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Register a new userStatistical abstraction for multi-scale spatio-temporal systems
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Added by
Michalis Michaelides
Publication date
2017
fields
Biology
and research's language is
English
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Spatio-temporal systems exhibiting multi-scale behaviour are common in applications ranging from cyber-physical systems to systems biology, yet they present formidable challenges for computational modelling and analysis. Here we consider a prototypic scenario where spatially distributed agents decide their movement based on external inputs and a fast-equilibrating internal computation. We propose a generally applicable strategy based on statistically abstracting the internal system using Gaussian Processes, a powerful class of non-parametric regression techniques from Bayesian Machine Learning. We show on a running example of bacterial chemotaxis that this approach leads to accurate and much faster simulations in a variety of scenarios.
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The recent availability of digital traces generated by phone calls and online logins has significantly increased the scientific understanding of human mobility. Until now, however, limited data resolution and coverage have hindered a coherent description of human displacements across different spatial and temporal scales. Here, we characterise mobility behaviour across several orders of magnitude by analysing ~850 individuals digital traces sampled every ~16 seconds for 25 months with ~10 meters spatial resolution. We show that the distributions of distances and waiting times between consecutive locations are best described by log-normal distributions and that natural time-scales emerge from the regularity of human mobility. We point out that log-normal distributions also characterise the patterns of discovery of new places, implying that they are not a simple consequence of the routine of modern life.
Because biological processes can make different loci have different evolutionary histories, species tree estimation requires multiple loci from across the genome. While many processes can result in discord between gene trees and species trees, incomplete lineage sorting (ILS), modeled by the multi-species coalescent, is considered to be a dominant cause for gene tree heterogeneity. Coalescent-based methods have been developed to estimate species trees, many of which operate by combining estimated gene trees, and so are called summary methods. Because summary methods are generally fast, they have become very popular techniques for estimating species trees from multiple loci. However, recent studies have established that summary methods can have reduced accuracy in the presence of gene tree estimation error, and also that many biological datasets have substantial gene tree estimation error, so that summary methods may not be highly accurate on biologically realistic conditions. Mirarab et al. (Science 2014) presented the statistical binning technique to improve gene tree estimation in multi-locus analyses, and showed that it improved the accuracy of MP-EST, one of the most popular coalescent-based summary methods. Statistical binning, which uses a simple statistical test for combinability and then uses the larger sets of genes to re-calculate gene trees, has good empirical performance, but using statistical binning within a phylogenomics pipeline does not have the desirable property of being statistically consistent. We show that weighting the recalculated gene trees by the bin sizes makes statistical binning statistically consistent under the multispecies coalescent, and maintains the good empirical performance. Thus, weighted statistical binning enables highly accurate genome-scale species tree estimation, and is also statistical consistent under the multi-species coalescent model.
Atmospheric trace-gas inversion refers to any technique used to predict spatial and temporal fluxes using mole-fraction measurements and atmospheric simulations obtained from computer models. Studies to date are most often of a data-assimilation flavour, which implicitly consider univariate statistical models with the flux as the variate of interest. This univariate approach typically assumes that the flux field is either a spatially correlated Gaussian process or a spatially uncorrelated non-Gaussian process with prior expectation fixed using flux inventories (e.g., NAEI or EDGAR in Europe). Here, we extend this approach in three ways. First, we develop a bivariate model for the mole-fraction field and the flux field. The bivariate approach allows optimal prediction of both the flux field and the mole-fraction field, and it leads to significant computational savings over the univariate approach. Second, we employ a lognormal spatial process for the flux field that captures both the lognormal characteristics of the flux field (when appropriate) and its spatial dependence. Third, we propose a new, geostatistical approach to incorporate the flux inventories in our updates, such that the posterior spatial distribution of the flux field is predominantly data-driven. The approach is illustrated on a case study of methane (CH$_4$) emissions in the United Kingdom and Ireland.
Lip-reading aims to recognize speech content from videos via visual analysis of speakers lip movements. This is a challenging task due to the existence of homophemes-words which involve identical or highly similar lip movements, as well as diverse lip appearances and motion patterns among the speakers. To address these challenges, we propose a novel lip-reading model which captures not only the nuance between words but also styles of different speakers, by a multi-grained spatio-temporal modeling of the speaking process. Specifically, we first extract both frame-level fine-grained features and short-term medium-grained features by the visual front-end, which are then combined to obtain discriminative representations for words with similar phonemes. Next, a bidirectional ConvLSTM augmented with temporal attention aggregates spatio-temporal information in the entire input sequence, which is expected to be able to capture the coarse-gained patterns of each word and robust to various conditions in speaker identity, lighting conditions, and so on. By making full use of the information from different levels in a unified framework, the model is not only able to distinguish words with similar pronunciations, but also becomes robust to appearance changes. We evaluate our method on two challenging word-level lip-reading benchmarks and show the effectiveness of the proposed method, which also demonstrate the above claims.
Spatio-temporal data sets are rapidly growing in size. For example, environmental variables are measured with ever-higher resolution by increasing numbers of automated sensors mounted on satellites and aircraft. Using such data, which are typically noisy and incomplete, the goal is to obtain complete maps of the spatio-temporal process, together with proper uncertainty quantification. We focus here on real-time filtering inference in linear Gaussian state-space models. At each time point, the state is a spatial field evaluated on a very large spatial grid, making exact inference using the Kalman filter computationally infeasible. Instead, we propose a multi-resolution filter (MRF), a highly scalable and fully probabilistic filtering method that resolves spatial features at all scales. We prove that the MRF matrices exhibit a particular block-sparse multi-resolution structure that is preserved under filtering operations through time. We also discuss inference on time-varying parameters using an approximate Rao-Blackwellized particle filter, in which the integrated likelihood is computed using the MRF. We compare the MRF to existing approaches in a simulation study and a real satellite-data application.
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