This is a representative implementation of Approximate Bayesian Computation (ABC) for Simulation-based Inference (SBI). A detailed explanation is provided in the background section and in "Accelerating Simulation-based Inference with Emerging AI Hardware", S Kulkarni, A Tsyplikhin, MM Krell, and CA Moritz, IEEE International Conference on Rebooting Computing (ICRC), 2020. In its core, the algorithm determines simulation parameters that best describe the observed data from COVID-19 infections to enable statistical inference.
The application is currently supported by Poplar SDK 1.2.
The data is provided in the script covid_data.py.
It was extracted from the
JHU CSSE COVID-19 Data.
It contains the COVID-19 numbers (detected active cases,
recovered cases, and detected cases that lead to death)
after the first day with 100 known infections.
See also: Dong E, Du H, Gardner L. An interactive web-based dashboard to track COVID-19 in real time. Lancet Inf Dis. 20(5):533-534. doi: 10.1016/S1473-3099(20)30120-1
| File | Description |
|---|---|
README.md |
How to run the model |
ABC_IPU.py |
Main algorithm script to run IPU model |
argparser.py |
Document and read command line parameters |
covid_data.py |
Provide already downloaded COVID-19 data |
requirements.txt |
Required Python 3.6 packages |
test_ABC.py |
Test script. Run using python -m pytest |
Install Poplar SDK 1.2 following the instructions in the
Getting Started guide for your IPU system
which can be found here:
https://docs.graphcore.ai/projects/ipu-hw-getting-started/en/1.2.0/.
Make sure to source the enable.sh script for Poplar as well as the drivers.
Make sure that the virtualenv package is installed for Python 3.6.
Activate a Python virtual environment with gc_tensorflow
installed for TensorFlow version 2.1 as follows:
virtualenv venv -p python3.6
source venv/bin/activate
pip install <path to gc_tensorflow_2.1.whl>
pip install -r requirements.txt
The use of Python 3.6 is crucial, because our code
assumes that the python command leads to
Python 3.6 in the virtual environment
and pip leads to pip3 in the installation script.
To execute the application, you can run for example
python ABC_IPU.py --enqueue-chunk-size 10000 --tolerance 5e5 --n-samples-target 100 --n-samples-per-batch 100000 --country US --samples-filepath US_5e5_100.txt
All command line options and defaults are explained in argparser.py.
We are looking at data from Italy in the Johns Hopkins University dataset
over a period of 49 days.
Data for the USA and New Zealand is also provided.
The data contains the active confirmed cases (A), confirmed recoveries (R),
and confirmed deaths(D). The data starts
when there is more than 100 recorded cases (2020-02-23 for Italy).
The model additionally considers the number of unconfirmed recoveries (Ru),
susceptible people (S), and undocumented infected (I).
The constant P is the total population record for the country.
All together, we have a state vector:
X = [S, I, A, R, D, Ru]
We initialize with S = P - A - R - D - I. An interesting model parameter
is k (kappa) which it the ratio between initial confirmed and unconfirmed cases:
I[0] = k * A[0]. Note the index denotes the time step,
that means I[0] is the number of undocumented infected people at t=0.
The parameter k is randomly sampled between 0 and 2 and
the purpose of the ABC algorithm is to find a good fit/estimate.
Ru[0] is set to zero.
There are several additional hyperparameters to model the COVID-19 spread which are all analyzed by the ABC algorithm. They are managed in a parameter vector and randomly sampled from uniform distributions with different boundaries:
param_vector = [alpha_0, alpha, n, beta, gamma, delta, eta, kappa]
upper_bound = [1.0, 100.0, 2.0, 1.0, 1.0, 1.0, 1.0, 2.0]
The first three are used to model the active transmission rate function::
g = alpha_0 + alpha/(1+(U)^n)
where U = A + R + D. So, n controls the rate of decrease, alpha is a scale factor, and
alpha_0 is the initial offset.
Different utility functions U could be chosen to model different
non-pharmaceutical interventions specific for policies in each country.
gamma is the case identification rate.
beta is the case recovery rate with the relative latent recovery rate eta.
delta is the case fatality rate.
For S, g * S * I/P cases are expected to transition to undocumented infected,
assuming that active confirmed cases (A) do not infect others
and that recovered people (R + Ru) cannot get reinfected.
The more unidentified infected people (I) the more people get infected.
Analyzing the change of g over time helps to understand certain policies.
With the identification rate, we get that gamma * I people change from
infected (I) to active confirmed cases (A).
With the recovery rate, we get that beta * A
identified infected people recover (R)
and together with the relative latent recovery rate,
we get that beta * eta * I people become unidentified recovered people (Ru).
Last, but not least, delta * A
is the number of active confirmed cases dying from COVID-19 (D).
Together, the rates are used to calculate the hazard function which
calculates the expected change in cases on average.
To map the average numbers to real simulated data,
the average rates are used in a Poisson sampling.
The respective sampled data is then used to adjust the estimated numbers from
one day to the other.
In our code, we simulate the Poisson distribution with a Normal distribution
with same mean h and a standard deviation of sqrt(h).
Since the values in h are sufficiently big, this is a good approximation.
See the Mathematical Model section of Hindsight is 2020 vision: a characterisation of the global response to the COVID-19 pandemic for further details of the model and its parameters.