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Register a new userConsistency of mechanistic causal discovery in continuous-time using Neural ODEs
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The discovery of causal mechanisms from time series data is a key problem in fields working with complex systems. Most identifiability results and learning algorithms assume the underlying dynamics to be discrete in time. Comparatively few, in contrast, explicitly define causal associations in infinitesimal intervals of time, independently of the scale of observation and of the regularity of sampling. In this paper, we consider causal discovery in continuous-time for the study of dynamical systems. We prove that for vector fields parameterized in a large class of neural networks, adaptive regularization schemes consistently recover causal graphs in systems of ordinary differential equations (ODEs). Using this insight, we propose a causal discovery algorithm based on penalized Neural ODEs that we show to be applicable to the general setting of irregularly-sampled multivariate time series and to strongly outperform the state of the art.
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Counterfactual estimation using synthetic controls is one of the most successful recent methodological developments in causal inference. Despite its popularity, the current description only considers time series aligned across units and synthetic controls expressed as linear combinations of observed control units. We propose a continuous-time alternative that models the latent counterfactual path explicitly using the formalism of controlled differential equations. This model is directly applicable to the general setting of irregularly-aligned multivariate time series and may be optimized in rich function spaces -- thereby improving on some limitations of existing approaches.
Going beyond correlations, the understanding and identification of causal relationships in observational time series, an important subfield of Causal Discovery, poses a major challenge. The lack of access to a well-defined ground truth for real-world data creates the need to rely on synthetic data for the evaluation of these methods. Existing benchmarks are limited in their scope, as they either are restricted to a static selection of data sets, or do not allow for a granular assessment of the methods performance when commonly made assumptions are violated. We propose a flexible and simple to use framework for generating time series data, which is aimed at developing, evaluating, and benchmarking time series causal discovery methods. In particular, the framework can be used to fine tune novel methods on vast amounts of data, without overfitting them to a benchmark, but rather so they perform well in real-world use cases. Using our framework, we evaluate prominent time series causal discovery methods and demonstrate a notable degradation in performance when their assumptions are invalidated and their sensitivity to choice of hyperparameters. Finally, we propose future research directions and how our framework can support both researchers and practitioners.
Causal Discovery methods aim to identify a DAG structure that represents causal relationships from observational data. In this article, we stress that it is important to test such methods for robustness in practical settings. As our main example, we analyze the NOTEARS method, for which we demonstrate a lack of scale-invariance. We show that NOTEARS is a method that aims to identify a parsimonious DAG from the data that explains the residual variance. We conclude that NOTEARS is not suitable for identifying truly causal relationships from the data.
Despite having been studied to a great extent, the task of conditional generation of sequences of frames, or videos, remains extremely challenging. It is a common belief that a key step towards solving this task resides in modelling accurately both spatial and temporal information in video signals. A promising direction to do so has been to learn latent variable models that predict the future in latent space and project back to pixels, as suggested in recent literature. Following this line of work and building on top of a family of models introduced in prior work, Neural ODE, we investigate an approach that models time-continuous dynamics over a continuous latent space with a differential equation with respect to time. The intuition behind this approach is that these trajectories in latent space could then be extrapolated to generate video frames beyond the time steps for which the model is trained. We show that our approach yields promising results in the task of future frame prediction on the Moving MNIST dataset with 1 and 2 digits.
Continuous-time event data are common in applications such as individual behavior data, financial transactions, and medical health records. Modeling such data can be very challenging, in particular for applications with many different types of events, since it requires a model to predict the event types as well as the time of occurrence. Recurrent neural networks that parameterize time-varying intensity functions are the current state-of-the-art for predictive modeling with such data. These models typically assume that all event sequences come from the same data distribution. However, in many applications event sequences are generated by different sources, or users, and their characteristics can be very different. In this paper, we extend the broad class of neural marked point process models to mixtures of latent embeddings, where each mixture component models the characteristic traits of a given user. Our approach relies on augmenting these models with a latent variable that encodes user characteristics, represented by a mixture model over user behavior that is trained via amortized variational inference. We evaluate our methods on four large real-world datasets and demonstrate systematic improvements from our approach over existing work for a variety of predictive metrics such as log-likelihood, next event ranking, and source-of-sequence identification.
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