arXiv subjects

Swapnil Mishra

Publications and source records attributed to Swapnil Mishra.

27 records · Page 2Linked to original sources

arXiv2020

Semi-Mechanistic Bayesian Modeling of COVID-19 with Renewal Processes

We propose a general Bayesian approach to modeling epidemics such as COVID-19. The approach grew out of specific analyses conducted during the pandemic, in particular an analysis concerning the effects of non-pharmaceutical interventions (NPIs) in reducing COVID-19 transmission in 11 European countries. The model parameterizes the time varying reproduction number $R_t$ through a regression framework in which covariates can e.g be governmental interventions or changes in mobility patterns. This allows a joint fit across regions and partial pooling to share strength. This innovation was critical to our timely estimates of the impact of lockdown and other NPIs in the European epidemics, whose validity was borne out by the subsequent course of the epidemic. Our framework provides a fully generative model for latent infections and observations deriving from them, including deaths, cases, hospitalizations, ICU admissions and seroprevalence surveys. One issue surrounding our model's use during the COVID-19 pandemic is the confounded nature of NPIs and mobility. We use our framework to explore this issue. We have open sourced an R package epidemia implementing our approach in Stan. Versions of the model are used by New York State, Tennessee and Scotland to estimate the current situation and make policy decisions.

stat.AP↗

arXiv2020

Inference of COVID-19 epidemiological distributions from Brazilian hospital data

Knowing COVID-19 epidemiological distributions, such as the time from patient admission to death, is directly relevant to effective primary and secondary care planning, and moreover, the mathematical modelling of the pandemic generally. We determine epidemiological distributions for patients hospitalised with COVID-19 using a large dataset ($N=21{,}000-157{,}000$) from the Brazilian Sistema de Informação de Vigilância Epidemiológica da Gripe database. A joint Bayesian subnational model with partial pooling is used to simultaneously describe the 26 states and one federal district of Brazil, and shows significant variation in the mean of the symptom-onset-to-death time, with ranges between 11.2-17.8 days across the different states, and a mean of 15.2 days for Brazil. We find strong evidence in favour of specific probability density function choices: for example, the gamma distribution gives the best fit for onset-to-death and the generalised log-normal for onset-to-hospital-admission. Our results show that epidemiological distributions have considerable geographical variation, and provide the first estimates of these distributions in a low and middle-income setting. At the subnational level, variation in COVID-19 outcome timings are found to be correlated with poverty, deprivation and segregation levels, and weaker correlation is observed for mean age, wealth and urbanicity.

q-bio.PE↗

arXiv2020

A unified machine learning approach to time series forecasting applied to demand at emergency departments

There were 25.6 million attendances at Emergency Departments (EDs) in England in 2019 corresponding to an increase of 12 million attendances over the past ten years. The steadily rising demand at EDs creates a constant challenge to provide adequate quality of care while maintaining standards and productivity. Managing hospital demand effectively requires an adequate knowledge of the future rate of admission. Using 8 years of electronic admissions data from two major acute care hospitals in London, we develop a novel ensemble methodology that combines the outcomes of the best performing time series and machine learning approaches in order to make highly accurate forecasts of demand, 1, 3 and 7 days in the future. Both hospitals face an average daily demand of 208 and 106 attendances respectively and experience considerable volatility around this mean. However, our approach is able to predict attendances at these emergency departments one day in advance up to a mean absolute error of +/- 14 and +/- 10 patients corresponding to a mean absolute percentage error of 6.8% and 8.6% respectively. Our analysis compares machine learning algorithms to more traditional linear models. We find that linear models often outperform machine learning methods and that the quality of our predictions for any of the forecasting horizons of 1, 3 or 7 days are comparable as measured in MAE. In addition to comparing and combining state-of-the-art forecasting methods to predict hospital demand, we consider two different hyperparameter tuning methods, enabling a faster deployment of our models without compromising performance. We believe our framework can readily be used to forecast a wide range of policy relevant indicators.

stat.AP↗

arXiv2020

On the derivation of the renewal equation from an age-dependent branching process: an epidemic modelling perspective

Renewal processes are a popular approach used in modelling infectious disease outbreaks. In a renewal process, previous infections give rise to future infections. However, while this formulation seems sensible, its application to infectious disease can be difficult to justify from first principles. It has been shown from the seminal work of Bellman and Harris that the renewal equation arises as the expectation of an age-dependent branching process. In this paper we provide a detailed derivation of the original Bellman Harris process. We introduce generalisations, that allow for time-varying reproduction numbers and the accounting of exogenous events, such as importations. We show how inference on the renewal equation is easy to accomplish within a Bayesian hierarchical framework. Using off the shelf MCMC packages, we fit to South Korea COVID-19 case data to estimate reproduction numbers and importations. Our derivation provides the mathematical fundamentals and assumptions underpinning the use of the renewal equation for modelling outbreaks.

q-bio.PE↗

arXiv2020

Estimating the number of infections and the impact of non-pharmaceutical interventions on COVID-19 in European countries: technical description update

Following the emergence of a novel coronavirus (SARS-CoV-2) and its spread outside of China, Europe has experienced large epidemics. In response, many European countries have implemented unprecedented non-pharmaceutical interventions including case isolation, the closure of schools and universities, banning of mass gatherings and/or public events, and most recently, wide-scale social distancing including local and national lockdowns. In this technical update, we extend a semi-mechanistic Bayesian hierarchical model that infers the impact of these interventions and estimates the number of infections over time. Our methods assume that changes in the reproductive number - a measure of transmission - are an immediate response to these interventions being implemented rather than broader gradual changes in behaviour. Our model estimates these changes by calculating backwards from temporal data on observed to estimate the number of infections and rate of transmission that occurred several weeks prior, allowing for a probabilistic time lag between infection and death. In this update we extend our original model [Flaxman, Mishra, Gandy et al 2020, Report #13, Imperial College London] to include (a) population saturation effects, (b) prior uncertainty on the infection fatality ratio, (c) a more balanced prior on intervention effects and (d) partial pooling of the lockdown intervention covariate. We also (e) included another 3 countries (Greece, the Netherlands and Portugal). The model code is available at https://github.com/ImperialCollegeLondon/covid19model/ We are now reporting the results of our updated model online at https://mrc-ide.github.io/covid19estimates/ We estimated parameters jointly for all M=14 countries in a single hierarchical model. Inference is performed in the probabilistic programming language Stan using an adaptive Hamiltonian Monte Carlo (HMC) sampler.

stat.AP↗

arXiv2018

Modeling Popularity in Asynchronous Social Media Streams with Recurrent Neural Networks

Understanding and predicting the popularity of online items is an important open problem in social media analysis. Considerable progress has been made recently in data-driven predictions, and in linking popularity to external promotions. However, the existing methods typically focus on a single source of external influence, whereas for many types of online content such as YouTube videos or news articles, attention is driven by multiple heterogeneous sources simultaneously - e.g. microblogs or traditional media coverage. Here, we propose RNN-MAS, a recurrent neural network for modeling asynchronous streams. It is a sequence generator that connects multiple streams of different granularity via joint inference. We show RNN-MAS not only to outperform the current state-of-the-art Youtube popularity prediction system by 17%, but also to capture complex dynamics, such as seasonal trends of unseen influence. We define two new metrics: promotion score quantifies the gain in popularity from one unit of promotion for a Youtube video; the loudness level captures the effects of a particular user tweeting about the video. We use the loudness level to compare the effects of a video being promoted by a single highly-followed user (in the top 1% most followed users) against being promoted by a group of mid-followed users. We find that results depend on the type of content being promoted: superusers are more successful in promoting Howto and Gaming videos, whereas the cohort of regular users are more influential for Activism videos. This work provides more accurate and explainable popularity predictions, as well as computational tools for content producers and marketers to allocate resources for promotion campaigns.

cs.SI↗

arXiv2018

SIR-Hawkes: Linking Epidemic Models and Hawkes Processes to Model Diffusions in Finite Populations

Among the statistical tools for online information diffusion modeling, both epidemic models and Hawkes point processes are popular choices. The former originate from epidemiology, and consider information as a viral contagion which spreads into a population of online users. The latter have roots in geophysics and finance, view individual actions as discrete events in continuous time, and modulate the rate of events according to the self-exciting nature of event sequences. Here, we establish a novel connection between these two frameworks. Namely, the rate of events in an extended Hawkes model is identical to the rate of new infections in the Susceptible-Infected-Recovered (SIR) model after marginalizing out recovery events -- which are unobserved in a Hawkes process. This result paves the way to apply tools developed for SIR to Hawkes, and vice versa. It also leads to HawkesN, a generalization of the Hawkes model which accounts for a finite population size. Finally, we derive the distribution of cascade sizes for HawkesN, inspired by methods in stochastic SIR. Such distributions provide nuanced explanations to the general unpredictability of popularity: the distribution for diffusion cascade sizes tends to have two modes, one corresponding to large cascade sizes and another one around zero.

cs.SI↗

arXiv2017

A Tutorial on Hawkes Processes for Events in Social Media

This chapter provides an accessible introduction for point processes, and especially Hawkes processes, for modeling discrete, inter-dependent events over continuous time. We start by reviewing the definitions and the key concepts in point processes. We then introduce the Hawkes process, its event intensity function, as well as schemes for event simulation and parameter estimation. We also describe a practical example drawn from social media data - we show how to model retweet cascades using a Hawkes self-exciting process. We presents a design of the memory kernel, and results on estimating parameters and predicting popularity. The code and sample event data are available as an online appendix

stat.ML↗

arXiv2016

Feature Driven and Point Process Approaches for Popularity Prediction

Predicting popularity, or the total volume of information outbreaks, is an important subproblem for understanding collective behavior in networks. Each of the two main types of recent approaches to the problem, feature-driven and generative models, have desired qualities and clear limitations. This paper bridges the gap between these solutions with a new hybrid approach and a new performance benchmark. We model each social cascade with a marked Hawkes self-exciting point process, and estimate the content virality, memory decay, and user influence. We then learn a predictive layer for popularity prediction using a collection of cascade history. To our surprise, Hawkes process with a predictive overlay outperform recent feature-driven and generative approaches on existing tweet data [43] and a new public benchmark on news tweets. We also found that a basic set of user features and event time summary statistics performs competitively in both classification and regression tasks, and that adding point process information to the feature set further improves predictions. From these observations, we argue that future work on popularity prediction should compare across feature-driven and generative modeling approaches in both classification and regression tasks.

cs.SI↗