Kwangho Kim

Kwangho Kim, Jisu Kim

In many modern machine learning pipelines, abundant pretrained representations serve as noisy proxy covariates, while task-specific labels remain scarce. We study semi-supervised regression in this setting, and propose a simple two stage estimator that learns kernel eigenfeatures from all proxy covariates and fits a ridge predictor on labeled data. We derive finite sample bounds showing that fast labeled sample rates are recovered when proxy perturbation is controlled and unlabeled proxy covariates are sufficiently abundant. We also show that distribution regression is a direct special case, with analogous guarantees when the finite bag size is large enough. Experiments show consistent gains over supervised and semi-supervised baselines, especially in low label regimes.

Kwangho Kim, José R. Zubizarreta

We propose a simple and general framework for nonparametric estimation of heterogeneous treatment effects under fairness constraints. Under standard regularity conditions, we show that the resulting estimators possess the double robustness property. We use this framework to characterize the trade-off between fairness and the maximum welfare achievable by the optimal policy. We evaluate the methods in a simulation study and illustrate them in a real-world case study.

Kwangho Kim, Edward H. Kennedy, José R. Zubizarreta

We study counterfactual classification as a new tool for decision-making under hypothetical (contrary to fact) scenarios. We propose a doubly-robust nonparametric estimator for a general counterfactual classifier, where we can incorporate flexible constraints by casting the classification problem as a nonlinear mathematical program involving counterfactuals. We go on to analyze the rates of convergence of the estimator and provide a closed-form expression for its asymptotic distribution. Our analysis shows that the proposed estimator is robust against nuisance model misspecification, and can attain fast $\sqrt{n}$ rates with tractable inference even when using nonparametric machine learning approaches. We study the empirical performance of our methods by simulation and apply them for recidivism risk prediction.

Kwangho Kim

We study counterfactual distribution learning for high-dimensional outcomes whose counterfactual law may concentrate near lower-dimensional structure. Standard isotropic smoothing treats all ambient directions equally, leading to unfavorable scaling and unstable local inference. We propose two diffusion-guided estimators based on semiparametric debiasing: diffusion-informed smoothing for counterfactual densities and diffusion-informed score smoothing for counterfactual scores. The estimators combine causal nuisance adjustment with geometry-adaptive localization driven by diffusion score information, removing first-order nuisance bias while aligning smoothing with local outcome geometry. We establish asymptotic expansions, risk bounds, and inference procedures for smoothed density and score-based targets, with ambient density inference obtained under additional approximation conditions. Under structural geometry conditions, the leading stochastic error is governed by an effective dimension induced by the diffusion-guided kernel, rather than by the ambient dimension. Semi-synthetic experiments based on CelebA show steeper error decay for geometry-adaptive methods, supporting the proposed effective-dimension theory.

Kwangho Kim, Jisu Kim, Edward H. Kennedy

Causal effects are often characterized with population summaries. These might provide an incomplete picture when there are heterogeneous treatment effects across subgroups. Since the subgroup structure is typically unknown, it is more challenging to identify and evaluate subgroup effects than population effects. We propose a new solution to this problem: \emph{Causal k-Means Clustering}, which harnesses the widely-used k-means clustering algorithm to uncover the unknown subgroup structure. Our problem differs significantly from the conventional clustering setup since the variables to be clustered are unknown counterfactual functions. We present a plug-in estimator which is simple and readily implementable using off-the-shelf algorithms, and study its rate of convergence. We also develop a new bias-corrected estimator based on nonparametric efficiency theory and double machine learning, and show that this estimator achieves fast root-n rates and asymptotic normality in large nonparametric models. Our proposed methods are especially useful for modern outcome-wide studies with multiple treatment levels. Further, our framework is extensible to clustering with generic pseudo-outcomes, such as partially observed outcomes or otherwise unknown functions. Finally, we explore finite sample properties via simulation, and illustrate the proposed methods using a study of mobile-supported self-management for chronic low back pain.

Kwangho Kim, Hajin Lee

Estimating causal effects is particularly challenging when outcomes arise in complex, non-Euclidean spaces, where conventional methods often fail to capture meaningful structural variation. We develop a framework for topological causal inference that defines treatment effects through differences in the topological structure of potential outcomes, summarized by power-weighted silhouette functions of persistence diagrams. We develop an efficient, doubly robust estimator in a fully nonparametric model, establish functional weak convergence, and construct a formal test of the null hypothesis of no topological effect. Empirical studies illustrate that the proposed method reliably quantifies topological treatment effects across diverse complex outcome types.

Kwangho Kim, Jisu Kim, Larry A. Wasserman et al.

Understanding treatment effect heterogeneity is vital for scientific and policy research. However, identifying and evaluating heterogeneous treatment effects pose significant challenges due to the typically unknown subgroup structure. Recently, a novel approach, causal k-means clustering, has emerged to assess heterogeneity of treatment effect by applying the k-means algorithm to unknown counterfactual regression functions. In this paper, we expand upon this framework by integrating hierarchical and density-based clustering algorithms. We propose plug-in estimators that are simple and readily implementable using off-the-shelf algorithms. Unlike k-means clustering, which requires the margin condition, our proposed estimators do not rely on strong structural assumptions on the outcome process. We go on to study their rate of convergence, and show that under the minimal regularity conditions, the additional cost of causal clustering is essentially the estimation error of the outcome regression functions. Our findings significantly extend the capabilities of the causal clustering framework, thereby contributing to the progression of methodologies for identifying homogeneous subgroups in treatment response, consequently facilitating more nuanced and targeted interventions. The proposed methods also open up new avenues for clustering with generic pseudo-outcomes. We explore finite sample properties via simulation, and illustrate the proposed methods in voting and employment projection datasets.

Kwangho Kim

We study counterfactual regression, which aims to map input features to outcomes under hypothetical scenarios that differ from those observed in the data. This is particularly useful for decision-making when adapting to sudden shifts in treatment patterns is essential. We propose a doubly robust-style estimator for counterfactual regression within a generalizable framework that accommodates a broad class of risk functions and flexible constraints, drawing on tools from semiparametric theory and stochastic optimization. Our approach uses incremental interventions to enhance adaptability while maintaining consistency with standard methods. We formulate the target estimand as the optimal solution to a stochastic optimization problem and develop an efficient estimation strategy, where we can leverage rapid development of modern optimization algorithms. We go on to analyze the rates of convergence and characterize the asymptotic distributions. Our analysis shows that the proposed estimators can achieve $\sqrt{n}$-consistency and asymptotic normality for a broad class of problems. Numerical illustrations highlight their effectiveness in adapting to unseen counterfactual scenarios while maintaining parametric convergence rates.

Kwangho Kim, Jisu Kim, Manzil Zaheer et al.

We propose PLLay, a novel topological layer for general deep learning models based on persistence landscapes, in which we can efficiently exploit the underlying topological features of the input data structure. In this work, we show differentiability with respect to layer inputs, for a general persistent homology with arbitrary filtration. Thus, our proposed layer can be placed anywhere in the network and feed critical information on the topological features of input data into subsequent layers to improve the learnability of the networks toward a given task. A task-optimal structure of PLLay is learned during training via backpropagation, without requiring any input featurization or data preprocessing. We provide a novel adaptation for the DTM function-based filtration, and show that the proposed layer is robust against noise and outliers through a stability analysis. We demonstrate the effectiveness of our approach by classification experiments on various datasets.

Kwangho Kim, Edward H. Kennedy, Ashley I. Naimi

Modern longitudinal studies collect feature data at many timepoints, often of the same order of sample size. Such studies are typically affected by {dropout} and positivity violations. We tackle these problems by generalizing effects of recent incremental interventions (which shift propensity scores rather than set treatment values deterministically) to accommodate multiple outcomes and subject dropout. We give an identifying expression for incremental intervention effects when dropout is conditionally ignorable (without requiring treatment positivity), and derive the nonparametric efficiency bound for estimating such effects. Then we present efficient nonparametric estimators, showing that they converge at fast parametric rates and yield uniform inferential guarantees, even when nuisance functions are estimated flexibly at slower rates. We also study the variance ratio of incremental intervention effects relative to more conventional deterministic effects in a novel infinite time horizon setting, where the number of timepoints can grow with sample size, and show that incremental intervention effects yield near-exponential gains in statistical precision in this setup. Finally we conclude with simulations and apply our methods in a study of the effect of low-dose aspirin on pregnancy outcomes.

Kwangho Kim, Jisu Kim, Alessandro Rinaldo

We develop a novel algorithm for feature extraction in time series data by leveraging tools from topological data analysis. Our algorithm provides a simple, efficient way to successfully harness topological features of the attractor of the underlying dynamical system for an observed time series. The proposed methodology relies on the persistent landscapes and silhouette of the Rips complex obtained after a de-noising step based on principal components applied to a time-delayed embedding of a noisy, discrete time series sample. We analyze the stability properties of the proposed approach and show that the resulting TDA-based features are robust to sampling noise. Experiments on synthetic and real-world data demonstrate the effectiveness of our approach. We expect our method to provide new insights on feature extraction from granular, noisy time series data.

Kwangho Kim, Jisu Kim, Edward H. Kennedy

Comparing counterfactual distributions can provide more nuanced and valuable measures for causal effects, going beyond typical summary statistics such as averages. In this work, we consider characterizing causal effects via distributional distances, focusing on two kinds of target parameters. The first is the counterfactual outcome density. We propose a doubly robust-style estimator for the counterfactual density and study its rates of convergence and limiting distributions. We analyze asymptotic upper bounds on the $L_q$ and the integrated $L_q$ risks of the proposed estimator, and propose a bootstrap-based confidence band. The second is a novel distributional causal effect defined by the $L_1$ distance between different counterfactual distributions. We study three approaches for estimating the proposed distributional effect: smoothing the counterfactual density, smoothing the $L_1$ distance, and imposing a margin condition. For each approach, we analyze asymptotic properties and error bounds of the proposed estimator, and discuss potential advantages and disadvantages. We go on to present a bootstrap approach for obtaining confidence intervals, and propose a test of no distributional effect. We conclude with a numerical illustration and a real-world example.