Bayesian filtering unifies adaptive and non-adaptive neural network optimization methods

We formulate the problem of neural network optimization as Bayesian filtering, where the observations are the backpropagated gradients. While neural network optimization has previously been studied using natural gradient methods which are closely related to Bayesian inference, they were unable to recover standard optimizers such as Adam and RMSprop with a root-mean-square gradient normalizer, instead getting a mean-square normalizer. To recover the root-mean-square normalizer, we find it necessary to account for the temporal dynamics of all the other parameters as they are geing optimized. The resulting optimizer, AdaBayes, adaptively transitions between SGD-like and Adam-like behaviour, automatically recovers AdamW, a state of the art variant of Adam with decoupled weight decay, and has generalisation performance competitive with SGD

Dynamic Bayesian Combination of Multiple Imperfect Classifiers

Classifier combination methods need to make best use of the outputs of multiple, imperfect classifiers to enable higher accuracy classifications. In many situations, such as when human decisions need to be combined, the base decisions can vary enormously in reliability. A Bayesian approach to such uncertain combination allows us to infer the differences in performance between individuals and to incorporate any available prior knowledge about their abilities when training data is sparse. In this paper we explore Bayesian classifier combination, using the computationally efficient framework of variational Bayesian inference. We apply the approach to real data from a large citizen science project, Galaxy Zoo Supernovae, and show that our method far outperforms other established approaches to imperfect decision combination. We go on to analyse the putative community structure of the decision makers, based on their inferred decision making strategies, and show that natural groupings are formed. Finally we present a dynamic Bayesian classifier combination approach and investigate the changes in base classifier performance over time.Comment: 35 pages, 12 figure

Enhanced particle PHD filtering for multiple human tracking

PhD ThesisVideo-based single human tracking has found wide application but multiple human tracking is more challenging and enhanced processing techniques are required to estimate the positions and number of targets in each frame. In this thesis, the particle probability hypothesis density (PHD) lter is therefore the focus due to its ability to estimate both localization and cardinality information related to multiple human targets. To improve the tracking performance of the particle PHD lter, a number of enhancements are proposed. The Student's-t distribution is employed within the state and measurement models of the PHD lter to replace the Gaussian distribution because of its heavier tails, and thereby better predict particles with larger amplitudes. Moreover, the variational Bayesian approach is utilized to estimate the relationship between the measurement noise covariance matrix and the state model, and a joint multi-dimensioned Student's-t distribution is exploited. In order to obtain more observable measurements, a backward retrodiction step is employed to increase the measurement set, building upon the concept of a smoothing algorithm. To make further improvement, an adaptive step is used to combine the forward ltering and backward retrodiction ltering operations through the similarities of measurements achieved over discrete time. As such, the errors in the delayed measurements generated by false alarms and environment noise are avoided. In the nal work, information describing human behaviour is employed iv Abstract v to aid particle sampling in the prediction step of the particle PHD lter, which is captured in a social force model. A novel social force model is proposed based on the exponential function. Furthermore, a Markov Chain Monte Carlo (MCMC) step is utilized to resample the predicted particles, and the acceptance ratio is calculated by the results from the social force model to achieve more robust prediction. Then, a one class support vector machine (OCSVM) is applied in the measurement model of the PHD lter, trained on human features, to mitigate noise from the environment and to achieve better tracking performance. The proposed improvements of the particle PHD lters are evaluated with benchmark datasets such as the CAVIAR, PETS2009 and TUD datasets and assessed with quantitative and global evaluation measures, and are compared with state-of-the-art techniques to con rm the improvement of multiple human tracking performance