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Erwan Scornet

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10 papers

2 author rows

NeurIPS Conference 2025 Conference Paper

A Unified Framework for the Transportability of Population-Level Causal Measures

Ahmed Boughdiri
Clément Berenfeld
Julie Josse
Erwan Scornet

Generalization methods offer a powerful solution to one of the key drawbacks of randomized controlled trials (RCTs): their limited representativeness. By enabling the transport of treatment effect estimates to target populations subject to distributional shifts, these methods are increasingly recognized as the future of meta-analysis, the current gold standard in evidence-based medicine. Yet most existing approaches focus on the risk difference, overlooking the diverse range of causal measures routinely reported in clinical research. Reporting multiple effect measures—both absolute (e. g. , risk difference, number needed to treat) and relative (e. g. , risk ratio, odds ratio)—is essential to ensure clinical relevance, policy utility, and interpretability across contexts. To address this gap, we propose a unified framework for transporting a broad class of first-moment population causal effect measures under covariate shift. We provide identification results under two conditional exchangeability assumptions, derive both classical and semiparametric estimators, and evaluate their performance through theoretical analysis, simulations, and real-world applications. Our analysis shows the specificity of different causal measures and thus the interest of studying them all: for instance, two common approaches (one-step, estimating equation) lead to similar estimators for the risk difference but to two distinct estimators for the odds ratio.

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ICML Conference 2025 Conference Paper

Quantifying Treatment Effects: Estimating Risk Ratios via Observational Studies

Ahmed Boughdiri
Julie Josse
Erwan Scornet

The Risk Difference (RD), an absolute measure of effect, is widely used and well-studied in both randomized controlled trials (RCTs) and observational studies. Complementary to the RD, the Risk Ratio (RR), as a relative measure, is critical for a comprehensive understanding of intervention effects: RD can downplay small absolute changes, while RR can highlight them. Despite its significance, the theoretical study of RR has received less attention, particularly in observational settings. This paper addresses this gap by tackling the estimation of RR in observational data. We propose several RR estimators and establish their theoretical properties, including asymptotic normality and confidence intervals. Through analyses on simulated and real-world datasets, we evaluate the performance of these estimators in terms of bias, efficiency, and robustness to generative data models. We also examine the coverage and length of the associated confidence intervals. Due to the non-linear nature of RR, influence function theory yields two distinct efficient estimators with different convergence assumptions. Based on theoretical and empirical insights, we recommend, among all estimators, one of the two doubly-robust estimators, which, intriguingly, challenges conventional expectations.

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ICML Conference 2024 Conference Paper

Random features models: a way to study the success of naive imputation

Alexis Ayme
Claire Boyer
Aymeric Dieuleveut
Erwan Scornet

Constant (naive) imputation is still widely used in practice as this is a first easy-to-use technique to deal with missing data. Yet, this simple method could be expected to induce a large bias for prediction purposes, as the imputed input may strongly differ from the true underlying data. However, recent works suggest that this bias is low in the context of high-dimensional linear predictors when data is supposed to be missing completely at random (MCAR). This paper completes the picture for linear predictors by confirming the intuition that the bias is negligible and that surprisingly naive imputation also remains relevant in very low dimension. To this aim, we consider a unique underlying random features model, which offers a rigorous framework for studying predictive performances, whilst the dimension of the observed features varies. Building on these theoretical results, we establish finite-sample bounds on stochastic gradient (SGD) predictors applied to zero-imputed data, a strategy particularly well suited for large-scale learning. If the MCAR assumption appears to be strong, we show that similar favorable behaviors occur for more complex missing data scenarios.

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ICML Conference 2023 Conference Paper

Naive imputation implicitly regularizes high-dimensional linear models

Alexis Ayme
Claire Boyer
Aymeric Dieuleveut
Erwan Scornet

Two different approaches exist to handle missing values for prediction: either imputation, prior to fitting any predictive algorithms, or dedicated methods able to natively incorporate missing values. While imputation is widely (and easily) use, it is unfortunately biased when low-capacity predictors (such as linear models) are applied afterward. However, in practice, naive imputation exhibits good predictive performance. In this paper, we study the impact of imputation in a high-dimensional linear model with MCAR missing data. We prove that zero imputation performs an implicit regularization closely related to the ridge method, often used in high-dimensional problems. Leveraging on this connection, we establish that the imputation bias is controlled by a ridge bias, which vanishes in high dimension. As a predictor, we argue in favor of the averaged SGD strategy, applied to zero-imputed data. We establish an upper bound on its generalization error, highlighting that imputation is benign in the $d \gg \sqrt{n}$ regime. Experiments illustrate our findings.

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ICLR Conference 2023 Conference Paper

Sparse tree-based Initialization for Neural Networks

Patrick Lutz
Ludovic Arnould
Claire Boyer
Erwan Scornet

Dedicated neural network (NN) architectures have been designed to handle specific data types (such as CNN for images or RNN for text), which ranks them among state-of-the-art methods for dealing with these data. Unfortunately, no architecture has been found for dealing with tabular data yet, for which tree ensemble methods (tree boosting, random forests) usually show the best predictive performances. In this work, we propose a new sparse initialization technique for (potentially deep) multilayer perceptrons (MLP): we first train a tree-based procedure to detect feature interactions and use the resulting information to initialize the network, which is subsequently trained via standard gradient descent (GD) strategies. Numerical experiments on several tabular data sets showthe benefits of this new, simple and easy-to-use method, both in terms of generalization capacity and computation time, compared to default MLP initialization and even to existing complex deep learning solutions. In fact, this wise MLP initialization raises the performances of the resulting NN methods to that of gradient boosting on tabular data. Besides, such initializations are able to preserve the sparsity of weights introduced in the first layers of the network throughout the training, which emphasizes that the first layers act as a sparse feature extractor (like convolutional layers in CNN).

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ICML Conference 2022 Conference Paper

Near-optimal rate of consistency for linear models with missing values

Alexis Ayme
Claire Boyer
Aymeric Dieuleveut
Erwan Scornet

Missing values arise in most real-world data sets due to the aggregation of multiple sources and intrinsically missing information (sensor failure, unanswered questions in surveys. ..). In fact, the very nature of missing values usually prevents us from running standard learning algorithms. In this paper, we focus on the extensively-studied linear models, but in presence of missing values, which turns out to be quite a challenging task. Indeed, the Bayes predictor can be decomposed as a sum of predictors corresponding to each missing pattern. This eventually requires to solve a number of learning tasks, exponential in the number of input features, which makes predictions impossible for current real-world datasets. First, we propose a rigorous setting to analyze a least-square type estimator and establish a bound on the excess risk which increases exponentially in the dimension. Consequently, we leverage the missing data distribution to propose a new algorithm, and derive associated adaptive risk bounds that turn out to be minimax optimal. Numerical experiments highlight the benefits of our method compared to state-of-the-art algorithms used for predictions with missing values.

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ICML Conference 2021 Conference Paper

Analyzing the tree-layer structure of Deep Forests

Ludovic Arnould
Claire Boyer
Erwan Scornet

Random forests on the one hand, and neural networks on the other hand, have met great success in the machine learning community for their predictive performance. Combinations of both have been proposed in the literature, notably leading to the so-called deep forests (DF) (Zhou & Feng, 2019). In this paper, our aim is not to benchmark DF performances but to investigate instead their underlying mechanisms. Additionally, DF architecture can be generally simplified into more simple and computationally efficient shallow forest networks. Despite some instability, the latter may outperform standard predictive tree-based methods. We exhibit a theoretical framework in which a shallow tree network is shown to enhance the performance of classical decision trees. In such a setting, we provide tight theoretical lower and upper bounds on its excess risk. These theoretical results show the interest of tree-network architectures for well-structured data provided that the first layer, acting as a data encoder, is rich enough.

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NeurIPS Conference 2021 Conference Paper

What’s a good imputation to predict with missing values?

Marine Le Morvan
Julie Josse
Erwan Scornet
Gael Varoquaux

How to learn a good predictor on data with missing values? Most efforts focus on first imputing as well as possible and second learning on the completed data to predict the outcome. Yet, this widespread practice has no theoretical grounding. Here we show that for almost all imputation functions, an impute-then-regress procedure with a powerful learner is Bayes optimal. This result holds for all missing-values mechanisms, in contrast with the classic statistical results that require missing-at-random settings to use imputation in probabilistic modeling. Moreover, it implies that perfect conditional imputation is not needed for good prediction asymptotically. In fact, we show that on perfectly imputed data the best regression function will generally be discontinuous, which makes it hard to learn. Crafting instead the imputation so as to leave the regression function unchanged simply shifts the problem to learning discontinuous imputations. Rather, we suggest that it is easier to learn imputation and regression jointly. We propose such a procedure, adapting NeuMiss, a neural network capturing the conditional links across observed and unobserved variables whatever the missing-value pattern. Our experiments confirm that joint imputation and regression through NeuMiss is better than various two step procedures in a finite-sample regime.

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NeurIPS Conference 2020 Conference Paper

NeuMiss networks: differentiable programming for supervised learning with missing values.

Marine Le Morvan
Julie Josse
Thomas Moreau
Erwan Scornet
Gael Varoquaux

The presence of missing values makes supervised learning much more challenging. Indeed, previous work has shown that even when the response is a linear function of the complete data, the optimal predictor is a complex function of the observed entries and the missingness indicator. As a result, the computational or sample complexities of consistent approaches depend on the number of missing patterns, which can be exponential in the number of dimensions. In this work, we derive the analytical form of the optimal predictor under a linearity assumption and various missing data mechanisms including Missing at Random (MAR) and self-masking (Missing Not At Random). Based on a Neumann-series approximation of the optimal predictor, we propose a new principled architecture, named NeuMiss networks. Their originality and strength come from the use of a new type of non-linearity: the multiplication by the missingness indicator. We provide an upper bound on the Bayes risk of NeuMiss networks, and show that they have good predictive accuracy with both a number of parameters and a computational complexity independent of the number of missing data patterns. As a result they scale well to problems with many features, and remain statistically efficient for medium-sized samples. Moreover, we show that, contrary to procedures using EM or imputation, they are robust to the missing data mechanism, including difficult MNAR settings such as self-masking.

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NeurIPS Conference 2017 Conference Paper

Universal consistency and minimax rates for online Mondrian Forests

Jaouad Mourtada
Stéphane Gaïffas
Erwan Scornet

We establish the consistency of an algorithm of Mondrian Forests~\cite{lakshminarayanan2014mondrianforests, lakshminarayanan2016mondrianuncertainty}, a randomized classification algorithm that can be implemented online. First, we amend the original Mondrian Forest algorithm proposed in~\cite{lakshminarayanan2014mondrianforests}, that considers a \emph{fixed} lifetime parameter. Indeed, the fact that this parameter is fixed actually hinders statistical consistency of the original procedure. Our modified Mondrian Forest algorithm grows trees with increasing lifetime parameters $\lambda_n$, and uses an alternative updating rule, allowing to work also in an online fashion. Second, we provide a theoretical analysis establishing simple conditions for consistency. Our theoretical analysis also exhibits a surprising fact: our algorithm achieves the minimax rate (optimal rate) for the estimation of a Lipschitz regression function, which is a strong extension of previous results~\cite{arlot2014purf_bias} to an \emph{arbitrary dimension}.

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