arXiv subjects

Mauricio Barahona

Publications and source records attributed to Mauricio Barahona.

At least 55 records · Page 3Linked to original sources

arXiv2021

Geometric graphs from data to aid classification tasks with graph convolutional networks

Traditional classification tasks learn to assign samples to given classes based solely on sample features. This paradigm is evolving to include other sources of information, such as known relations between samples. Here we show that, even if additional relational information is not available in the data set, one can improve classification by constructing geometric graphs from the features themselves, and using them within a Graph Convolutional Network. The improvement in classification accuracy is maximized by graphs that capture sample similarity with relatively low edge density. We show that such feature-derived graphs increase the alignment of the data to the ground truth while improving class separation. We also demonstrate that the graphs can be made more efficient using spectral sparsification, which reduces the number of edges while still improving classification performance. We illustrate our findings using synthetic and real-world data sets from various scientific domains.

cs.LG↗

arXiv2021

Similarity measure for sparse time course data based on Gaussian processes

We propose a similarity measure for sparsely sampled time course data in the form of a log-likelihood ratio of Gaussian processes (GP). The proposed GP similarity is similar to a Bayes factor and provides enhanced robustness to noise in sparse time series, such as those found in various biological settings, e.g., gene transcriptomics. We show that the GP measure is equivalent to the Euclidean distance when the noise variance in the GP is negligible compared to the noise variance of the signal. Our numerical experiments on both synthetic and real data show improved performance of the GP similarity when used in conjunction with two distance-based clustering methods.

cs.LG↗

arXiv2021

Quantifying the Alignment of Graph and Features in Deep Learning

We show that the classification performance of graph convolutional networks (GCNs) is related to the alignment between features, graph, and ground truth, which we quantify using a subspace alignment measure (SAM) corresponding to the Frobenius norm of the matrix of pairwise chordal distances between three subspaces associated with features, graph, and ground truth. The proposed measure is based on the principal angles between subspaces and has both spectral and geometrical interpretations. We showcase the relationship between the SAM and the classification performance through the study of limiting cases of GCNs and systematic randomizations of both features and graph structure applied to a constructive example and several examples of citation networks of different origins. The analysis also reveals the relative importance of the graph and features for classification purposes.

cs.LG↗

arXiv2021

Kernel Two-Sample and Independence Tests for Non-Stationary Random Processes

Two-sample and independence tests with the kernel-based MMD and HSIC have shown remarkable results on i.i.d. data and stationary random processes. However, these statistics are not directly applicable to non-stationary random processes, a prevalent form of data in many scientific disciplines. In this work, we extend the application of MMD and HSIC to non-stationary settings by assuming access to independent realisations of the underlying random process. These realisations - in the form of non-stationary time-series measured on the same temporal grid - can then be viewed as i.i.d. samples from a multivariate probability distribution, to which MMD and HSIC can be applied. We further show how to choose suitable kernels over these high-dimensional spaces by maximising the estimated test power with respect to the kernel hyper-parameters. In experiments on synthetic data, we demonstrate superior performance of our proposed approaches in terms of test power when compared to current state-of-the-art functional or multivariate two-sample and independence tests. Finally, we employ our methods on a real socio-economic dataset as an example application.

stat.ME↗

arXiv2020

Opportunities at the interface of network science and metabolic modelling

Metabolism plays a central role in cell physiology because it provides the molecular machinery for growth. At the genome-scale, metabolism is made up of thousands of reactions interacting with one another. Untangling this complexity is key to understand how cells respond to genetic, environmental, or therapeutic perturbations. Here we discuss the roles of two complementary strategies for the analysis of genome-scale metabolic models: Flux Balance Analysis (FBA) and network science. While FBA estimates metabolic flux on the basis of an optimisation principle, network approaches reveal emergent properties of the global metabolic connectivity. We highlight how the integration of both approaches promises to deliver insights on the structure and function of metabolic systems with wide-ranging implications in discovery science, precision medicine and industrial biotechnology.

q-bio.MN↗

arXiv2020

Approximations of countably-infinite linear programs over bounded measure spaces

We study a class of countably-infinite-dimensional linear programs (CILPs) whose feasible sets are bounded subsets of appropriately defined spaces of measures. The optimal value, optimal points, and minimal points of these CILPs can be approximated by solving finite-dimensional linear programs. We show how to construct finite-dimensional programs that lead to approximations with easy-to-evaluate error bounds, and we prove that the errors converge to zero as the size of the finite-dimensional programs approaches that of the original problem. We discuss the use of our methods in the computation of the stationary distributions, occupation measures, and exit distributions of Markov~chains.

math.OC↗

arXiv2020

Graph-based Topic Extraction from Vector Embeddings of Text Documents: Application to a Corpus of News Articles

Production of news content is growing at an astonishing rate. To help manage and monitor the sheer amount of text, there is an increasing need to develop efficient methods that can provide insights into emerging content areas, and stratify unstructured corpora of text into `topics' that stem intrinsically from content similarity. Here we present an unsupervised framework that brings together powerful vector embeddings from natural language processing with tools from multiscale graph partitioning that can reveal natural partitions at different resolutions without making a priori assumptions about the number of clusters in the corpus. We show the advantages of graph-based clustering through end-to-end comparisons with other popular clustering and topic modelling methods, and also evaluate different text vector embeddings, from classic Bag-of-Words to Doc2Vec to the recent transformers based model Bert. This comparative work is showcased through an analysis of a corpus of US news coverage during the presidential election year of 2016.

cs.CL↗

arXiv2020

Network memory in the movement of hospital patients carrying drug-resistant bacteria

Hospitals constitute highly interconnected systems that bring into contact an abundance of infectious pathogens and susceptible individuals, thus making infection outbreaks both common and challenging. In recent years, there has been a sharp incidence of antimicrobial-resistance amongst healthcare-associated infections, a situation now considered endemic in many countries. Here we present network-based analyses of a data set capturing the movement of patients harbouring drug-resistant bacteria across three large London hospitals. We show that there are substantial memory effects in the movement of hospital patients colonised with drug-resistant bacteria. Such memory effects break first-order Markovian transitive assumptions and substantially alter the conclusions from the analysis, specifically on node rankings and the evolution of diffusive processes. We capture variable length memory effects by constructing a lumped-state memory network, which we then use to identify overlapping communities of wards. We find that these communities of wards display a quasi-hierarchical structure at different levels of granularity which is consistent with different aspects of patient flows related to hospital locations and medical specialties.

physics.soc-ph↗

arXiv2020

Computation of single-cell metabolite distributions using mixture models

Metabolic heterogeneity is widely recognised as the next challenge in our understanding of non-genetic variation. A growing body of evidence suggests that metabolic heterogeneity may result from the inherent stochasticity of intracellular events. However, metabolism has been traditionally viewed as a purely deterministic process, on the basis that highly abundant metabolites tend to filter out stochastic phenomena. Here we bridge this gap with a general method for prediction of metabolite distributions across single cells. By exploiting the separation of time scales between enzyme expression and enzyme kinetics, our method produces estimates for metabolite distributions without the lengthy stochastic simulations that would be typically required for large metabolic models. The metabolite distributions take the form of Gaussian mixture models that are directly computable from single-cell expression data and standard deterministic models for metabolic pathways. The proposed mixture models provide a systematic method to predict the impact of biochemical parameters on metabolite distributions. Our method lays the groundwork for identifying the molecular processes that shape metabolic heterogeneity and its functional implications in disease.

q-bio.MN↗

arXiv2020

Stationary distributions of continuous-time Markov chains: a review of theory and truncation-based approximations

Computing the stationary distributions of a continuous-time Markov chain (CTMC) involves solving a set of linear equations. In most cases of interest, the number of equations is infinite or too large, and the equations cannot be solved analytically or numerically. Several approximation schemes overcome this issue by truncating the state space to a manageable size. In this review, we first give a comprehensive theoretical account of the stationary distributions and their relation to the long-term behaviour of CTMCs that is readily accessible to non-experts and free of irreducibility assumptions made in standard texts. We then review truncation-based approximation schemes for CTMCs with infinite state spaces paying particular attention to the schemes' convergence and the errors they introduce, and we illustrate their performance with an example of a stochastic reaction network of relevance in biology and chemistry. We conclude by discussing computational trade-offs associated with error control and several open questions.

math.PR↗

arXiv2020

Scale-dependent measure of network centrality from diffusion dynamics

Classic measures of graph centrality capture distinct aspects of node importance, from the local (e.g., degree) to the global (e.g., closeness). Here we exploit the connection between diffusion and geometry to introduce a multiscale centrality measure. A node is defined to be central if it breaks the metricity of the diffusion as a consequence of the effective boundaries and inhomogeneities in the graph. Our measure is naturally multiscale, as it is computed relative to graph neighbourhoods within the varying time horizon of the diffusion. We find that the centrality of nodes can differ widely at different scales. In particular, our measure correlates with degree (i.e., hubs) at small scales and with closeness (i.e., bridges) at large scales, and also reveals the existence of multi-centric structures in complex networks. By examining centrality across scales, our measure thus provides an evaluation of node importance relative to local and global processes on the network.

physics.soc-ph↗

arXiv2020

Data-driven modelling and characterisation of task completion sequences in online courses

The intrinsic temporality of learning demands the adoption of methodologies capable of exploiting time-series information. In this study we leverage the sequence data framework and show how data-driven analysis of temporal sequences of task completion in online courses can be used to characterise personal and group learners' behaviors, and to identify critical tasks and course sessions in a given course design. We also introduce a recently developed probabilistic Bayesian model to learn sequence trajectories of students and predict student performance. The application of our data-driven sequence-based analyses to data from learners undertaking an on-line Business Management course reveals distinct behaviors within the cohort of learners, identifying learners or groups of learners that deviate from the nominal order expected in the course. Using course grades a posteriori, we explore differences in behavior between high and low performing learners. We find that high performing learners follow the progression between weekly sessions more regularly than low performing learners, yet within each weekly session high performing learners are less tied to the nominal task order. We then model the sequences of high and low performance students using the probablistic Bayesian model and show that we can learn engagement behaviors associated with performance. We also show that the data sequence framework can be used for task centric analysis; we identify critical junctures and differences among types of tasks within the course design. We find that non-rote learning tasks, such as interactive tasks or discussion posts, are correlated with higher performance. We discuss the application of such analytical techniques as an aid to course design, intervention, and student supervision.

cs.SI↗

arXiv2020

Severability of mesoscale components and local time scales in dynamical networks

A major goal of dynamical systems theory is the search for simplified descriptions of the dynamics of a large number of interacting states. For overwhelmingly complex dynamical systems, the derivation of a reduced description on the entire dynamics at once is computationally infeasible. Other complex systems are so expansive that despite the continual onslaught of new data only partial information is available. To address this challenge, we define and optimise for a local quality function severability for measuring the dynamical coherency of a set of states over time. The theoretical underpinnings of severability lie in our local adaptation of the Simon-Ando-Fisher time-scale separation theorem, which formalises the intuition of local wells in the Markov landscape of a dynamical process, or the separation between a microscopic and a macroscopic dynamics. Finally, we demonstrate the practical relevance of severability by applying it to examples drawn from power networks, image segmentation, social networks, metabolic networks, and word association.

physics.soc-ph↗

arXiv2020

Non-linear interlinkages and key objectives amongst the Paris Agreement and the Sustainable Development Goals

The United Nations' ambitions to combat climate change and prosper human development are manifested in the Paris Agreement and the Sustainable Development Goals (SDGs), respectively. These are inherently inter-linked as progress towards some of these objectives may accelerate or hinder progress towards others. We investigate how these two agendas influence each other by defining networks of 18 nodes, consisting of the 17 SDGs and climate change, for various groupings of countries. We compute a non-linear measure of conditional dependence, the partial distance correlation, given any subset of the remaining 16 variables. These correlations are treated as weights on edges, and weighted eigenvector centralities are calculated to determine the most important nodes. We find that SDG 6, clean water and sanitation, and SDG 4, quality education, are most central across nearly all groupings of countries. In developing regions, SDG 17, partnerships for the goals, is strongly connected to the progress of other objectives in the two agendas whilst, somewhat surprisingly, SDG 8, decent work and economic growth, is not as important in terms of eigenvector centrality.

econ.EM↗

arXiv2020

Cellular memory enhances bacterial chemotactic navigation in rugged environments

The response of microbes to external signals is mediated by biochemical networks with intrinsic time scales. These time scales give rise to a memory that impacts cellular behaviour. Here we study theoretically the role of cellular memory in Escherichia coli chemotaxis. Using an agent-based model, we show that cells with memory navigating rugged chemoattractant landscapes can enhance their drift speed by extracting information from environmental correlations. Maximal advantage is achieved when the memory is comparable to the time scale of fluctuations as perceived during swimming. We derive an analytical approximation for the drift velocity in rugged landscapes that explains the enhanced velocity, and recovers standard Keller-Segel gradient-sensing results in the limits when memory and fluctuation time scales are well separated. Our numerics also show that cellular memory can induce bet-hedging at the population level resulting in long-lived multi-modal distributions in heterogeneous landscapes.

physics.bio-ph↗

arXiv2020

Graph-based data clustering via multiscale community detection

We present a graph-theoretical approach to data clustering, which combines the creation of a graph from the data with Markov Stability, a multiscale community detection framework. We show how the multiscale capabilities of the method allow the estimation of the number of clusters, as well as alleviating the sensitivity to the parameters in graph construction. We use both synthetic and benchmark real datasets to compare and evaluate several graph construction methods and clustering algorithms, and show that multiscale graph-based clustering achieves improved performance compared to popular clustering methods without the need to set externally the number of clusters.

cs.IR↗

arXiv2019

Learning spatiotemporal signals using a recurrent spiking network that discretizes time

Learning to produce spatiotemporal sequences is a common task that the brain has to solve. The same neural substrate may be used by the brain to produce different sequential behaviours. The way the brain learns and encodes such tasks remains unknown as current computational models do not typically use realistic biologically-plausible learning. Here, we propose a model where a spiking recurrent network of excitatory and inhibitory biophysical neurons drives a read-out layer: the dynamics of the driver recurrent network is trained to encode time which is then mapped through the read-out neurons to encode another dimension, such as space or a phase. Different spatiotemporal patterns can be learned and encoded through the synaptic weights to the read-out neurons that follow common Hebbian learning rules. We demonstrate that the model is able to learn spatiotemporal dynamics on time scales that are behaviourally relevant and we show that the learned sequences are robustly replayed during a regime of spontaneous activity.

q-bio.NC↗

arXiv2019

HyperTraPS: Inferring probabilistic patterns of trait acquisition in evolutionary and disease progression pathways

The explosion of data throughout the biomedical sciences provides unprecedented opportunities to learn about the dynamics of evolution and disease progression, but harnessing these large and diverse datasets remains challenging. Here, we describe a highly generalisable statistical platform to infer the dynamic pathways by which many, potentially interacting, discrete traits are acquired or lost over time in biomedical systems. The platform uses HyperTraPS (hypercubic transition path sampling) to learn progression pathways from cross-sectional, longitudinal, or phylogenetically-linked data with unprecedented efficiency, readily distinguishing multiple competing pathways, and identifying the most parsimonious mechanisms underlying given observations. Its Bayesian structure quantifies uncertainty in pathway structure and allows interpretable predictions of behaviours, such as which symptom a patient will acquire next. We exploit the model's topology to provide visualisation tools for intuitive assessment of multiple, variable pathways. We apply the method to ovarian cancer progression and the evolution of multidrug resistance in tuberculosis, demonstrating its power to reveal previously undetected dynamic pathways.

q-bio.QM↗