Christian Pedersen

Christian Pedersen, Michael Eickenberg, Shirley Ho

Convolutional neural networks (CNNs) have been shown to both extract more information than the traditional two-point statistics from cosmological fields, and marginalise over astrophysical effects extremely well. However, CNNs require large amounts of training data, which is potentially problematic in the domain of expensive cosmological simulations, and it is difficult to interpret the network. In this work we apply the learnable scattering transform, a kind of convolutional neural network that uses trainable wavelets as filters, to the problem of cosmological inference and marginalisation over astrophysical effects. We present two models based on the scattering transform, one constructed for performance, and one constructed for interpretability, and perform a comparison with a CNN. We find that scattering architectures are able to outperform a CNN, significantly in the case of small training data samples. Additionally we present a lightweight scattering network that is highly interpretable.

Christian Pedersen, Tiberiu Tesileanu, Tinghui Wu et al. · cambridge

In Elmarakeby et al., "Biologically informed deep neural network for prostate cancer discovery", a feedforward neural network with biologically informed, sparse connections (P-NET) was presented to model the state of prostate cancer. We verified the reproducibility of the study conducted by Elmarakeby et al., using both their original codebase, and our own re-implementation using more up-to-date libraries. We quantified the contribution of network sparsification by Reactome biological pathways, and confirmed its importance to P-NET's superior performance. Furthermore, we explored alternative neural architectures and approaches to incorporating biological information into the networks. We experimented with three types of graph neural networks on the same training data, and investigated the clinical prediction agreement between different models. Our analyses demonstrated that deep neural networks with distinct architectures make incorrect predictions for individual patient that are persistent across different initializations of a specific neural architecture. This suggests that different neural architectures are sensitive to different aspects of the data, an important yet under-explored challenge for clinical prediction tasks.

Jingwen Lyu, Yue Wang, Christian Pedersen et al.

Knowledge of ocean circulation is important for understanding and predicting weather and climate, and managing the blue economy. This circulation can be estimated through Sea Surface Height (SSH) observations, but requires decomposing the SSH into contributions from balanced and unbalanced motions (BMs and UBMs). This decomposition is particularly pertinent for the novel SWOT satellite, which measures SSH at an unprecedented spatial resolution. Specifically, the requirement, and the goal of this work, is to decompose instantaneous SSH into BMs and UBMs. While a few studies using deep learning (DL) approaches have shown promise in framing this decomposition as an image-to-image translation task, these models struggle to work well across a wide range of spatial scales and require extensive training data, which is scarce in this domain. These challenges are not unique to our task, and pervade many problems requiring multi-scale fidelity. We show that these challenges can be addressed by using zero-phase component analysis (ZCA) whitening and data augmentation; making this a viable option for SSH decomposition across scales.