arXiv subjects

Lihua Lei

Publications and source records attributed to Lihua Lei.

At least 37 records · Page 2Linked to original sources

arXiv2025

Conformal Risk Control

We extend conformal prediction to control the expected value of any monotone loss function. The algorithm generalizes split conformal prediction together with its coverage guarantee. Like conformal prediction, the conformal risk control procedure is tight up to an $\mathcal{O}(1/n)$ factor. We also introduce extensions of the idea to distribution shift, quantile risk control, multiple and adversarial risk control, and expectations of U-statistics. Worked examples from computer vision and natural language processing demonstrate the usage of our algorithm to bound the false negative rate, graph distance, and token-level F1-score.

stat.ME↗

arXiv2025

Inference for Synthetic Controls via Refined Placebo Tests

The synthetic control method is often applied to problems with one treated unit and a small number of control units. A common inferential task in this setting is to test null hypotheses regarding the average treatment effect on the treated. Inference procedures that are justified asymptotically are often unsatisfactory due to (1) small sample sizes that render large-sample approximation fragile and (2) simplification of the estimation procedure that is implemented in practice. An alternative is permutation inference, which is related to a common diagnostic called the placebo test. It has provable Type-I error guarantees in finite samples without simplification of the method, when the treatment is uniformly assigned. Despite this robustness, the placebo test suffers from low resolution since the null distribution is constructed from only $N$ reference estimates, where $N$ is the sample size. This creates a barrier for statistical inference at a common level like $α= 0.05$, especially when $N$ is small. We propose a novel leave-two-out procedure that bypasses this issue, while still maintaining the same finite-sample Type-I error guarantee under uniform assignment for a wide range of $N$. Unlike the placebo test whose Type-I error always equals the theoretical upper bound, our procedure often achieves a lower unconditional Type-I error than theory suggests; this enables useful inference in the challenging regime when $α< 1/N$. Empirically, our procedure achieves a higher power when the effect size is reasonably large and a comparable power otherwise. We generalize our procedure to non-uniform assignments and show how to conduct sensitivity analysis. From a methodological perspective, our procedure can be viewed as a new type of randomization inference different from permutation or rank-based inference, which is particularly effective in small samples.

stat.ME↗

arXiv2025

The Transfer Performance of Economic Models

Economists often estimate models using data from a particular domain, e.g. estimating risk preferences in a particular subject pool or for a specific class of lotteries. Whether a model's predictions extrapolate well across domains depends on whether the estimated model has captured generalizable structure. We provide a tractable formulation for this "out-of-domain" prediction problem and define the transfer error of a model based on how well it performs on data from a new domain. We derive finite-sample forecast intervals that are guaranteed to cover realized transfer errors with a user-selected probability when domains are iid, and use these intervals to compare the transferability of economic models and black box algorithms for predicting certainty equivalents. We find that in this application, the black box algorithms we consider outperform standard economic models when estimated and tested on data from the same domain, but the economic models generalize across domains better than the black-box algorithms do.

econ.TH↗

arXiv2025

Conformal Tail Risk Control for Large Language Model Alignment

Recent developments in large language models (LLMs) have led to their widespread usage for various tasks. The prevalence of LLMs in society implores the assurance on the reliability of their performance. In particular, risk-sensitive applications demand meticulous attention to unexpectedly poor outcomes, i.e., tail events, for instance, toxic answers, humiliating language, and offensive outputs. Due to the costly nature of acquiring human annotations, general-purpose scoring models have been created to automate the process of quantifying these tail events. This phenomenon introduces potential human-machine misalignment between the respective scoring mechanisms. In this work, we present a lightweight calibration framework for blackbox models that ensures the alignment of humans and machines with provable guarantees. Our framework provides a rigorous approach to controlling any distortion risk measure that is characterized by a weighted average of quantiles of the loss incurred by the LLM with high confidence. The theoretical foundation of our method relies on the connection between conformal risk control and a traditional family of statistics, i.e., L-statistics. To demonstrate the utility of our framework, we conduct comprehensive experiments that address the issue of human-machine misalignment.

cs.LG↗

arXiv2024

Improving knockoffs with conditional calibration

The knockoff filter of Barber and Candes (arXiv:1404.5609) is a flexible framework for multiple testing in supervised learning models, based on introducing synthetic predictor variables to control the false discovery rate (FDR). Using the conditional calibration framework of Fithian and Lei (arXiv:2007.10438), we introduce the calibrated knockoff procedure, a method that uniformly improves the power of any fixed-X or model-X knockoff procedure. We show theoretically and empirically that the improvement is especially notable in two contexts where knockoff methods can be nearly powerless: when the rejection set is small, and when the structure of the design matrix in fixed-X knockoffs prevents us from constructing good knockoff variables. In these contexts, calibrated knockoffs even outperform competing FDR-controlling methods like the (dependence-adjusted) procedure Benjamini-Hochberg in many scenarios.

stat.ME↗

arXiv2024

Causal Interpretation of Regressions With Ranks

In studies of educational production functions or intergenerational mobility, it is common to transform the key variables into percentile ranks. Yet, it remains unclear what the regression coefficient estimates with ranks of the outcome or the treatment. In this paper, we derive effective causal estimands for a broad class of commonly-used regression methods, including the ordinary least squares (OLS), two-stage least squares (2SLS), difference-in-differences (DiD), and regression discontinuity designs (RDD). Specifically, we introduce a novel primitive causal estimand, the Rank Average Treatment Effect (rank-ATE), and prove that it serves as the building block of the effective estimands of all the aforementioned econometrics methods. For 2SLS, DiD, and RDD, we show that direct applications to outcome ranks identify parameters that are difficult to interpret. To address this issue, we develop alternative methods to identify more interpretable causal parameters.

econ.EM↗

arXiv2024

Design-Robust Two-Way-Fixed-Effects Regression For Panel Data

We propose a new estimator for average causal effects of a binary treatment with panel data in settings with general treatment patterns. Our approach augments the popular two-way-fixed-effects specification with unit-specific weights that arise from a model for the assignment mechanism. We show how to construct these weights in various settings, including the staggered adoption setting, where units opt into the treatment sequentially but permanently. The resulting estimator converges to an average (over units and time) treatment effect under the correct specification of the assignment model, even if the fixed effect model is misspecified. We show that our estimator is more robust than the conventional two-way estimator: it remains consistent if either the assignment mechanism or the two-way regression model is correctly specified. In addition, the proposed estimator performs better than the two-way-fixed-effect estimator if the outcome model and assignment mechanism are locally misspecified. This strong double robustness property underlines and quantifies the benefits of modeling the assignment process and motivates using our estimator in practice. We also discuss an extension of our estimator to handle dynamic treatment effects.

econ.EM↗

arXiv2023

Adaptive novelty detection with false discovery rate guarantee

This paper studies the semi-supervised novelty detection problem where a set of "typical" measurements is available to the researcher. Motivated by recent advances in multiple testing and conformal inference, we propose AdaDetect, a flexible method that is able to wrap around any probabilistic classification algorithm and control the false discovery rate (FDR) on detected novelties in finite samples without any distributional assumption other than exchangeability. In contrast to classical FDR-controlling procedures that are often committed to a pre-specified p-value function, AdaDetect learns the transformation in a data-adaptive manner to focus the power on the directions that distinguish between inliers and outliers. Inspired by the multiple testing literature, we further propose variants of AdaDetect that are adaptive to the proportion of nulls while maintaining the finite-sample FDR control. The methods are illustrated on synthetic datasets and real-world datasets, including an application in astrophysics.

stat.ME↗

arXiv2023

Total Variation Floodgate for Variable Importance Inference in Classification

Inferring variable importance is the key problem of many scientific studies, where researchers seek to learn the effect of a feature $X$ on the outcome $Y$ in the presence of confounding variables $Z$. Focusing on classification problems, we define the expected total variation (ETV), which is an intuitive and deterministic measure of variable importance that does not rely on any model context. We then introduce algorithms for statistical inference on the ETV under design-based/model-X assumptions. These algorithms build on the floodgate notion for regression problems (Zhang and Janson 2020). The algorithms we introduce can leverage any user-specified regression function and produce asymptotic lower confidence bounds for the ETV. We show the effectiveness of our algorithms with simulations and a case study in conjoint analysis on the US general election.

stat.ME↗

arXiv2023

Chromium Self-Traceable Length Standard: Investigating Geometry and Diffraction for Length Traceability Chain

Natural constant-based metrology methods offer an effective approach to achieving traceability in nanometric measurements. The Cr grating, fabricated by atom lithography and featuring a pitch of $d=212.7705\pm0.0049~{\rm nm}$ traceable to the Cr transition frequency $^{7}S_{3}$ $\rightarrow$ $^{7}P_{4}^{0}$, demonstrates potential as a self-traceable length standard in nano-length metrology by grating interferometer. This research aims to analyze and engineer the diffraction characteristics that enhance the Cr grating as a self-traceable length standard within the length traceability chain based on the Cr transition frequency. Accordingly, we investigate the geometric morphology and diffraction characteristics of the Cr grating, analyzes the influence of the grating's polarization-sensitive characteristics on the Littrow configuration grating interferometer, and establishes the criteria for Cr grating fabrication. Experimentally, we fabricate an expanded Cr grating by scanning atom lithography, characterize its diffraction performance, and conduct preliminary verification of length measurement in a self-traceable grating interferometer. This work adheres to the international trend of flattened metrology development, offering a valuable reference for advancing subsequent metrological technologies throughout the new traceability chain.

physics.ins-det↗

arXiv2023

Nanometer displacement measurement based on metrological self-mixing grating interferometer traceable to the pitch standard of one-dimension chromium self-traceable grating

Traceability of precision instrument and measuring method is the core issue in metrology science. In the field of nanometer length measurement, the laser interferometers are usually used to trace the measurement value to the laser wavelength, but the laser wavelength is sensitive to the environment disturbance. Chromium self-traceable grating is an ideal nanometer length reference grating with pitch traceability, fabricated by the atomic lithography technique. The new nanometer length traceability chain can be established based on the pitch traceability of chromium self-traceable grating, which is often used to calibrate the systematic error of the atomic force microscope. In this paper, the metrological self-mixing grating interferometer based on the chromium self-traceable grating (SMGI-Cr) is firstly established, whose interfere phase is traceable to the pitch of the chromium self-traceable grating directly and traceable to the chromium atomic transition frequency of energy level 7 S 3 to 7 P 4 indirectly. The nanometer displacement measurement is also achieved by the SMGI-Cr. The measurement error is no more than 0.2366%, compared to a commercial interferometer.

physics.app-ph↗

arXiv2023

Conformalized Survival Analysis

Existing survival analysis techniques heavily rely on strong modelling assumptions and are, therefore, prone to model misspecification errors. In this paper, we develop an inferential method based on ideas from conformal prediction, which can wrap around any survival prediction algorithm to produce calibrated, covariate-dependent lower predictive bounds on survival times. In the Type I right-censoring setting, when the censoring times are completely exogenous, the lower predictive bounds have guaranteed coverage in finite samples without any assumptions other than that of operating on independent and identically distributed data points. Under a more general conditionally independent censoring assumption, the bounds satisfy a doubly robust property which states the following: marginal coverage is approximately guaranteed if either the censoring mechanism or the conditional survival function is estimated well. Further, we demonstrate that the lower predictive bounds remain valid and informative for other types of censoring. The validity and efficiency of our procedure are demonstrated on synthetic data and real COVID-19 data from the UK Biobank.

stat.ME↗

arXiv2023

Policy Learning under Biased Sample Selection

Practitioners often use data from a randomized controlled trial to learn a treatment assignment policy that can be deployed on a target population. A recurring concern in doing so is that, even if the randomized trial was well-executed (i.e., internal validity holds), the study participants may not represent a random sample of the target population (i.e., external validity fails)--and this may lead to policies that perform suboptimally on the target population. We consider a model where observable attributes can impact sample selection probabilities arbitrarily but the effect of unobservable attributes is bounded by a constant, and we aim to learn policies with the best possible performance guarantees that hold under any sampling bias of this type. In particular, we derive the partial identification result for the worst-case welfare in the presence of sampling bias and show that the optimal max-min, max-min gain, and minimax regret policies depend on both the conditional average treatment effect (CATE) and the conditional value-at-risk (CVaR) of potential outcomes given covariates. To avoid finite-sample inefficiencies of plug-in estimates, we further provide an end-to-end procedure for learning the optimal max-min and max-min gain policies that does not require the separate estimation of nuisance parameters.

econ.EM↗

arXiv2023

Length traceability chain based on chromium atom transition frequency

Precise positioning measurement plays an important role in in today advanced manufacturing industry, and length traceability chain has been optimizing and enriching to fulfill the developing and various precise positioning requirement. In this paper, we propose a new length traceability chain based on chromium atom transition frequency, which is a combining utilization of fundamental physical constant accuracy and grating interferometer environmental robustness. The selftraceable grating pitch standard, the selftraceable angle standard and the selftraceable grating interferometer are promising to improve the measurement accuracy, consistency and selfcalibration ability in situ for precise positioning.

physics.ins-det↗

arXiv2022

What Estimators Are Unbiased For Linear Models?

The recent thought-provoking paper by Hansen [2022, Econometrica] proved that the Gauss-Markov theorem continues to hold without the requirement that competing estimators are linear in the vector of outcomes. Despite the elegant proof, it was shown by the authors and other researchers that the main result in the earlier version of Hansen's paper does not extend the classic Gauss-Markov theorem because no nonlinear unbiased estimator exists under his conditions. To address the issue, Hansen [2022] added statements in the latest version with new conditions under which nonlinear unbiased estimators exist. Motivated by the lively discussion, we study a fundamental problem: what estimators are unbiased for a given class of linear models? We first review a line of highly relevant work dating back to the 1960s, which, unfortunately, have not drawn enough attention. Then, we introduce notation that allows us to restate and unify results from earlier work and Hansen [2022]. The new framework also allows us to highlight differences among previous conclusions. Lastly, we establish new representation theorems for unbiased estimators under different restrictions on the linear model, allowing the coefficients and covariance matrix to take only a finite number of values, the higher moments of the estimator and the dependent variable to exist, and the error distribution to be discrete, absolutely continuous, or dominated by another probability measure. Our results substantially generalize the claims of parallel commentaries on Hansen [2022] and a remarkable result by Koopmann [1982].

econ.EM↗

arXiv2022

Learn then Test: Calibrating Predictive Algorithms to Achieve Risk Control

We introduce a framework for calibrating machine learning models so that their predictions satisfy explicit, finite-sample statistical guarantees. Our calibration algorithms work with any underlying model and (unknown) data-generating distribution and do not require model refitting. The framework addresses, among other examples, false discovery rate control in multi-label classification, intersection-over-union control in instance segmentation, and the simultaneous control of the type-1 error of outlier detection and confidence set coverage in classification or regression. Our main insight is to reframe the risk-control problem as multiple hypothesis testing, enabling techniques and mathematical arguments different from those in the previous literature. We use the framework to provide new calibration methods for several core machine learning tasks, with detailed worked examples in computer vision and tabular medical data.

cs.LG↗

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↗

arXiv2021

Consistency of Spectral Clustering on Hierarchical Stochastic Block Models

We study the hierarchy of communities in real-world networks under a generic stochastic block model, in which the connection probabilities are structured in a binary tree. Under such model, a standard recursive bi-partitioning algorithm is dividing the network into two communities based on the Fiedler vector of the unnormalized graph Laplacian and repeating the split until a stopping rule indicates no further community structures. We prove the strong consistency of this method under a wide range of model parameters, which include sparse networks with node degrees as small as $O(\log n)$. In addition, unlike most of existing work, our theory covers multiscale networks where the connection probabilities may differ by orders of magnitude, which comprise an important class of models that are practically relevant but technically challenging to deal with. Finally we demonstrate the performance of our algorithm on synthetic data and real-world examples.

math.ST↗