arXiv subjects

Steve Kroon

Publications and source records attributed to Steve Kroon.

14 recordsLinked to original sources

arXiv2022

Graphical Residual Flows

Graphical flows add further structure to normalizing flows by encoding non-trivial variable dependencies. Previous graphical flow models have focused primarily on a single flow direction: the normalizing direction for density estimation, or the generative direction for inference. However, to use a single flow to perform tasks in both directions, the model must exhibit stable and efficient flow inversion. This work introduces graphical residual flows, a graphical flow based on invertible residual networks. Our approach to incorporating dependency information in the flow, means that we are able to calculate the Jacobian determinant of these flows exactly. Our experiments confirm that graphical residual flows provide stable and accurate inversion that is also more time-efficient than alternative flows with similar task performance. Furthermore, our model provides performance competitive with other graphical flows for both density estimation and inference tasks.

cs.LG↗

arXiv2022

SIReN-VAE: Leveraging Flows and Amortized Inference for Bayesian Networks

Initial work on variational autoencoders assumed independent latent variables with simple distributions. Subsequent work has explored incorporating more complex distributions and dependency structures: including normalizing flows in the encoder network allows latent variables to entangle non-linearly, creating a richer class of distributions for the approximate posterior, and stacking layers of latent variables allows more complex priors to be specified for the generative model. This work explores incorporating arbitrary dependency structures, as specified by Bayesian networks, into VAEs. This is achieved by extending both the prior and inference network with graphical residual flows - residual flows that encode conditional independence by masking the weight matrices of the flow's residual blocks. We compare our model's performance on several synthetic datasets and show its potential in data-sparse settings.

cs.LG↗

arXiv2021

Distributed Identification of Central Nodes with Less Communication

This paper is concerned with distributed detection of central nodes in complex networks using closeness centrality. Closeness centrality plays an essential role in network analysis. Evaluating closeness centrality exactly requires complete knowledge of the network; for large networks, this may be inefficient, so closeness centrality should be approximated. Distributed tasks such as leader election can make effective use of centrality information for highly central nodes, but complete network information is not locally available. This paper refines a distributed centrality computation algorithm by You et al. [24] by pruning nodes which are almost certainly not most central. For example, in a large network, leave nodes can not play a central role. This leads to a reduction in the number of messages exchanged to determine the centrality of the remaining nodes. Our results show that our approach reduces the number of messages for networks which contain many prunable nodes. Our results also show that reducing the number of messages may

cs.SI↗

arXiv2020

Performance-Agnostic Fusion of Probabilistic Classifier Outputs

We propose a method for combining probabilistic outputs of classifiers to make a single consensus class prediction when no further information about the individual classifiers is available, beyond that they have been trained for the same task. The lack of relevant prior information rules out typical applications of Bayesian or Dempster-Shafer methods, and the default approach here would be methods based on the principle of indifference, such as the sum or product rule, which essentially weight all classifiers equally. In contrast, our approach considers the diversity between the outputs of the various classifiers, iteratively updating predictions based on their correspondence with other predictions until the predictions converge to a consensus decision. The intuition behind this approach is that classifiers trained for the same task should typically exhibit regularities in their outputs on a new task; the predictions of classifiers which differ significantly from those of others are thus given less credence using our approach. The approach implicitly assumes a symmetric loss function, in that the relative cost of various prediction errors are not taken into account. Performance of the model is demonstrated on different benchmark datasets. Our proposed method works well in situations where accuracy is the performance metric; however, it does not output calibrated probabilities, so it is not suitable in situations where such probabilities are required for further processing.

cs.LG↗

arXiv2020

If dropout limits trainable depth, does critical initialisation still matter? A large-scale statistical analysis on ReLU networks

Recent work in signal propagation theory has shown that dropout limits the depth to which information can propagate through a neural network. In this paper, we investigate the effect of initialisation on training speed and generalisation for ReLU networks within this depth limit. We ask the following research question: given that critical initialisation is crucial for training at large depth, if dropout limits the depth at which networks are trainable, does initialising critically still matter? We conduct a large-scale controlled experiment, and perform a statistical analysis of over $12000$ trained networks. We find that (1) trainable networks show no statistically significant difference in performance over a wide range of non-critical initialisations; (2) for initialisations that show a statistically significant difference, the net effect on performance is small; (3) only extreme initialisations (very small or very large) perform worse than criticality. These findings also apply to standard ReLU networks of moderate depth as a special case of zero dropout. Our results therefore suggest that, in the shallow-to-moderate depth setting, critical initialisation provides zero performance gains when compared to off-critical initialisations and that searching for off-critical initialisations that might improve training speed or generalisation, is likely to be a fruitless endeavour.

stat.ML↗

arXiv2019

Stochastic Gradient Annealed Importance Sampling for Efficient Online Marginal Likelihood Estimation

We consider estimating the marginal likelihood in settings with independent and identically distributed (i.i.d.) data. We propose estimating the predictive distributions in a sequential factorization of the marginal likelihood in such settings by using stochastic gradient Markov Chain Monte Carlo techniques. This approach is far more efficient than traditional marginal likelihood estimation techniques such as nested sampling and annealed importance sampling due to its use of mini-batches to approximate the likelihood. Stability of the estimates is provided by an adaptive annealing schedule. The resulting stochastic gradient annealed importance sampling (SGAIS) technique, which is the key contribution of our paper, enables us to estimate the marginal likelihood of a number of models considerably faster than traditional approaches, with no noticeable loss of accuracy. An important benefit of our approach is that the marginal likelihood is calculated in an online fashion as data becomes available, allowing the estimates to be used for applications such as online weighted model combination.

stat.ML↗

arXiv2019

Stabilising priors for robust Bayesian deep learning

Bayesian neural networks (BNNs) have developed into useful tools for probabilistic modelling due to recent advances in variational inference enabling large scale BNNs. However, BNNs remain brittle and hard to train, especially: (1) when using deep architectures consisting of many hidden layers and (2) in situations with large weight variances. We use signal propagation theory to quantify these challenges and propose self-stabilising priors. This is achieved by a reformulation of the ELBO to allow the prior to influence network signal propagation. Then, we develop a stabilising prior, where the distributional parameters of the prior are adjusted before each forward pass to ensure stability of the propagating signal. This stabilised signal propagation leads to improved convergence and robustness making it possible to train deeper networks and in more noisy settings.

cs.LG↗

arXiv2019

On the expected behaviour of noise regularised deep neural networks as Gaussian processes

Recent work has established the equivalence between deep neural networks and Gaussian processes (GPs), resulting in so-called neural network Gaussian processes (NNGPs). The behaviour of these models depends on the initialisation of the corresponding network. In this work, we consider the impact of noise regularisation (e.g. dropout) on NNGPs, and relate their behaviour to signal propagation theory in noise regularised deep neural networks. For ReLU activations, we find that the best performing NNGPs have kernel parameters that correspond to a recently proposed initialisation scheme for noise regularised ReLU networks. In addition, we show how the noise influences the covariance matrix of the NNGP, producing a stronger prior towards simple functions away from the training points. We verify our theoretical findings with experiments on MNIST and CIFAR-10 as well as on synthetic data.

cs.LG↗

arXiv2019

A Coordinated Search Strategy for Multiple Solitary Robots: An Extension

The problem of coordination without a priori information about the environment is important in robotics. Applications vary from formation control to search and rescue. This paper considers the problem of search by a group of solitary robots: self-interested robots without a priori knowledge about each other, and with restricted communication capacity. When the capacity of robots to communicate is limited, they may obliviously search in overlapping regions (i.e. be subject to interference). Interference hinders robot progress, and strategies have been proposed in the literature to mitigate interference [1], [2]. Interaction of solitary robots has attracted much interest in robotics, but the problem of mitigating interference when time for search is limited remains an important area of research. We propose a coordination strategy based on the method of cellular decomposition [3] where we employ the concept of soft obstacles: a robot considers cells assigned to other robots as obstacles. The performance of the proposed strategy is demonstrated by means of simulation experiments. Simulations indicate the utility of the strategy in situations where a known upper bound on the search time precludes search of the entire environment.

cs.RO↗

arXiv2018

Critical initialisation for deep signal propagation in noisy rectifier neural networks

Stochastic regularisation is an important weapon in the arsenal of a deep learning practitioner. However, despite recent theoretical advances, our understanding of how noise influences signal propagation in deep neural networks remains limited. By extending recent work based on mean field theory, we develop a new framework for signal propagation in stochastic regularised neural networks. Our noisy signal propagation theory can incorporate several common noise distributions, including additive and multiplicative Gaussian noise as well as dropout. We use this framework to investigate initialisation strategies for noisy ReLU networks. We show that no critical initialisation strategy exists using additive noise, with signal propagation exploding regardless of the selected noise distribution. For multiplicative noise (e.g. dropout), we identify alternative critical initialisation strategies that depend on the second moment of the noise distribution. Simulations and experiments on real-world data confirm that our proposed initialisation is able to stably propagate signals in deep networks, while using an initialisation disregarding noise fails to do so. Furthermore, we analyse correlation dynamics between inputs. Stronger noise regularisation is shown to reduce the depth to which discriminatory information about the inputs to a noisy ReLU network is able to propagate, even when initialised at criticality. We support our theoretical predictions for these trainable depths with simulations, as well as with experiments on MNIST and CIFAR-10

stat.ML↗

arXiv2018

Learning Dynamics of Linear Denoising Autoencoders

Denoising autoencoders (DAEs) have proven useful for unsupervised representation learning, but a thorough theoretical understanding is still lacking of how the input noise influences learning. Here we develop theory for how noise influences learning in DAEs. By focusing on linear DAEs, we are able to derive analytic expressions that exactly describe their learning dynamics. We verify our theoretical predictions with simulations as well as experiments on MNIST and CIFAR-10. The theory illustrates how, when tuned correctly, noise allows DAEs to ignore low variance directions in the inputs while learning to reconstruct them. Furthermore, in a comparison of the learning dynamics of DAEs to standard regularised autoencoders, we show that noise has a similar regularisation effect to weight decay, but with faster training dynamics. We also show that our theoretical predictions approximate learning dynamics on real-world data and qualitatively match observed dynamics in nonlinear DAEs.

stat.ML↗

arXiv2017

No evidence for extensions to the standard cosmological model

We compute the Bayesian Evidence for models considered in the main analysis of Planck cosmic microwave background data. By utilising carefully-defined nearest-neighbour distances in parameter space, we reuse the Monte Carlo Markov Chains already produced for parameter inference to compute Bayes factors $B$ for many different model-dataset combinations. Standard 6-parameter flat $Λ$CDM model is favoured over all other models considered, with curvature being mildly favoured only when CMB lensing is not included. Many alternative models are strongly disfavoured by the data, including primordial correlated isocurvature models ($\ln B=-7.8$), non-zero scalar-to-tensor ratio ($\ln B=-4.3$), running of the spectral index ($\ln B = -4.7$), curvature ($\ln B=-3.6$), non-standard numbers of neutrinos ($\ln B=-3.1$), non-standard neutrino masses ($\ln B=-3.2$), non-standard lensing potential ($\ln B=-4.6$), evolving dark energy ($\ln B=-3.2$), sterile neutrinos ($\ln B=-6.9$), and extra sterile neutrinos with a non-zero scalar-to-tensor ratio ($\ln B=-10.8$). Other models are less strongly disfavoured with respect to flat $Λ$CDM. As with all analyses based on Bayesian Evidence, the final numbers depend on the widths of the parameter priors. We adopt the priors used in the Planck analysis, while performing a prior sensitivity analysis. Our quantitative conclusion is that extensions beyond the standard cosmological model are disfavoured by Planck data. Only when newer Hubble constant measurements are included does $Λ$CDM become disfavoured, and only mildly, compared with a dynamical dark energy model ($\ln B\sim +2$).

astro-ph.CO↗

arXiv2017

Marginal Likelihoods from Monte Carlo Markov Chains

In this paper, we present a method for computing the marginal likelihood, also known as the model likelihood or Bayesian evidence, from Markov Chain Monte Carlo (MCMC), or other sampled posterior distributions. In order to do this, one needs to be able to estimate the density of points in parameter space, and this can be challenging in high numbers of dimensions. Here we present a Bayesian analysis, where we obtain the posterior for the marginal likelihood, using $k$th nearest-neighbour distances in parameter space, using the Mahalanobis distance metric, under the assumption that the points in the chain (thinned if required) are independent. We generalise the algorithm to apply to importance-sampled chains, where each point is assigned a weight. We illustrate this with an idealised posterior of known form with an analytic marginal likelihood, and show that for chains of length $\sim 10^5$ points, the technique is effective for parameter spaces with up to $\sim 20$ dimensions. We also argue that $k=1$ is the optimal choice, and discuss failure modes for the algorithm. In a companion paper (Heavens et al. 2017) we apply the technique to the main MCMC chains from the 2015 Planck analysis of cosmic background radiation data, to infer that quantitatively the simplest 6-parameter flat $Λ$CDM standard model of cosmology is preferred over all extensions considered.

stat.CO↗

arXiv2013

Binary Jumbled String Matching for Highly Run-Length Compressible Texts

The Binary Jumbled String Matching problem is defined as: Given a string $s$ over $\{a,b\}$ of length $n$ and a query $(x,y)$, with $x,y$ non-negative integers, decide whether $s$ has a substring $t$ with exactly $x$ $a$'s and $y$ $b$'s. Previous solutions created an index of size O(n) in a pre-processing step, which was then used to answer queries in constant time. The fastest algorithms for construction of this index have running time $O(n^2/\log n)$ [Burcsi et al., FUN 2010; Moosa and Rahman, IPL 2010], or $O(n^2/\log^2 n)$ in the word-RAM model [Moosa and Rahman, JDA 2012]. We propose an index constructed directly from the run-length encoding of $s$. The construction time of our index is $O(n+ρ^2\log ρ)$, where O(n) is the time for computing the run-length encoding of $s$ and $ρ$ is the length of this encoding---this is no worse than previous solutions if $ρ= O(n/\log n)$ and better if $ρ= o(n/\log n)$. Our index $L$ can be queried in $O(\log ρ)$ time. While $|L|= O(\min(n, ρ^{2}))$ in the worst case, preliminary investigations have indicated that $|L|$ may often be close to $ρ$. Furthermore, the algorithm for constructing the index is conceptually simple and easy to implement. In an attempt to shed light on the structure and size of our index, we characterize it in terms of the prefix normal forms of $s$ introduced in [Fici and Lipták, DLT 2011].

cs.DS↗