Noisy Monte Carlo: convergence of Markov chains with approximate transition kernels

Monte Carlo algorithms often aim to draw from a distribution π by simulating a Markov chain with transition kernel P such that π is invariant under P. However, there are many situations for which it is impractical or impossible to draw from the transition kernel P. For instance, this is the case with massive datasets, where is it prohibitively expensive to calculate the likelihood and is also the case for intractable likelihood models arising from, for example, Gibbs random fields, such as those found in spatial statistics and network analysis. A natural approach in these cases is to replace P by an approximation Pˆ. Using theory from the stability of Markov chains we explore a variety of situations where it is possible to quantify how ’close’ the chain given by the transition kernel Pˆ is to the chain given by P . We apply these results to several examples from spatial statistics and network analysis.

Fractional order and non-linear system identification algorithms for biomedical applications

We discuss the modelling of dielectric responses of amorphous biological samples. Such samples are commonly encountered in impedance spectroscopy studies as well as in UV, IR, optical and THz transient spectroscopy experiments and in pump-probe studies. In many occasions, the samples may display quenched absorption bands. A systems identification framework may be developed to provide parsimonious representations of such responses. To achieve this, it is appropriate to augment the standard models found in the identification literature to incorporate fractional order dynamics. Extensions of models using the forward shift operator, state space models as well as their non-linear Hammerstein-Wiener counterpart models are highlighted. We also discuss the need to extend the theory of electromagnetically excited networks which can account for fractional order behaviour in the non-linear regime by incorporating nonlinear elements to account for the observed non-linearities. The proposed approach leads to the development of a range of new chemometrics tools for biomedical data analysis and classification.

Weighted alpha-rate dominating sets in social networks

We are looking into variants of a domination set problem in social networks. While randomised algorithms for solving the minimum weighted domination set problem and the minimum alpha and alpha-rate domination problem on simple graphs are already present in the literature, we propose here a randomised algorithm for the minimum weighted alpha-rate domination set problem which is, to the best of our knowledge, the first such algorithm. A theoretical approximation bound based on a simple randomised rounding technique is given. The algorithm is implemented in Python and applied to a UK Twitter mentions networks using a measure of individuals’ influence (klout) as weights. We argue that the weights of vertices could be interpreted as the costs of getting those individuals on board for a campaign or a behaviour change intervention. The minimum weighted alpha-rate dominating set problem can therefore be seen as finding a set that minimises the total cost and each individual in a network has at least alpha percentage of its neighbours in the chosen set. We also test our algorithm on generated graphs with several thousand vertices and edges. Our results on this real-life Twitter networks and generated graphs show that the implementation is reasonably efficient and thus can be used for real-life applications when creating social network based interventions, designing social media campaigns and potentially improving users’ social media experience.

Stochastic climate theory and modeling

Stochastic methods are a crucial area in contemporary climate research and are increasingly being used in comprehensive weather and climate prediction models as well as reduced order climate models. Stochastic methods are used as subgrid-scale parameterizations (SSPs) as well as for model error representation, uncertainty quantification, data assimilation, and ensemble prediction. The need to use stochastic approaches in weather and climate models arises because we still cannot resolve all necessary processes and scales in comprehensive numerical weather and climate prediction models. In many practical applications one is mainly interested in the largest and potentially predictable scales and not necessarily in the small and fast scales. For instance, reduced order models can simulate and predict large-scale modes. Statistical mechanics and dynamical systems theory suggest that in reduced order models the impact of unresolved degrees of freedom can be represented by suitable combinations of deterministic and stochastic components and non-Markovian (memory) terms. Stochastic approaches in numerical weather and climate prediction models also lead to the reduction of model biases. Hence, there is a clear need for systematic stochastic approaches in weather and climate modeling. In this review, we present evidence for stochastic effects in laboratory experiments. Then we provide an overview of stochastic climate theory from an applied mathematics perspective. We also survey the current use of stochastic methods in comprehensive weather and climate prediction models and show that stochastic parameterizations have the potential to remedy many of the current biases in these comprehensive models.

Standardized evaluation of algorithms for computer-aided diagnosis of dementia based on structural MRI: The CADDementia challenge

Algorithms for computer-aided diagnosis of dementia based on structural MRI have demonstrated high performance in the literature, but are difficult to compare as different data sets and methodology were used for evaluation. In addition, it is unclear how the algorithms would perform on previously unseen data, and thus, how they would perform in clinical practice when there is no real opportunity to adapt the algorithm to the data at hand. To address these comparability, generalizability and clinical applicability issues, we organized a grand challenge that aimed to objectively compare algorithms based on a clinically representative multi-center data set. Using clinical practice as the starting point, the goal was to reproduce the clinical diagnosis. Therefore, we evaluated algorithms for multi-class classification of three diagnostic groups: patients with probable Alzheimer's disease, patients with mild cognitive impairment and healthy controls. The diagnosis based on clinical criteria was used as reference standard, as it was the best available reference despite its known limitations. For evaluation, a previously unseen test set was used consisting of 354 T1-weighted MRI scans with the diagnoses blinded. Fifteen research teams participated with a total of 29 algorithms. The algorithms were trained on a small training set (n = 30) and optionally on data from other sources (e.g., the Alzheimer's Disease Neuroimaging Initiative, the Australian Imaging Biomarkers and Lifestyle flagship study of aging). The best performing algorithm yielded an accuracy of 63.0% and an area under the receiver-operating-characteristic curve (AUC) of 78.8%. In general, the best performances were achieved using feature extraction based on voxel-based morphometry or a combination of features that included volume, cortical thickness, shape and intensity. The challenge is open for new submissions via the web-based framework: http://caddementia.grand-challenge.org.

Rapid preconditioning of data for accelerating convex hull algorithms

Given a dataset of two-dimensional points in the plane with integer coordinates, the method proposed reduces a set of n points down to a set of s points s ≤ n, such that the convex hull on the set of s points is the same as the convex hull of the original set of n points. The method is O(n). It helps any convex hull algorithm run faster. The empirical analysis of a practical case shows a percentage reduction in points of over 98%, that is reflected as a faster computation with a speedup factor of at least 4.

Distributed parallelization of greedy Mobile Network Optimization algorithms

The Mobile Network Optimization (MNO) technologies have advanced at a tremendous pace in recent years. And the Dynamic Network Optimization (DNO) concept emerged years ago, aimed to continuously optimize the network in response to variations in network traffic and conditions. Yet, DNO development is still at its infancy, mainly hindered by a significant bottleneck of the lengthy optimization runtime. This paper identifies parallelism in greedy MNO algorithms and presents an advanced distributed parallel solution. The solution is designed, implemented and applied to real-life projects whose results yield a significant, highly scalable and nearly linear speedup up to 6.9 and 14.5 on distributed 8-core and 16-core systems respectively. Meanwhile, optimization outputs exhibit self-consistency and high precision compared to their sequential counterpart. This is a milestone in realizing the DNO. Further, the techniques may be applied to similar greedy optimization algorithm based applications.

Asynchronous distributed parallelization of mobile network optimization algorithms

It has been years since the introduction of the Dynamic Network Optimization (DNO) concept, yet the DNO development is still at its infant stage, largely due to a lack of breakthrough in minimizing the lengthy optimization runtime. Our previous work, a distributed parallel solution, has achieved a significant speed gain. To cater for the increased optimization complexity pressed by the uptake of smartphones and tablets, however, this paper examines the potential areas for further improvement and presents a novel asynchronous distributed parallel design that minimizes the inter-process communications. The new approach is implemented and applied to real-life projects whose results demonstrate an augmented acceleration of 7.5 times on a 16-core distributed system compared to 6.1 of our previous solution. Moreover, there is no degradation in the optimization outcome. This is a solid sprint towards the realization of DNO.

Advances in the stochastic modelling of satellite-derived rainfall estimates using a sparse calibration dataset

As satellite technology develops, satellite rainfall estimates are likely to become ever more important in the world of food security. It is therefore vital to be able to identify the uncertainty of such estimates and for end users to be able to use this information in a meaningful way. This paper presents new developments in the methodology of simulating satellite rainfall ensembles from thermal infrared satellite data. Although the basic sequential simulation methodology has been developed in previous studies, it was not suitable for use in regions with more complex terrain and limited calibration data. Developments in this work include the creation of a multithreshold, multizone calibration procedure, plus investigations into the causes of an overestimation of low rainfall amounts and the best way to take into account clustered calibration data. A case study of the Ethiopian highlands has been used as an illustration.

Reducing noise associated with the Monte Carlo Independent Column Approximation for weather forecasting models

The Monte Carlo Independent Column Approximation (McICA) is a flexible method for representing subgrid-scale cloud inhomogeneity in radiative transfer schemes. It does, however, introduce conditional random errors but these have been shown to have little effect on climate simulations, where spatial and temporal scales of interest are large enough for effects of noise to be averaged out. This article considers the effect of McICA noise on a numerical weather prediction (NWP) model, where the time and spatial scales of interest are much closer to those at which the errors manifest themselves; this, as we show, means that noise is more significant. We suggest methods for efficiently reducing the magnitude of McICA noise and test these methods in a global NWP version of the UK Met Office Unified Model (MetUM). The resultant errors are put into context by comparison with errors due to the widely used assumption of maximum-random-overlap of plane-parallel homogeneous cloud. For a simple implementation of the McICA scheme, forecasts of near-surface temperature are found to be worse than those obtained using the plane-parallel, maximum-random-overlap representation of clouds. However, by applying the methods suggested in this article, we can reduce noise enough to give forecasts of near-surface temperature that are an improvement on the plane-parallel maximum-random-overlap forecasts. We conclude that the McICA scheme can be used to improve the representation of clouds in NWP models, with the provision that the associated noise is sufficiently small.

Equation for the microwave backscatter cross section of aggregate snowflakes using the self-similar Rayleigh–Gans approximation

In this paper an equation is derived for the mean backscatter cross section of an ensemble of snowflakes at centimeter and millimeter wavelengths. It uses the Rayleigh–Gans approximation, which has previously been found to be applicable at these wavelengths due to the low density of snow aggregates. Although the internal structure of an individual snowflake is random and unpredictable, the authors find from simulations of the aggregation process that their structure is “self-similar” and can be described by a power law. This enables an analytic expression to be derived for the backscatter cross section of an ensemble of particles as a function of their maximum dimension in the direction of propagation of the radiation, the volume of ice they contain, a variable describing their mean shape, and two variables describing the shape of the power spectrum. The exponent of the power law is found to be −. In the case of 1-cm snowflakes observed by a 3.2-mm-wavelength radar, the backscatter is 40–100 times larger than that of a homogeneous ice–air spheroid with the same mass, size, and aspect ratio.

Efficiency of evolutionary algorithms in water network pipe sizing

The pipe sizing of water networks via evolutionary algorithms is of great interest because it allows the selection of alternative economical solutions that meet a set of design requirements. However, available evolutionary methods are numerous, and methodologies to compare the performance of these methods beyond obtaining a minimal solution for a given problem are currently lacking. A methodology to compare algorithms based on an efficiency rate (E) is presented here and applied to the pipe-sizing problem of four medium-sized benchmark networks (Hanoi, New York Tunnel, GoYang and R-9 Joao Pessoa). E numerically determines the performance of a given algorithm while also considering the quality of the obtained solution and the required computational effort. From the wide range of available evolutionary algorithms, four algorithms were selected to implement the methodology: a PseudoGenetic Algorithm (PGA), Particle Swarm Optimization (PSO), a Harmony Search and a modified Shuffled Frog Leaping Algorithm (SFLA). After more than 500,000 simulations, a statistical analysis was performed based on the specific parameters each algorithm requires to operate, and finally, E was analyzed for each network and algorithm. The efficiency measure indicated that PGA is the most efficient algorithm for problems of greater complexity and that HS is the most efficient algorithm for less complex problems. However, the main contribution of this work is that the proposed efficiency ratio provides a neutral strategy to compare optimization algorithms and may be useful in the future to select the most appropriate algorithm for different types of optimization problems.