, ensuring statistical guarantees. It applies to tasks such as class identification, full predictive distribution approximation, and probability-threshold decisions, stopping sampling once the desired confidence is achieved. Experiments demonstrate efficient computational budgeting, allocating more samples to ambiguous inputs, preserving decision reliability, and reducing overall latency compared to a fixed sample budget.
arXiv:2608. 03566v1 Announce Type: cross Abstract: The drift diffusion model (DDM) is a cornerstone of cognitive decision-making research.
We consider the problem of sampling compositional and discrete objects from a given unnormalized posterior distribution. Notably, recent studies have shown that this problem can be efficiently solved by learning a deterministic Markov Decision Process (MDP) that progressively builds each object in proportion to the posterior.
arXiv:2606. 01468v1 Announce Type: cross Abstract: Due to their explicit priors and ability to model uncertainty, Bayesian methods have played a major role in dynamical latent variable modeling of single-cell neural recordings.
The paper introduces a new class of Bayesian neural networks that place Dirichlet Process priors on the data-generating distribution instead of on network weights, aiming to better capture epistemic uncertainty. Using this framework, the authors develop DP-DQN, a reinforcement learning algorithm that maintains posterior distributions over value functions and performs efficient Thompson sampling. DP-DQN combines data-driven posterior reweighting via the Bayesian Bootstrap with generative prior hypotheses from the DP base measure, enabling deep exploration with a single neural network without requiring multi-network ensembles.
arXiv:2310.02423v3 Announce Type: replace Abstract: We present a new algorithm for amortized inference in sparse probabilistic graphical models (PGMs), which we call $\Delta$-amortized inference ($\D...
SelectPFN is a prior‑data‑fitted network that jointly performs Bayesian variable selection and prediction for sparse nonlinear regression. In a single forward pass it outputs posterior inclusion probabilities for each variable and makes predictions using only sampled subsets, ensuring excluded variables cannot influence the result. The method achieves exact finite‑sample false discovery rate control via column‑permutation equivariance and knockoff statistics, and outperforms lasso, BART, DART, LassoNet, and other sparse neural networks on synthetic and real data with up to 500 predictors.
arXiv:2609.39525v1 Announce Type: new Abstract: Casting Bayesian inference as a neural network optimization problem targeting an amortized posterior is attractive, as it extends to otherwise intracta...