Search Results for « Deep Variational Bayes Filters »

Variational Bayes (VB) replaces the posterior with the closest member of a tractable family, maximizing the evidence lower bound. The bound is slack by exactly the Kullback-Leibler divergence between surrogate and posterior-an information gap that is never observed and never closed by computation-while the mean-field surrogate that makes VB tractable removes posterior correlation by construction. We argue this compromise is now an anachronism, because scalable full Bayes is available through two complementary routes. The first is conditional Gaussianization: many likelihoods and priors are mean-scale mixtures of normals, so that conditional on a latent variable every full conditional is exactly Gaussian. Pólya-Gamma augmentation, support-vector-machine augmentation, the quantile asymmetric-Laplace mixture, and global-local shrinkage are instances of one envelopeand-duality construction, with conjugate, parallel, exact Gibbs samplers. The second is the Noise Outsourcing Theorem: the posterior is a measurable map θ = f (y, ε) of independent noise, and f is learned by simulation and supervised deep learning as an implicit quantile network-one forward pass per draw, with all dependence intact, no density, no Markov chain, and likelihood-free. The theorem applies in time, giving a weight-free generative particle filter. Sparsity and MAP estimation follow from the same machinery. Three experiments quantify the contrast: mean-field VB destroys a posterior correlation of-0.92, deflates standard deviations to 38%, opens a 0.93-nat gap, and drops 95% coverage to 58%, while exact inference is calibrated; a learned generative map recovers bounded, skewed, and bimodal posteriors that a Gaussian surrogate cannot represent. 

<div>In this work, we propose a novel extended target tracking algorithm, which is capable of representing a target or a group of targets with multiple ellipses. Each ellipse is modeled by an unknown symmetric positive-definite random matrix. The proposed model requires solving two challenging problems. First, the data association problem between the measurements and the sub-objects. Second, the inference problem that involves non-conjugate priors and likelihoods which needs to be solved within the recursive filtering framework. We utilize the variational Bayes inference method to solve the association problem and to approximate the intractable true posterior. The performance of the proposed solution is demonstrated in simulations and real-data experiments. The results show that our method outperforms the state-of-the-art methods in accuracy with lower computational complexity.</div>

The Variational Bayesian method (VB) is used to solve the probability distributions of latent variables with the minimum free energy criterion. This criterion is not easy to understand, and the computation is complex. For these reasons, this paper proposes the Semantic Variational Bayes' method (SVB). The Semantic Information Theory the author previously proposed extends the rate-distortion function R(D) to the rate-fidelity function R(G), where R is the minimum mutual information for given semantic mutual information G. SVB came from the parameter solution of R(G), where the variational and iterative methods originated from Shannon et al.'s research on the rate-distortion function. The constraint functions SVB uses include likelihood, truth, membership, similarity, and distortion functions. SVB uses the maximum information efficiency (G/R) criterion, including the maximum semantic information criterion for optimizing model parameters and the minimum mutual information criterion for optimizing the Shannon channel. For the same tasks, SVB is computationally simpler than VB. The computational experiments in the paper include 1) using a mixture model as an example to show that the mixture model converges as G/R increases; 2) demonstrating the application of SVB in data compression with a group of error ranges as the constraint; 3) illustrating how the semantic information measure and SVB can be used for maximum entropy control and reinforcement learning in control tasks with given range constraints, providing numerical evidence for balancing control's purposiveness and efficiency. Further research is needed to apply SVB to neural networks and deep learning.