arXiv subjects

Kenta Takatsu

Publications and source records attributed to Kenta Takatsu.

11 recordsLinked to original sources

arXiv2026

From Isotonic to Lipschitz Regression: A New Interpolative Perspective on Shape-restricted Estimation

This manuscript bridges nonparametric smoothness-based and shape-restricted estimation, which may appear as two disjoint paradigms in the field. The proposed approach is motivated by a conceptually simple observation: every Lipschitz function is a sum of a monotonic and a linear function. This principle is further generalized to the higher-order monotonicity and multivariate settings. A family of estimators is proposed based on a sample-splitting procedure, inheriting desirable methodological, theoretical, and computational properties of shape-restricted estimators. The theoretical analysis provides convergence guarantees of the estimator under heteroscedastic and heavy-tailed errors, as well as adaptivity to the unknown ``complexity" of the true regression function. The generality of the proposed decomposition framework is demonstrated through new approximation results and numerical studies.

stat.ME↗

arXiv2026

Honest Inference for Stochastic Optimization

This manuscript studies a general approach to construct confidence sets for the solution of stochastic optimization, rendering empirical risk minimization as special cases. Statistical inference for stochastic optimization poses significant challenges due to the non-standard limiting behaviors of the corresponding estimator, which arise in settings with increasing dimension of parameters, non-smooth objectives, or constraints. We propose a simple and unified method that guarantees validity in both regular and irregular cases. We provide a unified treatment of validity, conservativeness, and the size of the resulting confidence sets. In particular, the presented width analysis demonstrates the adaptive behavior of the confidence set to the unknown degree of instance-specific regularity. We apply the proposed method to several high-dimensional and irregular statistical problems. Numerical results for all statistical applications are provided.

math.ST↗

arXiv2026

Learning from Discriminatory Training Data

Supervised learning systems are trained using historical data and, if the data was tainted by discrimination, they may unintentionally learn to discriminate against protected groups. We propose that fair learning methods, despite training on potentially discriminatory datasets, shall perform well on fair test datasets. Such dataset shifts crystallize application scenarios for specific fair learning methods. For instance, the removal of direct discrimination can be represented as a particular dataset shift problem. For this scenario, we propose a learning method that provably minimizes model error on fair datasets, while blindly training on datasets poisoned with direct additive discrimination. The method is compatible with existing legal systems and provides a solution to the widely discussed issue of protected groups' intersectionality by striking a balance between the protected groups. Technically, the method applies probabilistic interventions, has causal and counterfactual formulations, and is computationally lightweight - it can be used with any supervised learning model to prevent direct and indirect discrimination via proxies while maximizing model accuracy for business necessity.

cs.LG↗

arXiv2025

On the Precise Asymptotics of Universal Inference

In statistical inference, confidence set procedures are typically evaluated based on their validity and width properties. Even when procedures achieve rate-optimal widths, confidence sets can still be excessively wide in practice due to elusive constants, leading to extreme conservativeness, where the empirical coverage probability of nominal $1-α$ level confidence sets approaches one. This manuscript studies this gap between validity and conservativeness, using universal inference (Wasserman et al., 2020) with a regular parametric model under model misspecification as a running example. We identify the source of asymptotic conservativeness and propose a general remedy based on studentization and bias correction. The resulting method attains exact asymptotic coverage at the nominal $1-α$ level, even under model misspecification, provided that the product of the estimation errors of two unknowns is negligible, exhibiting an intriguing resemblance to double robustness in semiparametric theory.

math.ST↗

arXiv2025

The Berry-Esseen Bound for High-dimensional Self-normalized Sums

This manuscript studies the Gaussian approximation of the coordinate-wise maximum of self-normalized statistics in high-dimensional settings. We derive an explicit Berry-Esseen bound under weak assumptions on the absolute moments. When the third absolute moment is finite, our bound scales as $\log^{5/4}(d)/n^{1/8}$ where $n$ is the sample size and $d$ is the dimension. Hence, our bound tends to zero as long as $\log(d)=o(n^{1/10})$. Our results on self-normalized statistics represent substantial advancements, as such a bound has not been previously available in the high-dimensional central limit theorem (CLT) literature.

math.PR↗

arXiv2024

Generalized van Trees inequality: Local minimax bounds for non-smooth functionals and irregular statistical models

In a decision-theoretic framework, the minimax lower bound provides the worst-case performance of estimators relative to a given class of statistical models. For parametric and semiparametric models, the Hájek--Le Cam local asymptotic minimax (LAM) theorem provides the sharp local asymptotic lower bound. Despite its relative generality, this result comes with limitations as it only applies to the estimation of differentiable functionals under regular statistical models. On the other hand, minimax lower bound techniques such as Fano's or Assoud's are applicable in more general settings but are not sharp enough to imply the LAM theorem. To address this gap, we provide new non-asymptotic minimax lower bounds under minimal regularity assumptions, which imply sharp asymptotic constants. The proposed lower bounds do not require the differentiability of functionals or regularity of statistical models, extending the efficiency theory to broader situations where standard results fail. The use of the new lower bounds is illustrated through the local minimax lower bound constants for estimating the density at a point and directionally differentiable parameters.

math.ST↗

arXiv2023

Debiased inference for a covariate-adjusted regression function

In this article, we study nonparametric inference for a covariate-adjusted regression function. This parameter captures the average association between a continuous exposure and an outcome after adjusting for other covariates. In particular, under certain causal conditions, this parameter corresponds to the average outcome had all units been assigned to a specific exposure level, known as the causal dose-response curve. We propose a debiased local linear estimator of the covariate-adjusted regression function, and demonstrate that our estimator converges pointwise to a mean-zero normal limit distribution. We use this result to construct asymptotically valid confidence intervals for function values and differences thereof. In addition, we use approximation results for the distribution of the supremum of an empirical process to construct asymptotically valid uniform confidence bands. Our methods do not require undersmoothing, permit the use of data-adaptive estimators of nuisance functions, and our estimator attains the optimal rate of convergence for a twice differentiable function. We illustrate the practical performance of our estimator using numerical studies and an analysis of the effect of air pollution exposure on cardiovascular mortality.

stat.ME↗

arXiv2023

Doubly robust machine learning for an instrumental variable study of surgical care for cholecystitis

Comparative effectiveness research frequently employs the instrumental variable design since randomized trials can be infeasible for many reasons. In this study, we investigate and compare treatments for emergency cholecystitis -- inflammation of the gallbladder. A standard treatment for cholecystitis is surgical removal of the gallbladder, while alternative non-surgical treatments include managed care and pharmaceutical options. As randomized trials are judged to violate the principle of equipoise, we consider an instrument for operative care: the surgeon's tendency to operate. Standard instrumental variable estimation methods, however, often rely on parametric models that are prone to bias from model misspecification. We outline instrumental variable estimation methods based on the doubly robust machine learning framework. These methods enable us to employ various machine learning techniques for nuisance parameter estimation and deliver consistent estimates and fast rates of convergence for valid inference. We use these methods to estimate the primary target causal estimand in an IV design. Additionally, we expand these methods to develop estimators for heterogeneous causal effects, profiling principal strata, and a sensitivity analyses for a key instrumental variable assumption. We conduct a simulation study to demonstrate scenarios where more flexible estimation methods outperform standard methods. Our findings indicate that operative care is generally more effective for cholecystitis patients, although the benefits of surgery can be less pronounced for key patient subgroups.

stat.AP↗

arXiv2023

U-Statistics for Importance-Weighted Variational Inference

We propose the use of U-statistics to reduce variance for gradient estimation in importance-weighted variational inference. The key observation is that, given a base gradient estimator that requires $m > 1$ samples and a total of $n > m$ samples to be used for estimation, lower variance is achieved by averaging the base estimator on overlapping batches of size $m$ than disjoint batches, as currently done. We use classical U-statistic theory to analyze the variance reduction, and propose novel approximations with theoretical guarantees to ensure computational efficiency. We find empirically that U-statistic variance reduction can lead to modest to significant improvements in inference performance on a range of models, with little computational cost.

cs.LG↗

arXiv2020

Causal Inference using Gaussian Processes with Structured Latent Confounders

Latent confounders---unobserved variables that influence both treatment and outcome---can bias estimates of causal effects. In some cases, these confounders are shared across observations, e.g. all students taking a course are influenced by the course's difficulty in addition to any educational interventions they receive individually. This paper shows how to semiparametrically model latent confounders that have this structure and thereby improve estimates of causal effects. The key innovations are a hierarchical Bayesian model, Gaussian processes with structured latent confounders (GP-SLC), and a Monte Carlo inference algorithm for this model based on elliptical slice sampling. GP-SLC provides principled Bayesian uncertainty estimates of individual treatment effect with minimal assumptions about the functional forms relating confounders, covariates, treatment, and outcome. Finally, this paper shows GP-SLC is competitive with or more accurate than widely used causal inference techniques on three benchmark datasets, including the Infant Health and Development Program and a dataset showing the effect of changing temperatures on state-wide energy consumption across New England.

stat.ME↗

arXiv2019

A General Framework for Counterfactual Learning-to-Rank

Implicit feedback (e.g., click, dwell time) is an attractive source of training data for Learning-to-Rank, but its naive use leads to learning results that are distorted by presentation bias. For the special case of optimizing average rank for linear ranking functions, however, the recently developed SVM-PropRank method has shown that counterfactual inference techniques can be used to provably overcome the distorting effect of presentation bias. Going beyond this special case, this paper provides a general and theoretically rigorous framework for counterfactual learning-to-rank that enables unbiased training for a broad class of additive ranking metrics (e.g., Discounted Cumulative Gain (DCG)) as well as a broad class of models (e.g., deep networks). Specifically, we derive a relaxation for propensity-weighted rank-based metrics which is subdifferentiable and thus suitable for gradient-based optimization. We demonstrate the effectiveness of this general approach by instantiating two new learning methods. One is a new type of unbiased SVM that optimizes DCG -- called SVM PropDCG --, and we show how the resulting optimization problem can be solved via the Convex Concave Procedure (CCP). The other is Deep PropDCG, where the ranking function can be an arbitrary deep network. In addition to the theoretical support, we empirically find that SVM PropDCG significantly outperforms existing linear rankers in terms of DCG. Moreover, the ability to train non-linear ranking functions via Deep PropDCG further improves performance.

cs.IR↗