The results suggest that the Cauchy mean-field approximation introduces a sharp-promoting bias, making it a suitable modeling choice for signals with discontinuous structure, and a computationally appealing alternative to full Bayesian inference methods such as MCMC.
Recovering piecewise-smooth functions with jump discontinuities from noisy, indirect, and incomplete data is a central task in computational inverse problems. Bayesian neural networks (BNNs) with heavy-tailed weight priors have emerged as effective edge-preserving priors for such problems. However, posterior inference...
Reliable uncertainty quantification remains an important challenge in AI. Hierarchical Bayesian methods provide a principled framework for this by representing unknown quantities through posterior distributions. Joint inference of neural-network parameters and prior hyperparameters is challenging for conventional Marko...
N. K. Chada, S. Cotter, K. J. H. Law et al.· 0 citations
Implicit-process priors specify distributions over functions through sample-forward mechanisms such as Bayesian neural networks and stochastic simulators, but their function-space densities are typically unavailable. We introduce Generalized Matheron Variational Implicit Processes (GMVIP), a pathwise variational family...
Luis A. Ortega, Andrés R. Masegosa, Thomas D. Nielsen· 0 citations
Reliable uncertainty quantification (UQ) is essential for deploying neural networks in scientific and high-stakes applications, but full Bayesian inference over the network parameters is computationally infeasible. We propose a low-rank generalized Laplace approximation for neural-network UQ based on a small number of...
Bayesian inference in compound loss models must often be repeated across policies, market scenarios, and prior specifications. Outside conjugate cases, this may require repeated numerical integration or Markov chain Monte Carlo (MCMC). We formulate this problem as amortized posterior approximation and construct a condi...
Aleksandar Arandjelović, P. Shevchenko, G. Tzougas· 0 citations
Sampling from the posterior is the central task of computational Bayesian inverse problems. The standard workhorse in Bayesian inference - Markov chain Monte Carlo (MCMC) - is sequential, yields correlated samples, and must be rerun for each observation. Conditional flow matching offers an amortized alternative: a tran...
Jan Blechschmidt, O. Ernst, Moritz Poguntke et al.· 0 citations
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