Enhancing Low-Cost Sensor Reliability for Air Quality Monitoring using Deep Learning and Monte Carlo-based Uncertainty Quantification

Abstract

Increasing levels of harmful air pollutants, particularly particulate matter smaller than 2.5 μm (PM2.5), pose a significant global public health risk. While accurate monitoring is essential, a critical challenge persists: high-cost, government-grade sensors are sparsely deployed, while more accessible low-cost sensors lack accuracy. Deep learning models, such as Long Short-Term Memory (LSTM) networks, offer a powerful solution for calibrating these sensors, yet they often lack reliability as they do not report the confidence of their predictions. This absence of Uncertainty Quantification (UQ) undermines trust and can lead to flawed decision-making in environmental management. This study aims to address this gap by separating and quantifying two forms of uncertainty: aleatoric (inherent data noise) and epistemic (the model's own confidence). To achieve this, an LSTM model was developed to predict both a mean value and its corresponding variance by training with a Negative Log-Likelihood (NLL) loss function, allowing it to learn aleatoric uncertainty directly. To estimate the model's epistemic uncertainty, Monte Carlo Dropout (MCD) was applied during inference. By performing multiple forward passes with Dropout active, a prediction distribution was generated whose variance serves as a strong measure of model confidence. An experiment was conducted to find the optimal dropout probability by training and evaluating models with rates from 0.05 to 0.5. While the model with a 0.05 dropout rate achieved the lowest Test RMSE (0.9174) and the 0.35 rate yielded the lowest ECE (0.0228), the results revealed that the model with a dropout rate of 0.10 demonstrated the best overall performance. It achieved the lowest Test NLL of 0.2825, a Test RMSE of 0.9200 (R² of 0.9846), and well-calibrated uncertainty with 97.63% coverage and an ECE of 0.0338. This work presents a validated framework for enhancing the trustworthiness of deep learning models in air quality applications, ensuring that predictions are not only accurate but also reliable.