Moving Beyond Blindfolded Models: Dynamic Modeling using Particle Filtering/Sequential Monte Carlo [SMC]/PMCMC Methods

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This page covers some of our recent work using dynamic modeling with the machine learning/computational statistics based sequential Monte Carlo (SMC) technique of Particle Filtering (and its stronger relative, Particle MCMC). This work has been greatly aided by ongoing guidance on statistican subtleties from exceptional Mathematical Statistician colleague Dr. Juxin Liu, with whom much of the below is joint work. We are indebted to Dr. Liu for her ongoing collaboration and sharing her expertise in this area.

Informally speaking, this allows for a model that learns as new data becomes available, by recurrently regrounding estimates of the current system state in the model against observed data. In contrast to traditional models -- which are rendered increasingly obsolete and give stale projections as time passes since their creation -- this use of SMC methods/particle filtering provides strong support for probabilistically estimating the current state of the system (e.g., people in different points in the health continuum), probabilistically projecting forward, and probabilistic assessment of intervention tradeoffs from the current point -- considering all the evidence available to this point. For those seeking an intuitive way of thinking of this, this is similar to going from trying to get home with your eyes closed -- relaying purely based on your mental model of the way -- vs. a situation where you can "peek" at where you are every few minutes. To use another analogy, it is a bit like the difference between trying to find your destination in a confusing area of the city (with streets unexpectedly blocked by construction or closed for events) using only directions printed out ahead of time vs. with an up-to-date GPS system that reroutes you to your destination based on wherever you are currently located. Interested in learning more or diving into a technical explanation? Click here if you'd like to see a video of me offering a "spiral" exploration of particle filtering, whose later sections go into more technical specifics. Click here for the accompanying slides.

This use of particle filtering with dynamic models is a very general and versatile technique that offers ready application to other areas of health and health care. We have used this technique with a great deal with surveillance data across multiple pathogens (e.g., pertussis, measles, chickenpox, H1N1 influenza), modeling of health service delivery challenges, zoonoses, tuberculosis, the burden of opioids, and dynamics of stress regulation. Many exciting elements are still to come. Our capacity to investigate in this area is boosted through our creation of a standardized AnyLogic template that makes it straightforward to apply this approach to new areas.

While this approach can support very accurate projection forward, it does so not by any sort of curve-fitting, but on the basis of a) a dynamic model whose structures captures in mechanistic terms the underlying dynamics of the situation and b) a full regrounding of that entire system state (including both latent and observable elements) as new data arrives. It is notable that when considered in light of the "logic of the model" (the model structure), the incoming data observations typically serve to brightly illuminate the situation in many other latent regions of the model that are not themselves directly observable. Essentially, this leverages the logic of the dynamic model to explicate a more complete story of what time series data is really telling us. For example, for a communicable disease model, if there is a large number of incident cases being recorded, it often tells us that there needs to be a sizeable pool [or rapid incoming flow] of susceptible people upstream. Once one considers model structure more fully as well as multiple lines of incoming data, the depiction given of both upstream and latent downstream areas of the model can be quite clear, even though we don't have data that directly measures those regions. We know since Floris Takens' work that data on one part of a coupled complex system encodes information about all parts of the system. Used together with dynamic models, the techniques of Particle Filtering and PMCMC let data tell a much richer story: If we only listen carefully (and informed by a dynamic model), we discover how much the data whispers to us about what is going on in latent areas of the system.

Our most recent published contribution focused on measles, and is the subject of our just-published article in PLoS One led by doctoral student Xiaoyan Li: This work demonstrates the power of incoming data to keep models learning from evidence, to keep their estimate of the model state regrounded by that evidence. This ongoing regrounding of model state allows the models to project forward in a way that reflects the latest evidence. Critically, such models can be evaluate alternative interventions with higher accuracy. For measles, the particle filtered dynamic models provide significant "lookahead" for the shape of things to come, and are accurate in providing advance warning of a coming outbreak.

A preprint of another recent contribution accepted and forthcoming in JMIR Public Health demonstrates the benefits of using the machine learning/AI technique of particle filtering together with dynamic models in the context of incoming observations from a high-velocity source of "big data". Here, we have successfully used it to anticipate the evolution of influenza outbreaks across two jurisdictions on the basis of search volume time series; we have also used its PMCMC variant elsewhere (for the opioid epidemic) with other forms of high-temporal-resolution data such as twitter-based mentions.

Other work conducted by Xiaoyan Li focuses on another increasingly resurgent childhood infectious disease -- pertussis. Pertussis is particularly notable in light of the fact that both natural- and vaccine-induced pertussis immunity wanes in a pronounced way over the lifecourse. In a paper currently under review at PLoS Computational Biology (preprint available here), we investigated the advantages secured from application of the Particle Filtering SMC method to pertussis, particularly in terms of outbreak prediction, estimation of underlying epidemiological state -- including the prevalence of different levels of immunity in the population -- and capacity to evaluate intervention tradeoffs. The work evaluated a variety of articulated age-stratified models incorporating very substantial representations of waning of immunity. The focus here was on the pre-vaccination era, but coming adaptations of this work will present results for recent decades, and probe the dynamics of waning immunity.

Other work from our group -- pioneered by my remarkable student Lujie Duan, and supported by particle filter expert Xiaoyan Li and agent-based modeling virtuouso Wade McDonald -- has rendered this approach into a real-time streaming context with particle filtered dynamic models. This work with particle filtering/Sequential Monte Carlo mentions has further constructed re-usable techniques that support use of multiple sources of incoming streaming data together with dynamic models. Examples of excellent sources that we have targeted as streaming sources include (validated) counts of social media mentions, volumes of searches made on Google, and our Ethica smartphone and wearable-based health data collection system. Such an approach provides a means of keeping dynamic models learning from new data, always regrounded by such data in their estimates of the distribution of underlying states. This can provide real-time decision support recurrently incorporating new incoming evidence and supporting both projection and probabilistic evaluation of intervention tradeoffs in light the newly updated estimates of current state.

While Particle Filtering has served our research exceptionally well, much of our current and incipient lines of work are centered around Particle MCMC [PMCMC], which adds greatly to the analytic insights that can be obtained -- particularly in terms of sampling from static parameter values and from historic trajectories (the latter of which has also been explored within our particle filtering work, but reaches more complete potential with PMCMC). Lujie is also leading exceptionally exciting work accelerating PMCMC using Graphical Processing Units (GPUs) and distributed computing (via the Apache Spark platform that serves as a key tool for our work). We have applied PMCMC and several "big data" sources with dynamic models to opioid abuse, to very satisfactory effect, but this PMCMC is also serving as a key element of our work on remand counts, influenza, soon in multiple childhood infectious diseases.

Thanks to all of the students who have contributed so fundamentally to these efforts, and to Dr. Juxin Liu for her fundamental contributions that have made this work possible.

Selected papers from our group using Particle Filtering/SMC/PMCMC in health

Last update: April 2019