arXiv subjects

Junhyung Park

Publications and source records attributed to Junhyung Park.

At least 19 recordsLinked to original sources

arXiv2026

A fine-grained look at causal effects in causal spaces

The notion of causal effect is fundamental across many scientific disciplines. Traditionally, quantitative researchers have studied causal effects at the level of variables; for example, how a certain drug dose (W) causally affects a patient's blood pressure (Y). However, in many modern data domains, the raw variables-such as pixels in an image or tokens in a language model-do not have the semantic structure needed to formulate meaningful causal questions. In this paper, we offer a more fine-grained perspective by studying causal effects at the level of events, drawing inspiration from probability theory, where core notions such as independence are first given for events and sigma-algebras, before random variables enter the picture. Within the measure-theoretic framework of causal spaces, a recently introduced axiomatisation of causality, we first introduce several binary definitions that determine whether a causal effect is present, as well as proving some properties of them linking causal effect to (in)dependence under an intervention measure. Further, we provide quantifying measures that capture the strength and nature of causal effects on events, and show that we can recover the common measures of treatment effect as special cases.

stat.ME↗

arXiv2026

Causal-DRF: Conditional Kernel Treatment Effect Estimation using Distributional Random Forest

The conditional average treatment effect (CATE) is a commonly targeted statistical parameter for measuring the effect of a treatment conditional on covariates. However, the CATE will fail to capture effects of treatments beyond differences in conditional expectations. Inspired by causal forests for CATE estimation, we develop a forest-based method to estimate the conditional kernel treatment effect (CKTE), based on the recently introduced Distributional Random Forest (DRF) algorithm. Adapting the splitting criterion of DRF, we show how one forest fit can be used to obtain a consistent and asymptotically normal estimator of the CKTE, as well as an approximation of its sampling distribution. This allows to study the difference in distribution between control and treatment group and thus yields a more comprehensive understanding of the treatment effect.

stat.ME↗

arXiv2026

Counterfactual Spaces

We mathematically axiomatise the stochastics of counterfactuals, by introducing two related frameworks, called counterfactual probability spaces and counterfactual causal spaces, which we collectively term counterfactual spaces. They are, respectively, probability and causal spaces whose underlying measurable spaces are products of world-specific measurable spaces. In contrast to more familiar accounts of counterfactuals founded on causal models, we do not view interventions as a necessary component of a theory of counterfactuals. As an alternative to Pearl's celebrated ladder of causation, we view counterfactuals and interventions are orthogonal concepts, respectively mathematised in counterfactual probability spaces and causal spaces. The two concepts are then combined to form counterfactual causal spaces. At the heart of our theory is the notion of shared information between the worlds, encoded completely within the probability measure and causal kernels, and whose extremes are characterised by independence and synchronisation of worlds. Compared to existing frameworks, counterfactual spaces enable the mathematical treatment of a strictly broader spectrum of counterfactuals.

math.ST↗

arXiv2025

Ensemble-Based Global Search Framework for the Design Optimization of Fabrication-Constrained Freeform Devices

Although freeform devices with complex internal structures promise drastic increases in performance, the discreteness of the set of available materials presents challenges for gradient-based optimization necessary for the efficient exploration of the high-dimensional freeform parameter space. Several schemes have been devised to utilize a continuous latent parameter space that maps to actual discrete designs, but none thus far simultaneously achieves full differentiability and strictly feasible material choices during optimization. Here, we propose the Gaussian ensemble gradient descent framework, which transforms the piecewise-constant fabrication-constrained cost function by convolution with a Gaussian kernel to render it differentiable. The transformed cost and gradient are estimated through ensemble sampling, which is combined with variance reduction methods that greatly improve the sampling efficiency in high-dimensional parameter spaces. Furthermore, the use of ensemble sampling within a gradient descent framework leads to the effective hybridization of the exploration and exploitation strengths of population- and gradient-based methods, respectively.

math.OC↗

arXiv2025

Stochastic Deep Graph Clustering for Practical Group Formation

While prior work on group recommender systems (GRSs) has primarily focused on improving recommendation accuracy, most approaches assume static or predefined groups, making them unsuitable for dynamic, real-world scenarios. We reframe group formation as a core challenge in GRSs and propose DeepForm (Stochastic Deep Graph Clustering for Practical Group Formation), a framework designed to meet three key operational requirements: (1) the incorporation of high-order user information, (2) real-time group formation, and (3) dynamic adjustment of the number of groups. DeepForm employs a lightweight GCN architecture that effectively captures high-order structural signals. Stochastic cluster learning enables adaptive group reconfiguration without retraining, while contrastive learning refines groups under dynamic conditions. Experiments on multiple datasets demonstrate that DeepForm achieves superior group formation quality, efficiency, and recommendation accuracy compared with various baselines.

cs.LG↗

arXiv2025

Two Web Toolkits for Multimodal Piano Performance Dataset Acquisition and Fingering Annotation

Piano performance is a multimodal activity that intrinsically combines physical actions with the acoustic rendition. Despite growing research interest in analyzing the multimodal nature of piano performance, the laborious process of acquiring large-scale multimodal data remains a significant bottleneck, hindering further progress in this field. To overcome this barrier, we present an integrated web toolkit comprising two graphical user interfaces (GUIs): (i) PiaRec, which supports the synchronized acquisition of audio, video, MIDI, and performance metadata. (ii) ASDF, which enables the efficient annotation of performer fingering from the visual data. Collectively, this system can streamline the acquisition of multimodal piano performance datasets.

cs.SD↗

arXiv2025

PianoVAM: A Multimodal Piano Performance Dataset

The multimodal nature of music performance has driven increasing interest in data beyond the audio domain within the music information retrieval (MIR) community. This paper introduces PianoVAM, a comprehensive piano performance dataset that includes videos, audio, MIDI, hand landmarks, fingering labels, and rich metadata. The dataset was recorded using a Disklavier piano, capturing audio and MIDI from amateur pianists during their daily practice sessions, alongside synchronized top-view videos in realistic and varied performance conditions. Hand landmarks and fingering labels were extracted using a pretrained hand pose estimation model and a semi-automated fingering annotation algorithm. We discuss the challenges encountered during data collection and the alignment process across different modalities. Additionally, we describe our fingering annotation method based on hand landmarks extracted from videos. Finally, we present benchmarking results for both audio-only and audio-visual piano transcription using the PianoVAM dataset and discuss additional potential applications.

cs.SD↗

arXiv2025

On the sample complexity of semi-supervised multi-objective learning

In multi-objective learning (MOL), several possibly competing prediction tasks must be solved jointly by a single model. Achieving good trade-offs may require a model class $\mathcal{G}$ with larger capacity than what is necessary for solving the individual tasks. This, in turn, increases the statistical cost, as reflected in known MOL bounds that depend on the complexity of $\mathcal{G}$. We show that this cost is unavoidable for some losses, even in an idealized semi-supervised setting, where the learner has access to the Bayes-optimal solutions for the individual tasks as well as the marginal distributions over the covariates. On the other hand, for objectives defined with Bregman losses, we prove that the complexity of $\mathcal{G}$ may come into play only in terms of unlabeled data. Concretely, we establish sample complexity upper bounds, showing precisely when and how unlabeled data can significantly alleviate the need for labeled data. These rates are achieved by a simple, semi-supervised algorithm via pseudo-labeling.

stat.ML↗

arXiv2025

A Classical View on Benign Overfitting: The Role of Sample Size

Benign overfitting is a phenomenon in machine learning where a model perfectly fits (interpolates) the training data, including noisy examples, yet still generalizes well to unseen data. Understanding this phenomenon has attracted considerable attention in recent years. In this work, we introduce a conceptual shift, by focusing on almost benign overfitting, where models simultaneously achieve both arbitrarily small training and test errors. This behavior is characteristic of neural networks, which often achieve low (but non-zero) training error while still generalizing well. We hypothesize that this almost benign overfitting can emerge even in classical regimes, by analyzing how the interaction between sample size and model complexity enables larger models to achieve both good training fit but still approach Bayes-optimal generalization. We substantiate this hypothesis with theoretical evidence from two case studies: (i) kernel ridge regression, and (ii) least-squares regression using a two-layer fully connected ReLU neural network trained via gradient flow. In both cases, we overcome the strong assumptions often required in prior work on benign overfitting. Our results on neural networks also provide the first generalization result in this setting that does not rely on any assumptions about the underlying regression function or noise, beyond boundedness. Our analysis introduces a novel proof technique based on decomposing the excess risk into estimation and approximation errors, interpreting gradient flow as an implicit regularizer, that helps avoid uniform convergence traps. This analysis idea could be of independent interest.

cs.LG↗

arXiv2025

UKTA: Unified Korean Text Analyzer

Evaluating writing quality is complex and time-consuming often delaying feedback to learners. While automated writing evaluation tools are effective for English, Korean automated writing evaluation tools face challenges due to their inability to address multi-view analysis, error propagation, and evaluation explainability. To overcome these challenges, we introduce UKTA (Unified Korean Text Analyzer), a comprehensive Korea text analysis and writing evaluation system. UKTA provides accurate low-level morpheme analysis, key lexical features for mid-level explainability, and transparent high-level rubric-based writing scores. Our approach enhances accuracy and quadratic weighted kappa over existing baseline, positioning UKTA as a leading multi-perspective tool for Korean text analysis and writing evaluation.

cs.CL↗

arXiv2024

Benign Overfitting for Regression with Trained Two-Layer ReLU Networks

We study the least-square regression problem with a two-layer fully-connected neural network, with ReLU activation function, trained by gradient flow. Our first result is a generalization result, that requires no assumptions on the underlying regression function or the noise other than that they are bounded. We operate in the neural tangent kernel regime, and our generalization result is developed via a decomposition of the excess risk into estimation and approximation errors, viewing gradient flow as an implicit regularizer. This decomposition in the context of neural networks is a novel perspective of gradient descent, and helps us avoid uniform convergence traps. In this work, we also establish that under the same setting, the trained network overfits to the data. Together, these results, establishes the first result on benign overfitting for finite-width ReLU networks for arbitrary regression functions.

cs.LG↗

arXiv2024

A Measure-Theoretic Axiomatisation of Causality

Causality is a central concept in a wide range of research areas, yet there is still no universally agreed axiomatisation of causality. We view causality both as an extension of probability theory and as a study of \textit{what happens when one intervenes on a system}, and argue in favour of taking Kolmogorov's measure-theoretic axiomatisation of probability as the starting point towards an axiomatisation of causality. To that end, we propose the notion of a \textit{causal space}, consisting of a probability space along with a collection of transition probability kernels, called \textit{causal kernels}, that encode the causal information of the space. Our proposed framework is not only rigorously grounded in measure theory, but it also sheds light on long-standing limitations of existing frameworks including, for example, cycles, latent variables and stochastic processes.

cs.AI↗

arXiv2024

Products, Abstractions and Inclusions of Causal Spaces

Causal spaces have recently been introduced as a measure-theoretic framework to encode the notion of causality. While it has some advantages over established frameworks, such as structural causal models, the theory is so far only developed for single causal spaces. In many mathematical theories, not least the theory of probability spaces of which causal spaces are a direct extension, combinations of objects and maps between objects form a central part. In this paper, taking inspiration from such objects in probability theory, we propose the definitions of products of causal spaces, as well as (stochastic) transformations between causal spaces. In the context of causality, these quantities can be given direct semantic interpretations as causally independent components, abstractions and extensions.

math.ST↗

arXiv2024

Particle swarm optimization with Applications to Maximum Likelihood Estimation and Penalized Negative Binomial Regression

General purpose optimization routines such as nlminb, optim (R) or nlmixed (SAS) are frequently used to estimate model parameters in nonstandard distributions. This paper presents Particle Swarm Optimization (PSO), as an alternative to many of the current algorithms used in statistics. We find that PSO can not only reproduce the same results as the above routines, it can also produce results that are more optimal or when others cannot converge. In the latter case, it can also identify the source of the problem or problems. We highlight advantages of using PSO using four examples, where: (1) some parameters in a generalized distribution are unidentified using PSO when it is not apparent or computationally manifested using routines in R or SAS; (2) PSO can produce estimation results for the log-binomial regressions when current routines may not; (3) PSO provides flexibility in the link function for binomial regression with LASSO penalty, which is unsupported by standard packages like GLM and GENMOD in Stata and SAS, respectively, and (4) PSO provides superior MLE estimates for an EE-IW distribution compared with those from the traditional statistical methods that rely on moments.

stat.ML↗

arXiv2023

Kernel-based independence tests for causal structure learning on functional data

Measurements of systems taken along a continuous functional dimension, such as time or space, are ubiquitous in many fields, from the physical and biological sciences to economics and engineering.Such measurements can be viewed as realisations of an underlying smooth process sampled over the continuum. However, traditional methods for independence testing and causal learning are not directly applicable to such data, as they do not take into account the dependence along the functional dimension. By using specifically designed kernels, we introduce statistical tests for bivariate, joint, and conditional independence for functional variables. Our method not only extends the applicability to functional data of the HSIC and its d-variate version (d-HSIC), but also allows us to introduce a test for conditional independence by defining a novel statistic for the CPT based on the HSCIC, with optimised regularisation strength estimated through an evaluation rejection rate. Our empirical results of the size and power of these tests on synthetic functional data show good performance, and we then exemplify their application to several constraint- and regression-based causal structure learning problems, including both synthetic examples and real socio-economic data.

stat.ME↗

arXiv2023

A continuous Structural Intervention Distance to compare Causal Graphs

Understanding and adequately assessing the difference between a true and a learnt causal graphs is crucial for causal inference under interventions. As an extension to the graph-based structural Hamming distance and structural intervention distance, we propose a novel continuous-measured metric that considers the underlying data in addition to the graph structure for its calculation of the difference between a true and a learnt causal graph. The distance is based on embedding intervention distributions over each pair of nodes as conditional mean embeddings into reproducing kernel Hilbert spaces and estimating their difference by the maximum (conditional) mean discrepancy. We show theoretical results which we validate with numerical experiments on synthetic data.

stat.ML↗

arXiv2022

Towards Empirical Process Theory for Vector-Valued Functions: Metric Entropy of Smooth Function Classes

This paper provides some first steps in developing empirical process theory for functions taking values in a vector space. Our main results provide bounds on the entropy of classes of smooth functions taking values in a Hilbert space, by leveraging theory from differential calculus of vector-valued functions and fractal dimension theory of metric spaces. We demonstrate how these entropy bounds can be used to show the uniform law of large numbers and asymptotic equicontinuity of the function classes, and also apply it to statistical learning theory in which the output space is a Hilbert space. We conclude with a discussion on the extension of Rademacher complexities to vector-valued function classes.

math.ST↗

arXiv2021

Conditional Distributional Treatment Effect with Kernel Conditional Mean Embeddings and U-Statistic Regression

We propose to analyse the conditional distributional treatment effect (CoDiTE), which, in contrast to the more common conditional average treatment effect (CATE), is designed to encode a treatment's distributional aspects beyond the mean. We first introduce a formal definition of the CoDiTE associated with a distance function between probability measures. Then we discuss the CoDiTE associated with the maximum mean discrepancy via kernel conditional mean embeddings, which, coupled with a hypothesis test, tells us whether there is any conditional distributional effect of the treatment. Finally, we investigate what kind of conditional distributional effect the treatment has, both in an exploratory manner via the conditional witness function, and in a quantitative manner via U-statistic regression, generalising the CATE to higher-order moments. Experiments on synthetic, semi-synthetic and real datasets demonstrate the merits of our approach.

stat.ML↗