P. B. Graff

Philip B Graff, Amy Y Lien, John G Baker et al.

To draw inferences about gamma-ray burst (GRB) source populations based on Swift observations, it is essential to understand the detection efficiency of the Swift burst alert telescope (BAT). This study considers the problem of modeling the Swift/BAT triggering algorithm for long GRBs, a computationally expensive procedure, and models it using machine learning algorithms. A large sample of simulated GRBs from Lien 2014 is used to train various models: random forests, boosted decision trees (with AdaBoost), support vector machines, and artificial neural networks. The best models have accuracies of $\gtrsim97\%$ ($\lesssim 3\%$ error), which is a significant improvement on a cut in GRB flux which has an accuracy of $89.6\%$ ($10.4\%$ error). These models are then used to measure the detection efficiency of Swift as a function of redshift $z$, which is used to perform Bayesian parameter estimation on the GRB rate distribution. We find a local GRB rate density of $n_0 \sim 0.48^{+0.41}_{-0.23} \ {\rm Gpc}^{-3} {\rm yr}^{-1}$ with power-law indices of $n_1 \sim 1.7^{+0.6}_{-0.5}$ and $n_2 \sim -5.9^{+5.7}_{-0.1}$ for GRBs above and below a break point of $z_1 \sim 6.8^{+2.8}_{-3.2}$. This methodology is able to improve upon earlier studies by more accurately modeling Swift detection and using this for fully Bayesian model fitting. The code used in this is analysis is publicly available online (https://github.com/PBGraff/SwiftGRB_PEanalysis).

Cetin Savkli, Jeffrey Lin, Philip Graff et al.

We present a new method of generating mixture models for data with categorical attributes. The keys to this approach are an entropy-based density metric in categorical space and annealing of high-entropy/low-density components from an initial state with many components. Pruning of low-density components using the entropy-based density allows GALILEO to consistently find high-quality clusters and the same optimal number of clusters. GALILEO has shown promising results on a range of test datasets commonly used for categorical clustering benchmarks. We demonstrate that the scaling of GALILEO is linear in the number of records in the dataset, making this method suitable for very large categorical datasets.

Cetin Savkli, J. Ryan Carr, Philip Graff et al.

The problem of categorical data analysis in high dimensions is considered. A discussion of the fundamental difficulties of probability modeling is provided, and a solution to the derivation of high dimensional probability distributions based on Bayesian learning of clique tree decomposition is presented. The main contributions of this paper are an automated determination of the optimal clique tree structure for probability modeling, the resulting derived probability distribution, and a corresponding unified approach to clustering and anomaly detection based on the probability distribution.

Philip Graff, Farhan Feroz, Michael P. Hobson et al.

We present the first public release of our generic neural network training algorithm, called SkyNet. This efficient and robust machine learning tool is able to train large and deep feed-forward neural networks, including autoencoders, for use in a wide range of supervised and unsupervised learning applications, such as regression, classification, density estimation, clustering and dimensionality reduction. SkyNet uses a `pre-training' method to obtain a set of network parameters that has empirically been shown to be close to a good solution, followed by further optimisation using a regularised variant of Newton's method, where the level of regularisation is determined and adjusted automatically; the latter uses second-order derivative information to improve convergence, but without the need to evaluate or store the full Hessian matrix, by using a fast approximate method to calculate Hessian-vector products. This combination of methods allows for the training of complicated networks that are difficult to optimise using standard backpropagation techniques. SkyNet employs convergence criteria that naturally prevent overfitting, and also includes a fast algorithm for estimating the accuracy of network outputs. The utility and flexibility of SkyNet are demonstrated by application to a number of toy problems, and to astronomical problems focusing on the recovery of structure from blurred and noisy images, the identification of gamma-ray bursters, and the compression and denoising of galaxy images. The SkyNet software, which is implemented in standard ANSI C and fully parallelised using MPI, is available at http://www.mrao.cam.ac.uk/software/skynet/.