International initiatives such as the Molecular Taxonomy of Breast Cancer International Consortium are collecting multiple data sets at different genome-scales with the aim to identify novel cancer bio-markers and predict patient survival. To analyze such data, several machine learning, bioinformatics, and statistical methods have been applied, among them neural networks such as autoencoders. Although these models provide a good statistical learning framework to analyze multi-omic and/or clinical data, there is a distinct lack of work on how to integrate diverse patient data and identify the optimal design best suited to the available data.In this paper, we investigate several autoencoder architectures that integrate a variety of cancer patient data types (e.g., multi-omics and clinical data). We perform extensive analyses of these approaches and provide a clear methodological and computational framework for designing systems that enable clinicians to investigate cancer traits and translate the results into clinical applications. We demonstrate how these networks can be designed, built, and, in particular, applied to tasks of integrative analyses of heterogeneous breast cancer data. The results show that these approaches yield relevant data representations that, in turn, lead to accurate and stable diagnosis.

Reinforcement Learning (RL) has achieved impressive performance in many complex environments due to the integration with Deep Neural Networks (DNNs). At the same time, Genetic Algorithms (GAs), often seen as a competing approach to RL, had limited success in scaling up to the DNNs required to solve challenging tasks. Contrary to this dichotomic view, in the physical world, evolution and learning are complementary processes that continuously interact. The recently proposed Evolutionary Reinforcement Learning (ERL) framework has demonstrated mutual benefits to performance when combining the two methods. However, ERL has not fully addressed the scalability problem of GAs. In this paper, we show that this problem is rooted in an unfortunate combination of a simple genetic encoding for DNNs and the use of traditional biologically-inspired variation operators. When applied to these encodings, the standard operators are destructive and cause catastrophic forgetting of the traits the networks acquired. We propose a novel algorithm called Proximal Distilled Evolutionary Reinforcement Learning (PDERL) that is characterised by a hierarchical integration between evolution and learning. The main innovation of PDERL is the use of learning-based variation operators that compensate for the simplicity of the genetic representation. Unlike traditional operators, our proposals meet the functional requirements of variation operators when applied on directly-encoded DNNs. We evaluate PDERL in five robot locomotion settings from the OpenAI gym. Our method outperforms ERL, as well as two state-of-the-art RL algorithms, PPO and TD3, in all tested environments.

International initiatives such as the Molecular Taxonomy of Breast Cancer International Consortium (METABRIC) are collecting multiple data sets at different genome-scales with the aim to identify novel cancer bio-markers and predict patient survival. To analyse such data, several machine learning, bioinformatics and statistical methods have been applied, among them neural networks such as autoencoders. Although these models provide a good statistical learning framework to analyse multi-omic and/or clinical data, there is a distinct lack of work on how to integrate diverse patient data and identify the optimal design best suited to the available data.In this paper, we investigate several autoencoder architectures that integrate a variety of cancer patient data types (e.g., multi-omics and clinical data). We perform extensive analyses of these approaches and provide a clear methodological and computational framework for designing systems that enable clinicians to investigate cancer traits and translate the results into clinical applications. We demonstrate how these networks can be designed, built and, in particular, applied to tasks of integrative analyses of heterogeneous breast cancer data. The results show that these approaches yield relevant data representations that, in turn, lead to accurate and stable diagnosis.

The pairwise interaction paradigm of graph machine learning has predominantly governed the modelling of relational systems. However, graphs alone cannot capture the multi-level interactions present in many complex systems and the expressive power of such schemes was proven to be limited. To overcome these limitations, we propose Message Passing Simplicial Networks (MP-SNs), a class of models that perform message passing on simplicial complexes (SCs) -topological objects generalising graphs to higher dimensions. To theoretically analyse the expressivity of our model we introduce a Simplicial Weisfeiler-Lehman (SWL) colouring procedure for distinguishing non-isomorphic SCs. We relate the power of SWL to the problem of distinguishing non-isomorphic graphs and show that SWL and MPSNs are strictly more powerful than the WL test and not less powerful than the 3-WL test. We deepen the analysis by comparing our model with traditional graph neural networks with ReLU activations in terms of the number of linear regions of the functions they can represent. We empirically support our theoretical claims by showing that MPSNs can distinguish challenging strongly regular graphs for which GNNs fail and, when equipped with orientation equivariant layers, they can improve classification accuracy in oriented SCs compared to a GNN baseline. Additionally, we implement a library for message passing on simplicial complexes that we envision to release in due course.

Graph Neural Networks (GNNs) are limited in their expressive power, struggle with long-range interactions and lack a principled way to model higher-order structures. These problems can be attributed to the strong coupling between the computational graph and the input graph structure. The recently proposed Message Passing Simplicial Networks naturally decouple these elements by performing message passing on the clique complex of the graph. Nevertheless, these models are severely constrained by the rigid combinatorial structure of Simplicial Complexes (SCs). In this work, we extend recent theoretical results on SCs to regular Cell Complexes, topological objects that flexibly subsume SCs and graphs. We show that this generalisation provides a powerful set of graph "lifting" transformations, each leading to a unique hierarchical message passing procedure. The resulting methods, which we collectively call CW Networks (CWNs), are strictly more powerful than the WL test and, in certain cases, not less powerful than the 3-WL test. In particular, we demonstrate the effectiveness of one such scheme, based on rings, when applied to molecular graph problems. The proposed architecture benefits from provably larger expressivity than commonly used GNNs, principled modelling of higherorder signals and from compressing the distances between nodes. We demonstrate that our model achieves state-of-the-art results on a variety of molecular datasets.