Search Results for « Bayesian Learning »

We showcase how dropout variational inference can be applied to a large-scale deep learning model that predicts price movements from limit order books (LOBs), the canonical data source representing trading and pricing movements. We demonstrate that uncertainty information derived from posterior predictive distributions can be utilised for position sizing, avoiding unnecessary trades and improving profits. Further, we test our models by using millions of observations across several instruments and markets from the London Stock Exchange. Our results suggest that those Bayesian techniques not only deliver uncertainty information that can be used for trading but also improve predictive performance as stochastic regularisers. To the best of our knowledge, we are the first to apply Bayesian networks to LOBs.

Like all sub-fields of machine learning Bayesian Deep Learning is driven by empirical validation of its theoretical proposals. Given the many aspects of an experiment it is always possible that minor or even major experimental flaws can slip by both authors and reviewers. One of the most popular experiments used to evaluate approximate inference techniques is the regression experiment on UCI datasets. However, in this experiment, models which have been trained to convergence have often been compared with baselines trained only for a fixed number of iterations. We find that a well-established baseline, Monte Carlo dropout, when evaluated under the same experimental settings shows significant improvements. In fact, the baseline outperforms or performs competitively with methods that claimed to be superior to the very same baseline method when they were introduced. Hence, by exposing this flaw in experimental procedure, we highlight the importance of using identical experimental setups to evaluate, compare, and benchmark methods in Bayesian Deep Learning.

Some machine learning applications require continual learning - where data comes in a sequence of datasets, each is used for training and then permanently discarded. From a Bayesian perspective, continual learning seems straightforward: Given the model posterior one would simply use this as the prior for the next task. However, exact posterior evaluation is intractable with many models, especially with Bayesian neural networks (BNNs). Instead, posterior approximations are often sought. Unfortunately, when posterior approximations are used, prior-focused approaches do not succeed in evaluations designed to capture properties of realistic continual learning use cases. As an alternative to prior-focused methods, we introduce a new approximate Bayesian derivation of the continual learning loss. Our loss does not rely on the posterior from earlier tasks, and instead adapts the model itself by changing the likelihood term. We call these approaches likelihood-focused. We then combine prior- and likelihood-focused methods into one objective, tying the two views together under a single unifying framework of approximate Bayesian continual learning.

One of the main challenges of deep learning tools is their inability to capture model uncertainty. While Bayesian deep learning can be used to tackle the problem, Bayesian neural networks often require more time and computational power to train than deterministic networks. Our work explores whether fully Bayesian networks are needed to successfully capture model uncertainty. We vary the number and position of Bayesian layers in a network and compare their performance on active learning with the MNIST dataset. We found that we can fully capture the model uncertainty by using only a few Bayesian layers near the output of the network, combining the advantages of deterministic and Bayesian networks.

Decoding complex relationships among large numbers of variables with relatively few observations is one of the crucial issues in science. One approach to this problem is Gaussian graphical modeling, which describes conditional independence of variables through the presence or absence of edges in the underlying graph. In this paper, we introduce a novel and efficient Bayesian framework for Gaussian graphical model determination which is a trans-dimensional Markov Chain Monte Carlo (MCMC) approach based on a continuous-time birth-death process. We cover the theory and computational details of the method. It is easy to implement and computationally feasible for high-dimensional graphs. We show our method outperforms alternative Bayesian approaches in terms of convergence, mixing in the graph space and computing time. Unlike frequentist approaches, it gives a principled and, in practice, sensible approach for structure learning. We illustrate the efficiency of the method on a broad range of simulated data. We then apply the method on large-scale real applications from human and mammary gland gene expression studies to show its empirical usefulness. In addition, we implemented the method in the R package BDgraph which is freely available at http://CRAN.R-project.org/package=BDgraph