In artificial intelligence research, comprehending the internal representations of a large language model is still a fundamental challenge [Olah et al., 2020]. Neural network activations can now be broken down into interpretable features using sparse autoencoders (SAEs) [Cunningham et al., 2023, Templeton et al., 2024]. SAEs seek to deconstruct polysemantic neurons into monosemantic features that correlate to concepts that are comprehensible to humans by learning overcomplete sparse representations of model activations. Finding SAE features and confirming their legitimacy are not the same thing, though. The methods used in most interpretability research today are correlation with downstream tasks, automated explanation scoring, or manual inspection. These methods are unable to differentiate between real computational patterns and spurious correlations that result from the multiple testing problem, and they lack formal statistical guarantees. Random chance alone will yield a large number of apparent correlations with any target variable when thousands of candidate features are examined.

Model-X knockoff has garnered significant attention among various feature selection methods due to its guarantees for controlling the false discovery rate (FDR).

Model-X knockoff framework offers a model-free variable selection method that ensures finite sample false discovery rate (FDR) control. However, the complexity of generating knockoff variables, coupled with the model-free assumption, presents significant challenges for protecting data privacy in this context. In this paper, we propose a comprehensive framework for knockoff inference within the differential privacy paradigm. Our proposed method guarantees robust privacy protection while preserving the exact FDR control entailed by the original model-X knockoff procedure. We further conduct power analysis and establish sufficient conditions under which the noise added for privacy preservation does not asymptotically compromise power. Through various applications, we demonstrate that the differential privacy knockoff (DP-knockoff) method can be effectively utilized to safeguard privacy during variable selection with FDR control in both low and high dimensional settings.

We propose a unified theoretical framework for studying the robustness of the model-X knockoffs framework by investigating the asymptotic false discovery rate (FDR) control of the practically implemented approximate knockoffs procedure. This procedure deviates from the model-X knockoffs framework by substituting the true covariate distribution with a user-specified distribution that can be learned using in-sample observations. By replacing the distributional exchangeability condition of the model-X knockoff variables with three conditions on the approximate knockoff statistics, we establish that the approximate knockoffs procedure achieves the asymptotic FDR control. Using our unified framework, we further prove that an arguably most popularly used knockoff variable generation method--the Gaussian knockoffs generator based on the first two moments matching--achieves the asymptotic FDR control when the two-moment-based knockoff statistics are employed in the knockoffs inference procedure. For the first time in the literature, our theoretical results justify formally the effectiveness and robustness of the Gaussian knockoffs generator. Simulation and real data examples are conducted to validate the theoretical findings.

In modern scientific research, the objective is often to identify which variables are associated with an outcome among a large class of potential predictors. This goal can be achieved by selecting variables in a manner that controls the the false discovery rate (FDR), the proportion of irrelevant predictors among the selections. Knockoff filtering is a cutting-edge approach to variable selection that provides FDR control. Existing knockoff statistics frequently employ linear models to assess relationships between features and the response, but the linearity assumption is often violated in real world applications. This may result in poor power to detect truly prognostic variables. We introduce a knockoff statistic based on the conditional prediction function (CPF), which can pair with state-of-art machine learning predictive models, such as deep neural networks. The CPF statistics can capture the nonlinear relationships between predictors and outcomes while also accounting for correlation between features. We illustrate the capability of the CPF statistics to provide superior power over common knockoff statistics with continuous, categorical, and survival outcomes using repeated simulations. Knockoff filtering with the CPF statistics is demonstrated using (1) a residential building dataset to select predictors for the actual sales prices and (2) the TCGA dataset to select genes that are correlated with disease staging in lung cancer patients.

We investigate the robustness of the model-X knockoffs framework with respect to the misspecified or estimated feature distribution. We achieve such a goal by theoretically studying the feature selection performance of a practically implemented knockoffs algorithm, which we name as the approximate knockoffs (ARK) procedure, under the measures of the false discovery rate (FDR) and family wise error rate (FWER). The approximate knockoffs procedure differs from the model-X knockoffs procedure only in that the former uses the misspecified or estimated feature distribution. A key technique in our theoretical analyses is to couple the approximate knockoffs procedure with the model-X knockoffs procedure so that random variables in these two procedures can be close in realizations. We prove that if such coupled model-X knockoffs procedure exists, the approximate knockoffs procedure can achieve the asymptotic FDR or FWER control at the target level. We showcase three specific constructions of such coupled model-X knockoff variables, verifying their existence and justifying the robustness of the model-X knockoffs framework.

Interpretability and stability are two important features that are desired in many contemporary big data applications arising in economics and finance. While the former is enjoyed to some extent by many existing forecasting approaches, the latter in the sense of controlling the fraction of wrongly discovered features which can enhance greatly the interpretability is still largely underdeveloped in the econometric settings. To this end, in this paper we exploit the general framework of model-X knockoffs introduced recently in Cand\`{e}s, Fan, Janson and Lv (2018), which is nonconventional for reproducible large-scale inference in that the framework is completely free of the use of p-values for significance testing, and suggest a new method of intertwined probabilistic factors decoupling (IPAD) for stable interpretable forecasting with knockoffs inference in high-dimensional models. The recipe of the method is constructing the knockoff variables by assuming a latent factor model that is exploited widely in economics and finance for the association structure of covariates. Our method and work are distinct from the existing literature in that we estimate the covariate distribution from data instead of assuming that it is known when constructing the knockoff variables, our procedure does not require any sample splitting, we provide theoretical justifications on the asymptotic false discovery rate control, and the theory for the power analysis is also established. Several simulation examples and the real data analysis further demonstrate that the newly suggested method has appealing finite-sample performance with desired interpretability and stability compared to some popularly used forecasting methods.

Power and reproducibility are key to enabling refined scientific discoveries in contemporary big data applications with general high-dimensional nonlinear models. In this paper, we provide theoretical foundations on the power and robustness for the model-free knockoffs procedure introduced recently in Cand\`{e}s, Fan, Janson and Lv (2016) in high-dimensional setting when the covariate distribution is characterized by Gaussian graphical model. We establish that under mild regularity conditions, the power of the oracle knockoffs procedure with known covariate distribution in high-dimensional linear models is asymptotically one as sample size goes to infinity. When moving away from the ideal case, we suggest the modified model-free knockoffs method called graphical nonlinear knockoffs (RANK) to accommodate the unknown covariate distribution. We provide theoretical justifications on the robustness of our modified procedure by showing that the false discovery rate (FDR) is asymptotically controlled at the target level and the power is asymptotically one with the estimated covariate distribution. To the best of our knowledge, this is the first formal theoretical result on the power for the knockoffs procedure. Simulation results demonstrate that compared to existing approaches, our method performs competitively in both FDR control and power. A real data set is analyzed to further assess the performance of the suggested knockoffs procedure.

With the rapid growth of crowdsourcing platforms it has become easy and relatively inexpensive to collect a dataset labeled by multiple annotators in a short time. However due to the lack of control over the quality of the annotators, some abnormal annotators may be affected by position bias which can potentially degrade the quality of the final consensus labels. In this paper we introduce a statistical framework to model and detect annotator's position bias in order to control the false discovery rate (FDR) without a prior knowledge on the amount of biased annotators - the expected fraction of false discoveries among all discoveries being not too high, in order to assure that most of the discoveries are indeed true and replicable. The key technical development relies on some new knockoff filters adapted to our problem and new algorithms based on the Inverse Scale Space dynamics whose discretization is potentially suitable for large scale crowdsourcing data analysis. Our studies are supported by experiments with both simulated examples and real-world data. The proposed framework provides us a useful tool for quantitatively studying annotator's abnormal behavior in crowdsourcing data arising from machine learning, sociology, computer vision, multimedia, etc.