arXiv subjects

Edward De Brouwer

Publications and source records attributed to Edward De Brouwer.

28 records · Page 2Linked to original sources

arXiv2023

Anamnesic Neural Differential Equations with Orthogonal Polynomial Projections

Neural ordinary differential equations (Neural ODEs) are an effective framework for learning dynamical systems from irregularly sampled time series data. These models provide a continuous-time latent representation of the underlying dynamical system where new observations at arbitrary time points can be used to update the latent representation of the dynamical system. Existing parameterizations for the dynamics functions of Neural ODEs limit the ability of the model to retain global information about the time series; specifically, a piece-wise integration of the latent process between observations can result in a loss of memory on the dynamic patterns of previously observed data points. We propose PolyODE, a Neural ODE that models the latent continuous-time process as a projection onto a basis of orthogonal polynomials. This formulation enforces long-range memory and preserves a global representation of the underlying dynamical system. Our construction is backed by favourable theoretical guarantees and in a series of experiments, we demonstrate that it outperforms previous works in the reconstruction of past and future data, and in downstream prediction tasks.

cs.LG↗

arXiv2023

Deep Counterfactual Estimation with Categorical Background Variables

Referred to as the third rung of the causal inference ladder, counterfactual queries typically ask the "What if ?" question retrospectively. The standard approach to estimate counterfactuals resides in using a structural equation model that accurately reflects the underlying data generating process. However, such models are seldom available in practice and one usually wishes to infer them from observational data alone. Unfortunately, the correct structural equation model is in general not identifiable from the observed factual distribution. Nevertheless, in this work, we show that under the assumption that the main latent contributors to the treatment responses are categorical, the counterfactuals can be still reliably predicted. Building upon this assumption, we introduce CounterFactual Query Prediction (CFQP), a novel method to infer counterfactuals from continuous observations when the background variables are categorical. We show that our method significantly outperforms previously available deep-learning-based counterfactual methods, both theoretically and empirically on time series and image data. Our code is available at https://github.com/edebrouwer/cfqp.

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arXiv2022

Learning predictive checklists from continuous medical data

Checklists, while being only recently introduced in the medical domain, have become highly popular in daily clinical practice due to their combined effectiveness and great interpretability. Checklists are usually designed by expert clinicians that manually collect and analyze available evidence. However, the increasing quantity of available medical data is calling for a partially automated checklist design. Recent works have taken a step in that direction by learning predictive checklists from categorical data. In this work, we propose to extend this approach to accomodate learning checklists from continuous medical data using mixed-integer programming approach. We show that this extension outperforms a range of explainable machine learning baselines on the prediction of sepsis from intensive care clinical trajectories.

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arXiv2022

The magnitude vector of images

The magnitude of a finite metric space has recently emerged as a novel invariant quantity, allowing to measure the effective size of a metric space. Despite encouraging first results demonstrating the descriptive abilities of the magnitude, such as being able to detect the boundary of a metric space, the potential use cases of magnitude remain under-explored. In this work, we investigate the properties of the magnitude on images, an important data modality in many machine learning applications. By endowing each individual images with its own metric space, we are able to define the concept of magnitude on images and analyse the individual contribution of each pixel with the magnitude vector. In particular, we theoretically show that the previously known properties of boundary detection translate to edge detection abilities in images. Furthermore, we demonstrate practical use cases of magnitude for machine learning applications and propose a novel magnitude model that consists of a computationally efficient magnitude computation and a learnable metric. By doing so, we address the computational hurdle that used to make magnitude impractical for many applications and open the way for the adoption of magnitude in machine learning research.

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arXiv2022

Topological Graph Neural Networks

Graph neural networks (GNNs) are a powerful architecture for tackling graph learning tasks, yet have been shown to be oblivious to eminent substructures such as cycles. We present TOGL, a novel layer that incorporates global topological information of a graph using persistent homology. TOGL can be easily integrated into any type of GNN and is strictly more expressive (in terms the Weisfeiler--Lehman graph isomorphism test) than message-passing GNNs. Augmenting GNNs with TOGL leads to improved predictive performance for graph and node classification tasks, both on synthetic data sets, which can be classified by humans using their topology but not by ordinary GNNs, and on real-world data.

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arXiv2022

Predicting the impact of treatments over time with uncertainty aware neural differential equations

Predicting the impact of treatments from observational data only still represents a majorchallenge despite recent significant advances in time series modeling. Treatment assignments are usually correlated with the predictors of the response, resulting in a lack of data support for counterfactual predictions and therefore in poor quality estimates. Developments in causal inference have lead to methods addressing this confounding by requiring a minimum level of overlap. However,overlap is difficult to assess and usually notsatisfied in practice. In this work, we propose Counterfactual ODE (CF-ODE), a novel method to predict the impact of treatments continuously over time using Neural Ordinary Differential Equations equipped with uncertainty estimates. This allows to specifically assess which treatment outcomes can be reliably predicted. We demonstrate over several longitudinal data sets that CF-ODE provides more accurate predictions and more reliable uncertainty estimates than previously available methods.

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arXiv2020

Longitudinal modeling of MS patient trajectories improves predictions of disability progression

Research in Multiple Sclerosis (MS) has recently focused on extracting knowledge from real-world clinical data sources. This type of data is more abundant than data produced during clinical trials and potentially more informative about real-world clinical practice. However, this comes at the cost of less curated and controlled data sets. In this work, we address the task of optimally extracting information from longitudinal patient data in the real-world setting with a special focus on the sporadic sampling problem. Using the MSBase registry, we show that with machine learning methods suited for patient trajectories modeling, such as recurrent neural networks and tensor factorization, we can predict disability progression of patients in a two-year horizon with an ROC-AUC of 0.86, which represents a 33% decrease in the ranking pair error (1-AUC) compared to reference methods using static clinical features. Compared to the models available in the literature, this work uses the most complete patient history for MS disease progression prediction.

cs.LG↗

arXiv2020

Expressive Graph Informer Networks

Applying machine learning to molecules is challenging because of their natural representation as graphs rather than vectors.Several architectures have been recently proposed for deep learning from molecular graphs, but they suffer from informationbottlenecks because they only pass information from a graph node to its direct neighbors. Here, we introduce a more expressiveroute-based multi-attention mechanism that incorporates features from routes between node pairs. We call the resulting methodGraph Informer. A single network layer can therefore attend to nodes several steps away. We show empirically that the proposedmethod compares favorably against existing approaches in two prediction tasks: (1) 13C Nuclear Magnetic Resonance (NMR)spectra, improving the state-of-the-art with an MAE of 1.35 ppm and (2) predicting drug bioactivity and toxicity. Additionally, wedevelop a variant called injective Graph Informer that isprovablyas powerful as the Weisfeiler-Lehman test for graph isomorphism.Furthermore, we demonstrate that the route information allows the method to be informed about thenonlocal topologyof the graphand, thus, even go beyond the capabilities of the Weisfeiler-Lehman test.

stat.ML↗

arXiv2019

GRU-ODE-Bayes: Continuous modeling of sporadically-observed time series

Modeling real-world multidimensional time series can be particularly challenging when these are sporadically observed (i.e., sampling is irregular both in time and across dimensions)-such as in the case of clinical patient data. To address these challenges, we propose (1) a continuous-time version of the Gated Recurrent Unit, building upon the recent Neural Ordinary Differential Equations (Chen et al., 2018), and (2) a Bayesian update network that processes the sporadic observations. We bring these two ideas together in our GRU-ODE-Bayes method. We then demonstrate that the proposed method encodes a continuity prior for the latent process and that it can exactly represent the Fokker-Planck dynamics of complex processes driven by a multidimensional stochastic differential equation. Additionally, empirical evaluation shows that our method outperforms the state of the art on both synthetic data and real-world data with applications in healthcare and climate forecast. What is more, the continuity prior is shown to be well suited for low number of samples settings.

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arXiv2018

Deep Ensemble Tensor Factorization for Longitudinal Patient Trajectories Classification

We present a generative approach to classify scarcely observed longitudinal patient trajectories. The available time series are represented as tensors and factorized using generative deep recurrent neural networks. The learned factors represent the patient data in a compact way and can then be used in a downstream classification task. For more robustness and accuracy in the predictions, we used an ensemble of those deep generative models to mimic Bayesian posterior sampling. We illustrate the performance of our architecture on an intensive-care case study of in-hospital mortality prediction with 96 longitudinal measurement types measured across the first 48-hour from admission. Our combination of generative and ensemble strategies achieves an AUC of over 0.85, and outperforms the SAPS-II mortality score and GRU baselines.

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