Approximate Bayesian inference as a gauge theory
In a published paper [Sengupta, 2016], we have proposed that the brain (and other self-organized biological and artificial systems) can be characterized via the mathematical apparatus of a gauge theory. The picture that emerges from this approach suggests that any biological system (from a neuron to an organism) can be cast as resolving uncertainty about its external milieu, either by changing its internal states or its relationship to the environment. Using formal arguments, we have shown that a gauge theory for neuronal dynamics -- based on approximate Bayesian inference -- has the potential to shed new light on phenomena that have thus far eluded a formal description, such as attention and the link between action and perception. Here, we describe the technical apparatus that enables such a variational inference on manifolds. Particularly, the novel contribution of this paper is an algorithm that utlizes a Schild's ladder for parallel transport of sufficient statistics (means, covariances, etc.) on a statistical manifold.
Code (0)
등록된 구현이 없습니다.
Tasks
Bayesian InferenceVariational InferenceSimilar Papers 제목 키워드 기반
Bayesian inference as iterated random functions with applications to sequential inference in graphical models
We propose a general formalism of iterated random functions with semigroup property, under which exact and approximate Bayesian posterior updates can be viewed as specific instances. A convergence theory for iterated ran…
Bayesian InferenceChange Point DetectionPractical bounds on the error of Bayesian posterior approximations: A nonasymptotic approach
Bayesian inference typically requires the computation of an approximation to the posterior distribution. An important requirement for an approximate Bayesian inference algorithm is to output high-accuracy posterior mean …
Bayesian InferenceVariational InferenceGauged Mini-Bucket Elimination for Approximate Inference
Computing the partition function $Z$ of a discrete graphical model is a fundamental inference challenge. Since this is computationally intractable, variational approximations are often used in practice. Recently, so-call…
Gauge Equivariant Neural Networks for 2+1D U(1) Gauge Theory Simulations in Hamiltonian Formulation
Gauge Theory plays a crucial role in many areas in science, including high energy physics, condensed matter physics and quantum information science. In quantum simulations of lattice gauge theory, an important step is to…
Variational Monte CarloLoss-Calibrated Approximate Inference in Bayesian Neural Networks
Current approaches in approximate inference for Bayesian neural networks minimise the Kullback-Leibler divergence to approximate the true posterior over the weights. However, this approximation is without knowledge of th…
Autonomous DrivingSemantic Segmentation