arXiv subjects

Emmanuel Candès

Publications and source records attributed to Emmanuel Candès.

At least 19 recordsLinked to original sources

arXiv2026

Single-Asset Adaptive Leveraged Volatility Control

This paper introduces a methodology for constructing a market index composed of a liquid risky asset and a liquid risk-free asset that achieves a fixed target volatility. Existing volatility-targeting strategies typically scale portfolio exposure inversely with a variance forecast, but such open-loop approaches suffer from high turnover, leverage spikes, and sensitivity to estimation error -- issues that limit practical adoption in index construction. We propose a proportional-control approach for setting the index weights that explicitly corrects tracking error through feedback. The method requires only a few interpretable parameters, making it transparent and practical for index construction. We demonstrate in simulation that this approach is more effective at consistently achieving the target volatility than the open-loop alternative.

q-fin.PM↗

arXiv2026

Towards Execution-Grounded Automated AI Research

Automated AI research holds great potential to accelerate scientific discovery. However, current LLMs often generate plausible-looking but ineffective ideas. Execution grounding may help, but it is unclear whether automated execution is feasible and whether LLMs can learn from the execution feedback. To investigate these, we first build an automated executor to implement ideas and launch large-scale parallel GPU experiments to verify their effectiveness. We then convert two realistic research problems - LLM pre-training and post-training - into execution environments and demonstrate that our automated executor can implement a large fraction of the ideas sampled from frontier LLMs. We analyze two methods to learn from the execution feedback: evolutionary search and reinforcement learning. Execution-guided evolutionary search is sample-efficient: it finds a method that significantly outperforms the GRPO baseline (69.4% vs 48.0%) on post-training, and finds a pre-training recipe that outperforms the nanoGPT baseline (19.7 minutes vs 35.9 minutes) on pre-training, all within just ten search epochs. Frontier LLMs often generate meaningful algorithmic ideas during search, but they tend to saturate early and only occasionally exhibit scaling trends. Reinforcement learning from execution reward, on the other hand, suffers from mode collapse. It successfully improves the average reward of the ideator model but not the upper-bound, due to models converging on simple ideas. We thoroughly analyze the executed ideas and training dynamics to facilitate future efforts towards execution-grounded automated AI research.

cs.CL↗

arXiv2025

Synthetic bootstrapped pretraining

We introduce Synthetic Bootstrapped Pretraining (SBP), a language model (LM) pretraining procedure that first learns a model of relations between documents from the pretraining dataset and then leverages it to synthesize a vast new corpus for joint training. While the standard pretraining teaches LMs to learn causal correlations among tokens within a single document, it is not designed to efficiently model the rich, learnable inter-document correlations that can potentially lead to better performance. We validate SBP by designing a compute-matched pretraining setup and pretrain a 3B-parameter and a 6B-parameter model on up to 1T tokens from scratch. We find SBP consistently improves upon a strong repetition baseline and delivers up to 60% of performance improvement attainable by an oracle upper bound with access to 20x more unique data. Qualitative analysis reveals that the synthesized documents go beyond mere paraphrases -- SBP first abstracts a core concept from the seed material and then crafts a new narration on top of it. Besides strong empirical performance, SBP admits a natural Bayesian interpretation: the synthesizer implicitly learns to abstract the latent concepts shared between related documents.

cs.CL↗

arXiv2025

Robust Sampling for Active Statistical Inference

Active statistical inference is a new method for inference with AI-assisted data collection. Given a budget on the number of labeled data points that can be collected and assuming access to an AI predictive model, the basic idea is to improve estimation accuracy by prioritizing the collection of labels where the model is most uncertain. The drawback, however, is that inaccurate uncertainty estimates can make active sampling produce highly noisy results, potentially worse than those from naive uniform sampling. In this work, we present robust sampling strategies for active statistical inference. Robust sampling ensures that the resulting estimator is never worse than the estimator using uniform sampling. Furthermore, with reliable uncertainty estimates, the estimator usually outperforms standard active inference. This is achieved by optimally interpolating between uniform and active sampling, depending on the quality of the uncertainty scores, and by using ideas from robust optimization. We demonstrate the utility of the method on a series of real datasets from computational social science and survey research.

stat.ML↗

arXiv2025

Imputation-Powered Inference

Modern multi-modal and multi-site data frequently suffer from blockwise missingness, where subsets of features are missing for groups of individuals, creating complex patterns that challenge standard inference methods. Existing approaches have critical limitations: complete-case analysis discards informative data and is potentially biased; doubly robust estimators for non-monotone missingness-where the missingness patterns are not nested subsets of one another-can be theoretically efficient but lack closed-form solutions and often fail to scale; and blackbox imputation can leverage partially observed data to improve efficiency but provides no inferential guarantees when misspecified. To address the limitations of these existing methods, we propose imputation-powered inference (IPI), a model-lean framework that combines the flexibility of blackbox imputation with bias correction using fully observed data, drawing on ideas from prediction-powered inference and semiparametric inference. IPI enables valid and efficient M-estimation under missing completely at random (MCAR) blockwise missingness and improves subpopulation inference under a weaker assumption we formalize as first-moment MCAR, for which we also provide practical diagnostics. Simulation studies and a clinical application demonstrate that IPI may substantially improve subpopulation efficiency relative to complete-case analysis, while maintaining statistical validity in settings where both doubly robust estimators and naive imputation fail to achieve nominal coverage.

stat.ME↗

arXiv2025

Mosaic inference on panel data

Analysis of panel data via linear regression is widespread across disciplines. To perform statistical inference, such analyses typically assume that clusters of observations are jointly independent. For example, one might assume that observations in New York are independent of observations in New Jersey. Are such assumptions plausible? Might there be hidden dependencies between nearby clusters? This paper introduces a mosaic permutation test that can (i) test the cluster-independence assumption and (ii) produce confidence intervals for linear models without assuming the full cluster-independence assumption. The key idea behind our method is to apply a permutation test to carefully constructed residual estimates that obey the same invariances as the true errors. As a result, our method yields finite-sample valid inferences under a mild "local exchangeability" condition. This condition differs from the typical cluster-independence assumption, as neither assumption implies the other. Furthermore, our method is asymptotically valid under cluster-independence (with no exchangeability assumptions). Together, these results show our method is valid under assumptions that are arguably weaker than the assumptions underlying many classical methods. In experiments on well-studied datasets from the literature, we find that many existing methods produce variance estimates that are up to five times too small, whereas mosaic methods produce reliable results. We implement our methods in the python package mosaicperm.

stat.ME↗

arXiv2025

s1: Simple test-time scaling

Test-time scaling is a promising new approach to language modeling that uses extra test-time compute to improve performance. Recently, OpenAI's o1 model showed this capability but did not publicly share its methodology, leading to many replication efforts. We seek the simplest approach to achieve test-time scaling and strong reasoning performance. First, we curate a small dataset s1K of 1,000 questions paired with reasoning traces relying on three criteria we validate through ablations: difficulty, diversity, and quality. Second, we develop budget forcing to control test-time compute by forcefully terminating the model's thinking process or lengthening it by appending "Wait" multiple times to the model's generation when it tries to end. This can lead the model to double-check its answer, often fixing incorrect reasoning steps. After supervised finetuning the Qwen2.5-32B-Instruct language model on s1K and equipping it with budget forcing, our model s1-32B exceeds o1-preview on competition math questions by up to 27% (MATH and AIME24). Further, scaling s1-32B with budget forcing allows extrapolating beyond its performance without test-time intervention: from 50% to 57% on AIME24. Our model, data, and code are open-source at https://github.com/simplescaling/s1

cs.CL↗

arXiv2025

Automated Hypothesis Validation with Agentic Sequential Falsifications

Hypotheses are central to information acquisition, decision-making, and discovery. However, many real-world hypotheses are abstract, high-level statements that are difficult to validate directly. This challenge is further intensified by the rise of hypothesis generation from Large Language Models (LLMs), which are prone to hallucination and produce hypotheses in volumes that make manual validation impractical. Here we propose Popper, an agentic framework for rigorous automated validation of free-form hypotheses. Guided by Karl Popper's principle of falsification, Popper validates a hypothesis using LLM agents that design and execute falsification experiments targeting its measurable implications. A novel sequential testing framework ensures strict Type-I error control while actively gathering evidence from diverse observations, whether drawn from existing data or newly conducted procedures. We demonstrate Popper on six domains including biology, economics, and sociology. Popper delivers robust error control, high power, and scalability. Furthermore, compared to human scientists, Popper achieved comparable performance in validating complex biological hypotheses while reducing time by 10 folds, providing a scalable, rigorous solution for hypothesis validation.

cs.LG↗

arXiv2024

Synthetic continued pretraining

Pretraining on large-scale, unstructured internet text enables language models to acquire a significant amount of world knowledge. However, this knowledge acquisition is data-inefficient--to learn a given fact, models must be trained on hundreds to thousands of diverse representations of it. This poses a challenge when adapting a pretrained model to a small corpus of domain-specific documents, where each fact may appear rarely or only once. We propose to bridge this gap with synthetic continued pretraining: using the small domain-specific corpus to synthesize a large corpus more amenable to learning, and then performing continued pretraining on the synthesized corpus. We instantiate this proposal with EntiGraph, a synthetic data augmentation algorithm that extracts salient entities from the source documents and then generates diverse text by drawing connections between the sampled entities. Synthetic continued pretraining with EntiGraph enables a language model to answer questions and follow generic instructions related to the source documents without access to them. If, instead, the source documents are available at inference time, we show that the knowledge acquired through our approach compounds with retrieval-augmented generation. To better understand these results, we build a simple mathematical model of EntiGraph, and show how synthetic data augmentation can "rearrange" knowledge to enable more data-efficient learning.

cs.LG↗

arXiv2024

The mosaic permutation test: an exact and nonparametric goodness-of-fit test for factor models

Financial firms often rely on fundamental factor models to explain correlations among asset returns and manage risk. Yet after major events, e.g., COVID-19, analysts may reassess whether existing risk models continue to fit well: specifically, after accounting for a set of known factor exposures, are the residuals of the asset returns independent? With this motivation, we introduce the mosaic permutation test, a nonparametric goodness-of-fit test for preexisting factor models. Our method can leverage modern machine learning techniques to detect model violations while provably controlling the false positive rate, i.e., the probability of rejecting a well-fitting model, without making asymptotic approximations or parametric assumptions. This property helps prevent analysts from unnecessarily rebuilding accurate models, which can waste resources and increase risk. To illustrate our methodology, we apply the mosaic permutation test to the BlackRock Fundamental Equity Risk (BFRE) model. Although the BFRE model generally explains the most significant correlations among assets, we find evidence of unexplained correlations among certain real estate stocks, and we show that adding new factors improves model fit. We implement our methods in the python package mosaicperm.

stat.ME↗

arXiv2024

A Library of Mirrors: Deep Neural Nets in Low Dimensions are Convex Lasso Models with Reflection Features

We prove that training neural networks on 1-D data is equivalent to solving convex Lasso problems with discrete, explicitly defined dictionary matrices. We consider neural networks with piecewise linear activations and depths ranging from 2 to an arbitrary but finite number of layers. We first show that two-layer networks with piecewise linear activations are equivalent to Lasso models using a discrete dictionary of ramp functions, with breakpoints corresponding to the training data points. In certain general architectures with absolute value or ReLU activations, a third layer surprisingly creates features that reflect the training data about themselves. Additional layers progressively generate reflections of these reflections. The Lasso representation provides valuable insights into the analysis of globally optimal networks, elucidating their solution landscapes and enabling closed-form solutions in certain special cases. Numerical results show that reflections also occur when optimizing standard deep networks using standard non-convex optimizers. Additionally, we demonstrate our theory with autoregressive time series models.

cs.LG↗

arXiv2024

Controlled Variable Selection from Summary Statistics Only? A Solution via GhostKnockoffs and Penalized Regression

Identifying which variables do influence a response while controlling false positives pervades statistics and data science. In this paper, we consider a scenario in which we only have access to summary statistics, such as the values of marginal empirical correlations between each dependent variable of potential interest and the response. This situation may arise due to privacy concerns, e.g., to avoid the release of sensitive genetic information. We extend GhostKnockoffs (He et al. [2022]) and introduce variable selection methods based on penalized regression achieving false discovery rate (FDR) control. We report empirical results in extensive simulation studies, demonstrating enhanced performance over previous work. We also apply our methods to genome-wide association studies of Alzheimer's disease, and evidence a significant improvement in power.

stat.ME↗

arXiv2024

Bellman Conformal Inference: Calibrating Prediction Intervals For Time Series

We introduce Bellman Conformal Inference (BCI), a framework that wraps around any time series forecasting models and provides approximately calibrated prediction intervals. Unlike existing methods, BCI is able to leverage multi-step ahead forecasts and explicitly optimize the average interval lengths by solving a one-dimensional stochastic control problem (SCP) at each time step. In particular, we use the dynamic programming algorithm to find the optimal policy for the SCP. We prove that BCI achieves long-term coverage under arbitrary distribution shifts and temporal dependence, even with poor multi-step ahead forecasts. We find empirically that BCI avoids uninformative intervals that have infinite lengths and generates substantially shorter prediction intervals in multiple applications when compared with existing methods.

cs.LG↗

arXiv2024

Tight Distribution-Free Confidence Intervals for Local Quantile Regression

It is well known that it is impossible to construct useful confidence intervals (CIs) about the mean or median of a response $Y$ conditional on features $X = x$ without making strong assumptions about the joint distribution of $X$ and $Y$. This paper introduces a new framework for reasoning about problems of this kind by casting the conditional problem at different levels of resolution, ranging from coarse to fine localization. In each of these problems, we consider local quantiles defined as the marginal quantiles of $Y$ when $(X,Y)$ is resampled in such a way that samples $X$ near $x$ are up-weighted while the conditional distribution $Y \mid X$ does not change. We then introduce the Weighted Quantile method, which asymptotically produces the uniformly most accurate confidence intervals for these local quantiles no matter the (unknown) underlying distribution. Another method, namely, the Quantile Rejection method, achieves finite sample validity under no assumption whatsoever. We conduct extensive numerical studies demonstrating that both of these methods are valid. In particular, we show that the Weighted Quantile procedure achieves nominal coverage as soon as the effective sample size is in the range of 10 to 20.

stat.ME↗

arXiv2023

Uncertainty Quantification over Graph with Conformalized Graph Neural Networks

Graph Neural Networks (GNNs) are powerful machine learning prediction models on graph-structured data. However, GNNs lack rigorous uncertainty estimates, limiting their reliable deployment in settings where the cost of errors is significant. We propose conformalized GNN (CF-GNN), extending conformal prediction (CP) to graph-based models for guaranteed uncertainty estimates. Given an entity in the graph, CF-GNN produces a prediction set/interval that provably contains the true label with pre-defined coverage probability (e.g. 90%). We establish a permutation invariance condition that enables the validity of CP on graph data and provide an exact characterization of the test-time coverage. Moreover, besides valid coverage, it is crucial to reduce the prediction set size/interval length for practical use. We observe a key connection between non-conformity scores and network structures, which motivates us to develop a topology-aware output correction model that learns to update the prediction and produces more efficient prediction sets/intervals. Extensive experiments show that CF-GNN achieves any pre-defined target marginal coverage while significantly reducing the prediction set/interval size by up to 74% over the baselines. It also empirically achieves satisfactory conditional coverage over various raw and network features.

cs.LG↗

arXiv2023

Conformal Inference for Online Prediction with Arbitrary Distribution Shifts

We consider the problem of forming prediction sets in an online setting where the distribution generating the data is allowed to vary over time. Previous approaches to this problem suffer from over-weighting historical data and thus may fail to quickly react to the underlying dynamics. Here we correct this issue and develop a novel procedure with provably small regret over all local time intervals of a given width. We achieve this by modifying the adaptive conformal inference (ACI) algorithm of Gibbs and Candès (2021) to contain an additional step in which the step-size parameter of ACI's gradient descent update is tuned over time. Crucially, this means that unlike ACI, which requires knowledge of the rate of change of the data-generating mechanism, our new procedure is adaptive to both the size and type of the distribution shift. Our methods are highly flexible and can be used in combination with any baseline predictive algorithm that produces point estimates or estimated quantiles of the target without the need for distributional assumptions. We test our techniques on two real-world datasets aimed at predicting stock market volatility and COVID-19 case counts and find that they are robust and adaptive to real-world distribution shifts.

stat.ME↗

arXiv2023

Tractable Evaluation of Stein's Unbiased Risk Estimate with Convex Regularizers

Stein's unbiased risk estimate (SURE) gives an unbiased estimate of the $\ell_2$ risk of any estimator of the mean of a Gaussian random vector. We focus here on the case when the estimator minimizes a quadratic loss term plus a convex regularizer. For these estimators SURE can be evaluated analytically for a few special cases, and generically using recently developed general purpose methods for differentiating through convex optimization problems; these generic methods however do not scale to large problems. In this paper we describe methods for evaluating SURE that handle a wide class of estimators, and also scale to large problem sizes.

math.ST↗

arXiv2022

Testing for Outliers with Conformal p-values

This paper studies the construction of p-values for nonparametric outlier detection, taking a multiple-testing perspective. The goal is to test whether new independent samples belong to the same distribution as a reference data set or are outliers. We propose a solution based on conformal inference, a broadly applicable framework which yields p-values that are marginally valid but mutually dependent for different test points. We prove these p-values are positively dependent and enable exact false discovery rate control, although in a relatively weak marginal sense. We then introduce a new method to compute p-values that are both valid conditionally on the training data and independent of each other for different test points; this paves the way to stronger type-I error guarantees. Our results depart from classical conformal inference as we leverage concentration inequalities rather than combinatorial arguments to establish our finite-sample guarantees. Furthermore, our techniques also yield a uniform confidence bound for the false positive rate of any outlier detection algorithm, as a function of the threshold applied to its raw statistics. Finally, the relevance of our results is demonstrated by numerical experiments on real and simulated data.

stat.ME↗