  The Federated Learning (FL) paradigm faces several challenges that limit its
application in real-world environments. These challenges include the local
models' architecture heterogeneity and the unavailability of distributed
Internet of Things (IoT) nodes due to connectivity problems. These factors
posit the question of "how can the available models fill the training gap of
the unavailable models?". This question is referred to as the "Oblique
Federated Learning" problem. This problem is encountered in the studied
environment that includes distributed IoT nodes responsible for predicting CO2
concentrations. This paper proposes the Correlation-based FL (CorrFL) approach
influenced by the representational learning field to address this problem.
CorrFL projects the various model weights to a common latent space to address
the model heterogeneity. Its loss function minimizes the reconstruction loss
when models are absent and maximizes the correlation between the generated
models. The latter factor is critical because of the intersection of the
feature spaces of the IoT devices. CorrFL is evaluated on a realistic use case,
involving the unavailability of one IoT device and heightened activity levels
that reflect occupancy. The generated CorrFL models for the unavailable IoT
device from the available ones trained on the new environment are compared
against models trained on different use cases, referred to as the benchmark
model. The evaluation criteria combine the mean absolute error (MAE) of
predictions and the impact of the amount of exchanged data on the prediction
performance improvement. Through a comprehensive experimental procedure, the
CorrFL model outperformed the benchmark model in every criterion.
