Recent approaches build on implicit neural representations (INRs) to propose generative models over function spaces. However, they are computationally costly when dealing with inference tasks, such as missing data imputation, or directly cannot tackle them. In this work, we propose a novel deep generative model, named VaMoH. VaMoH combines the capabilities of modeling continuous functions using INRs and the inference capabilities of Variational Autoencoders (VAEs). In addition, VaMoH relies on a normalizing flow to define the prior, and a mixture of hypernetworks to parametrize the data log-likelihood. This gives VaMoH a high expressive capability and interpretability. Through experiments on a diverse range of data types, such as images, voxels, and climate data, we show that VaMoH can effectively learn rich distributions over continuous functions. Furthermore, it can perform inference-related tasks, such as conditional super-resolution generation and in-painting, as well or better than previous approaches, while being less computationally demanding.

In this work, we deepen on the use of normalizing flows for causal reasoning. Specifically, we first leverage recent results on non-linear ICA to show that causal models are identifiable from observational data given a causal ordering, and thus can be recovered using autoregressive normalizing flows (NFs). Second, we analyze different design and learning choices for *causal normalizing flows* to capture the underlying causal data-generating process. Third, we describe how to implement the *do-operator* in causal NFs, and thus, how to answer interventional and counterfactual questions. Finally, in our experiments, we validate our design and training choices through a comprehensive ablation study; compare causal NFs to other approaches for approximating causal models; and empirically demonstrate that causal NFs can be used to address real-world problems—where the presence of mixed discrete-continuous data and partial knowledge on the causal graph is the norm. The code for this work can be found at https://github.com/psanch21/causal-flows.

Biohybrid circuits of interacting living and model neurons are an advantageous means to study neural dynamics and to assess the role of specific neuron and network properties in the nervous system. Hybrid networks are also a necessary step to build effective artificial intelligence and brain hybridization. In this work, we deal with the automatized online and offline adaptation, exploration and parameter mapping to achieve a target dynamics in hybrid circuits and, in particular, those that yield dynamical invariants between living and model neurons. We address dynamical invariants that form robust cycle-by-cycle relationships between the intervals that build neural sequences from such interaction. Our methodology first attains automated adaptation of model neurons to work in the same amplitude regime and time scale of living neurons. Then, we address the automatized exploration and mapping of the synapse parameter space that lead to a specific dynamical invariant target. Our approach uses multiple configurations and parallel computing from electrophysiological recordings of living neurons to build full mappings, and genetic algorithms to achieve an instance of the target dynamics for the hybrid circuit in a short time. We illustrate and validate such strategy in the context of the study of functional sequences in neural rhythms, which can be easily generalized for any variety of hybrid circuit configuration. This approach facilitates both the building of hybrid circuits and the accomplishment of their scientific goal.

In this paper, we introduce VACA, a novel class of variational graph autoencoders for causal inference in the absence of hidden confounders, when only observational data and the causal graph are available. Without making any parametric assumptions, VACA mimics the necessary properties of a Structural Causal Model (SCM) to provide a flexible and practical framework for approximating interventions (do-operator) and abduction-action-prediction steps. As a result, and as shown by our empirical results, VACA accurately approximates the interventional and counterfactual distributions on diverse SCMs. Finally, we apply VACA to evaluate counterfactual fairness in fair classification problems, as well as to learn fair classifiers without compromising performance.