Sentence examples for bound on the log from inspiring English sources

The basic idea of convexity-based variational inference is to make use of Jensen's inequality to obtain an adjustable lower bound on the log likelihood [13].

To handle the uncertainty of the segment label, we treat the unknown labels as the hidden variables in the lower bound on the log posterior and maximize this lower bound via an EM-like algorithm.

The maximized F is a lower bound on the log model evidence, namely the probability of the data given the model (Stephan et al. 2009).

Variational learning requires approximating the joint distribution of the model in Equation (4) by a factorising Ansatz (6) Jensen's inequality allows obtaining a lower bound on the log marginal likelihood of the DAG.

Indeed, in statistics, Bayesian model selection is based upon a free-energy bound on the log-evidence for competing models [46].

In short, variational Bayes optimizes the (negative) free-energy F as a lower bound on the log-evidence, such that maximizing F minimizes the Kullback Leibler divergence between exact and approximate posterior distributions (for details, see Friston et al. 2007; Penny et al. 2007).

This can potentially be addressed by augmenting the VB method with a more accurate approximation as done in a recent study that proposed a new VB algorithm with improved variance estimates and a tighter lower bound on the log-marginal likelihood (Papastamoulis et al., 2014a).

First we construct a lower bound on the conditional log probability of the reads R given the transcript proportions θ and the known transcriptome T : (8) where the first line follows from Jensen's inequality in a similar fashion to standard VB methods.

The objective function maximized by ReML, as shown in Friston et al. [ 2002, 2007], is identical to the (negative) variational free-energy, F. For such linear models under Gaussian assumptions, the optimized free-energy provides a tight lower bound on the marginal log-likelihood of the generative model, or its "log-evidence," In, where the model is defined fully by L and.

Below we explore different choices for fMRI priors, evaluating them quantitatively by T-tests of the negative free-energy bound on the model log-evidence, and qualitatively in terms of the optimized hyperparameters, source reconstructions, and source time courses.

In the sequel, we will establish an upper bound on the Sugeno fuzzy integral of log-convex functions.