Code for the paper Digital imaging-in-flow (FlowCAM) and probabilistic machine learning to assess the sonolytic disinfection of cyanobacteria in sewage wastewater in Journal of Hazardous Materials.

Probabalistic modeling of Flowcam data

This project shows how to perform probabilistic modeling for tabular data. To this end, we employ one decision tree based approach ngboost and two neural network (NN) based approaches. The first NN based approach is aleoteric. This method qunatifies uncertainty in data generating process. To record aleoteric uncertainty in a NN, we have to modify the output layer. In this case, the output layer is a probability distribution instead of a fully connected layer. The parameters of this distribution are learned during model training. The other kind of uncertainty is epistemic uncertainty. This method quantifies uncertainty in our knowledge. It should be noted that recording epistemic uncertainty increases the learnable parameters of NN far more than vanilla or aleoteric NN. However, the good news is that this type of uncertainty can be reduced by collecting more data. Such NNs are also known as bayesian NNs. In such NNs, the weights (and biases) are distributions instead of scaler values. The parameter of these distributions are again learned during model training. We can also combine both aleoteric and epistemic uncertainties to make our NNs into a probablistic NN. Such a NNs have weights as distributions and output layer as distribution as well.

Following models are implemented

• ngboost

• bayesian NN (epistemic uncertainty)

• probabalistic NN (aleoteric uncertainty)

• probablistic bayesian NN (both epistemic and aleoteric)

Data

The input data consists of six parameters affecting the removal of microbes from wastewater such as wastewater concentration (initial cell count), solution pH, amount of ultravoilet radiation with which the wastewater sample was treated, the time at which the sample was treated etc. We have two targets, disinfection efficiency (%) and area. The disinfection efficiency is the measure of decrease in microbial cell counts after treating the sample. We build separate models of each category. Each model receives same inputs but predicts different target. A comprehensive analysis of data is given in 1. Exploratory Data Analysis

Reproducibility

To replicate the experiments, you need to install all requirements given in requirements file . If your results are quite different from what are presented here, then make sure that you are using the exact versions of the libraries which were used at the time of running of these scripts. These versions are printed at the start of each script. Download all the .py files in the scripts including utils.py (utils) file. The data is expected to be in the data folder under the scripts folder. Online reprducible examples running on readthedocs are at readthedocs.

These steps can be summarized as below

git clone https://github.com/AtrCheema/weil101.git

cd weil101

pip install -r docs/requirements.txt

make html