A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Percolation on complex networks has been used to study computer viruses, epidemics, and other casual processes. Here, we present conditions for the existence of a network specific, observation dependent, phase transition in the updated posterior of node states resulting from actively monitoring the network. Since tradi…
We challenge the longstanding assumption that the mean-field approximation for variational inference in Bayesian neural networks is severely restrictive, and show this is not the case in deep networks. We prove several results indicating that deep mean-field variational weight posteriors can induce similar distribution…
The choice of approximate posterior distribution is one of the core problems in variational inference. Most applications of variational inference employ simple families of posterior approximations in order to allow for efficient inference, focusing on mean-field or other simple structured approximations. This restricti…
We propose a new sampler that integrates the protocol of parallel tempering with the Nosé-Hoover (NH) dynamics. The proposed method can efficiently draw representative samples from complex posterior distributions with multiple isolated modes in the presence of noise arising from stochastic gradient. It potentially faci…
TM-VI uses flexible transformation models to approximate complex posteriors in Bayesian models.
problem Approximating complex posteriors in Bayesian models with limited flexibility.
method Transformation models for variational inference (TM-VI).
result TM-VI allows accurate approximation of complex posteriors in models with one parameter and works in a mean-field fashion for multi-parameter models.
Markov networks are extensively used to model complex sequential, spatial, and relational interactions in a wide range of fields. By learning the structure of independences of a domain, more accurate joint probability distributions can be obtained for inference tasks or, more directly, for interpreting the most signifi…
Increasingly complex datasets pose a number of challenges for Bayesian inference. Conventional posterior sampling based on Markov chain Monte Carlo can be too computationally intensive, is serial in nature and mixes poorly between posterior modes. Further, all models are misspecified, which brings into question the val…
Variational inference methods often focus on the problem of efficient model optimization, with little emphasis on the choice of the approximating posterior. In this paper, we review and implement the various methods that enable us to develop a rich family of approximating posteriors. We show that one particular method …
Thompson sampling (TS) is a class of algorithms for sequential decision-making, which requires maintaining a posterior distribution over a model. However, calculating exact posterior distributions is intractable for all but the simplest models. Consequently, efficient computation of an approximate posterior distributio…
We propose a novel approach to approximate complex high-dimensional posteriors using neural samplers.
problem Accurately capturing complex, multimodal, and correlated posteriors in high-dimensional spaces.
method Implicit variational inference with neural samplers and local linearisation bounds.
result Our method enables implicit distributions over tens of millions of latent variables, recovering correlations across layers in large Bayesian neural networks.
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 as regression where predictive accuracy is the quantity of interest, this couplin…
One of the core problems in variational inference is a choice of approximate posterior distribution. It is crucial to trade-off between efficient inference with simple families as mean-field models and accuracy of inference. We propose a variant of a greedy approximation of the posterior distribution with tractable bas…
The variational autoencoder (VAE) is a popular combination of deep latent variable model and accompanying variational learning technique. By using a neural inference network to approximate the model's posterior on latent variables, VAEs efficiently parameterize a lower bound on marginal data likelihood that can be opti…
Bayesian neural networks struggle with accuracy and uncertainty quantification in complex models.
problem Challenges in achieving high predictive performance and reliable uncertainty estimates in Bayesian neural networks.
method Investigates computational costs, accuracy, and uncertainty quantification in Bayesian neural networks with different inference techniques.
result Variational inference provides better uncertainty quantification than Markov chain Monte Carlo, and stacking/ensembling variational approximations can achieve similar accuracy at reduced cost.