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Researcher profile

Emmanuel J. Candès

Emmanuel J. Candès contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
MethodologyMachine Learningmath.STStatistics TheoryApplicationsComputer Visionq-fin.MFq-fin.RMq-fin.ST

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Published work

11 published item(s)

preprint2026arXiv

Enhancing a Risk Model by Adding Transient Statistical Factors

Estimating the covariance of asset returns, i.e., the risk model, is a key component of financial portfolio construction and evaluation. Most risk modeling approaches produce a factor model that decomposes the asset variability into two components: the first attributed to a small number of factors that are common among the assets and the second attributed to the idiosyncratic behavior of each asset. Third-party providers typically provide risk models to investors, and while these models are typically of high quality, they may fail to capture important information, e.g., changing market regimes and transient factors. To overcome these limitations, we propose a systematic method based on maximum likelihood estimation to enhance an existing factor model by both refining the given model and adding new statistical factors. Our approach relies only on the observed sequence of realized returns and on the choice of two hyperparameters: the number of additional factors and the half-life parameter that determines the weights assigned to returns in the log-likelihood objective. Importantly, our methodology applies to the situation where asset returns may be missing, making it suitable for typical equity datasets. We demonstrate our approach on the Barra short-term US risk model, a high-quality risk model used in practice, for a universe of US high-capitalization equities. We show that the proposed extension captures structure in the returns that is missed by the original model.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

One-Step Generative Modeling via Wasserstein Gradient Flows

Diffusion models and flow-based methods have shown impressive generative capability, especially for images, but their sampling is expensive because it requires many iterative updates. We introduce W-Flow, a framework for training a generator that transforms samples from a simple reference distribution into samples from a target data distribution in a single step. This is achieved in two steps: we first define an evolution from the reference distribution to the target distribution through a Wasserstein gradient flow that minimizes an energy functional; second, we train a static neural generator to compress this evolution into one-step generation. We instantiate the energy functional with the Sinkhorn divergence, which yields an efficient optimal-transport-based update rule that captures global distributional discrepancy and improves coverage of the target distribution. We further prove that the finite-sample training dynamics converge to the continuous-time distributional dynamics under suitable assumptions. Empirically, W-Flow sets a new state of the art for one-step ImageNet 256$\times$256 generation, achieving 1.29 FID, with improved mode coverage and domain transfer. Compared to multi-step diffusion models with similar FID scores, our method yields approximately 100$\times$ faster sampling. These results show that Wasserstein gradient flows provide a principled and effective foundation for fast and high-fidelity generative modeling.

0 citations0 reviewsNo code linkedOpen access
preprint2023arXiv

The Asymptotic Distribution of the MLE in High-dimensional Logistic Models: Arbitrary Covariance

We study the distribution of the maximum likelihood estimate (MLE) in high-dimensional logistic models, extending the recent results from Sur (2019) to the case where the Gaussian covariates may have an arbitrary covariance structure. We prove that in the limit of large problems holding the ratio between the number $p$ of covariates and the sample size $n$ constant, every finite list of MLE coordinates follows a multivariate normal distribution. Concretely, the $j$th coordinate $\hat β_j$ of the MLE is asymptotically normally distributed with mean $α_\star β_j$ and standard deviation $σ_\star/τ_j$; here, $β_j$ is the value of the true regression coefficient, and $τ_j$ the standard deviation of the $j$th predictor conditional on all the others. The numerical parameters $α_\star > 1$ and $σ_\star$ only depend upon the problem dimensionality $p/n$ and the overall signal strength, and can be accurately estimated. Our results imply that the MLE's magnitude is biased upwards and that the MLE's standard deviation is greater than that predicted by classical theory. We present a series of experiments on simulated and real data showing excellent agreement with the theory.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

A Power Analysis for Model-X Knockoffs with $\ell_{p}$-Regularized Statistics

Variable selection properties of procedures utilizing penalized-likelihood estimates is a central topic in the study of high dimensional linear regression problems. Existing literature emphasizes the quality of ranking of the variables by such procedures as reflected in the receiver operating characteristic curve or in prediction performance. Specifically, recent works have harnessed modern theory of approximate message-passing (AMP) to obtain, in a particular setting, exact asymptotic predictions of the type I-type II error tradeoff for selection procedures that rely on $\ell_{p}$-regularized estimators. In practice, effective ranking by itself is often not sufficient because some calibration for Type I error is required. In this work we study theoretically the power of selection procedures that similarly rank the features by the size of an $\ell_{p}$-regularized estimator, but further use Model-X knockoffs to control the false discovery rate in the realistic situation where no prior information about the signal is available. In analyzing the power of the resulting procedure, we extend existing results in AMP theory to handle the pairing between original variables and their knockoffs. This is used to derive exact asymptotic predictions for power. We apply the general results to compare the power of the knockoffs versions of Lasso and thresholded-Lasso selection, and demonstrate that in the i.i.d. covariate setting under consideration, tuning by cross-validation on the augmented design matrix is nearly optimal. We further demonstrate how the techniques allow to analyze also the Type S error, and a corresponding notion of power, when selections are supplemented with a decision on the sign of the coefficient.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Deploying the Conditional Randomization Test in High Multiplicity Problems

This paper introduces the sequential CRT, which is a variable selection procedure that combines the conditional randomization test (CRT) and Selective SeqStep+. Valid p-values are constructed via the flexible CRT, which are then ordered and passed through the selective SeqStep+ filter to produce a list of discoveries. We develop theory guaranteeing control on the false discovery rate (FDR) even though the p-values are not independent. We show in simulations that our novel procedure indeed controls the FDR and are competitive with -- and sometimes outperform -- state-of-the-art alternatives in terms of power. Finally, we apply our methodology to a breast cancer dataset with the goal of identifying biomarkers associated with cancer stage.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Sensitivity Analysis of Individual Treatment Effects: A Robust Conformal Inference Approach

We propose a model-free framework for sensitivity analysis of individual treatment effects (ITEs), building upon ideas from conformal inference. For any unit, our procedure reports the $Γ$-value, a number which quantifies the minimum strength of confounding needed to explain away the evidence for ITE. Our approach rests on the reliable predictive inference of counterfactuals and ITEs in situations where the training data is confounded. Under the marginal sensitivity model of Tan (2006), we characterize the shift between the distribution of the observations and that of the counterfactuals. We first develop a general method for predictive inference of test samples from a shifted distribution; we then leverage this to construct covariate-dependent prediction sets for counterfactuals. No matter the value of the shift, these prediction sets (resp. approximately) achieve marginal coverage if the propensity score is known exactly (resp. estimated). We describe a distinct procedure also attaining coverage, however, conditional on the training data. In the latter case, we prove a sharpness result showing that for certain classes of prediction problems, the prediction intervals cannot possibly be tightened. We verify the validity and performance of the new methods via simulation studies and apply them to analyze real datasets.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Achieving Equalized Odds by Resampling Sensitive Attributes

We present a flexible framework for learning predictive models that approximately satisfy the equalized odds notion of fairness. This is achieved by introducing a general discrepancy functional that rigorously quantifies violations of this criterion. This differentiable functional is used as a penalty driving the model parameters towards equalized odds. To rigorously evaluate fitted models, we develop a formal hypothesis test to detect whether a prediction rule violates this property, the first such test in the literature. Both the model fitting and hypothesis testing leverage a resampled version of the sensitive attribute obeying equalized odds, by construction. We demonstrate the applicability and validity of the proposed framework both in regression and multi-class classification problems, reporting improved performance over state-of-the-art methods. Lastly, we show how to incorporate techniques for equitable uncertainty quantification---unbiased for each group under study---to communicate the results of the data analysis in exact terms.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Classification with Valid and Adaptive Coverage

Conformal inference, cross-validation+, and the jackknife+ are hold-out methods that can be combined with virtually any machine learning algorithm to construct prediction sets with guaranteed marginal coverage. In this paper, we develop specialized versions of these techniques for categorical and unordered response labels that, in addition to providing marginal coverage, are also fully adaptive to complex data distributions, in the sense that they perform favorably in terms of approximate conditional coverage compared to alternative methods. The heart of our contribution is a novel conformity score, which we explicitly demonstrate to be powerful and intuitive for classification problems, but whose underlying principle is potentially far more general. Experiments on synthetic and real data demonstrate the practical value of our theoretical guarantees, as well as the statistical advantages of the proposed methods over the existing alternatives.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

The limits of distribution-free conditional predictive inference

We consider the problem of distribution-free predictive inference, with the goal of producing predictive coverage guarantees that hold conditionally rather than marginally. Existing methods such as conformal prediction offer marginal coverage guarantees, where predictive coverage holds on average over all possible test points, but this is not sufficient for many practical applications where we would like to know that our predictions are valid for a given individual, not merely on average over a population. On the other hand, exact conditional inference guarantees are known to be impossible without imposing assumptions on the underlying distribution. In this work we aim to explore the space in between these two, and examine what types of relaxations of the conditional coverage property would alleviate some of the practical concerns with marginal coverage guarantees while still being possible to achieve in a distribution-free setting.

0 citations0 reviewsNo code linkedOpen access
preprint2019arXiv

A comparison of some conformal quantile regression methods

We compare two recently proposed methods that combine ideas from conformal inference and quantile regression to produce locally adaptive and marginally valid prediction intervals under sample exchangeability (Romano et al., 2019; Kivaranovic et al., 2019). First, we prove that these two approaches are asymptotically efficient in large samples, under some additional assumptions. Then we compare them empirically on simulated and real data. Our results demonstrate that the method in Romano et al. (2019) typically yields tighter prediction intervals in finite samples. Finally, we discuss how to tune these procedures by fixing the relative proportions of observations used for training and conformalization.

0 citations0 reviewsNo code linkedOpen access
preprint2018arXiv

Deep Knockoffs

This paper introduces a machine for sampling approximate model-X knockoffs for arbitrary and unspecified data distributions using deep generative models. The main idea is to iteratively refine a knockoff sampling mechanism until a criterion measuring the validity of the produced knockoffs is optimized; this criterion is inspired by the popular maximum mean discrepancy in machine learning and can be thought of as measuring the distance to pairwise exchangeability between original and knockoff features. By building upon the existing model-X framework, we thus obtain a flexible and model-free statistical tool to perform controlled variable selection. Extensive numerical experiments and quantitative tests confirm the generality, effectiveness, and power of our deep knockoff machines. Finally, we apply this new method to a real study of mutations linked to changes in drug resistance in the human immunodeficiency virus.

0 citations0 reviewsNo code linkedOpen access