arXiv subjects

Jonghwa Park

Publications and source records attributed to Jonghwa Park.

9 recordsLinked to original sources

arXiv2026

Bounding adapted Wasserstein metrics

The Wasserstein distance $\mathcal{W}_p$ is an important instance of an optimal transport cost. Its numerous mathematical properties as well as applications to various fields such as mathematical finance and statistics have been well studied in recent years. The adapted Wasserstein distance $\mathcal{A}\mathcal{W}_p$ extends this theory to laws of discrete time stochastic processes in their natural filtrations, making it particularly well suited for analyzing time-dependent stochastic optimization problems. While the topological differences between $\mathcal{A}\mathcal{W}_p$ and $\mathcal{W}_p$ are well understood, their differences as metrics remain largely unexplored beyond the trivial bound $\mathcal{W}_p\lesssim \mathcal{A}\mathcal{W}_p$. This paper closes this gap by providing upper bounds of $\mathcal{A}\mathcal{W}_p$ in terms of $\mathcal{W}_p$ through investigation of the smooth adapted Wasserstein distance. Our upper bounds are explicit and are given by a sum of $\mathcal{W}_p$, Eder's modulus of continuity and a term characterizing the tail behavior of measures. As a consequence, upper bounds on $\mathcal{W}_p$ automatically hold for $\mathcal{AW}_p$ under mild regularity assumptions on the measures considered. A particular instance of our findings is the inequality $\mathcal{A}\mathcal{W}_1\le C\sqrt{\mathcal{W}_1}$ on the set of measures that have Lipschitz kernels. Our work also reveals how smoothing of measures affects the adapted weak topology. In fact, we find that the topology induced by the smooth adapted Wasserstein distance exhibits a non-trivial interpolation property, which we characterize explicitly: it lies in between the adapted weak topology and the weak topology, and the inclusion is governed by the decay of the smoothing parameter.

math.PR↗

arXiv2026

SKY-Piano: A Multimodal Piano Performance Dataset

Music information retrieval research on piano performance increasingly involves diverse modalities of data and annotations beyond audio and MIDI. We present SKY-Piano, a multimodal piano performance dataset that includes 11 hours of performance recordings of motion, multi-view video, audio, MIDI from 7 professional and 12 amateur pianists along with MusicXML scores. The performance pieces were selected considering playing technique, difficulty, and performer expertise on a shared core repertoire. The motion data include both hand and body motion, released in both flagged form, where samples lost to marker occlusion are marked as unreliable, and imputed form, where those gaps are reconstructed, together with Visual3D body-segment kinematics and other time-synchronized modalities. To easily browse different modalities of data at a glance, we provide an interactive web browser. In addition, we developed a fingering annotation model and tool for deriving pseudo fingering annotations from the MIDI and motion data. Lastly, we present MIDI-to-motion generation through a fine-tuning experiment as a use case of the dataset.

cs.SD↗

arXiv2026

Hedging short-maturity Asian options in local volatility models

This paper discusses the short-maturity behavior of Asian option prices and hedging portfolios. We consider the risk-neutral valuation and the delta value of the Asian option having a Hölder continuous payoff function in a local volatility model. The main idea of this analysis is that the local volatility model can be approximated by a Gaussian process at short maturity. By combining this approximation argument with Malliavin calculus, we derive short-maturity asymptotics for Asian option prices and deltas, and express them in terms of the local volatility function and the initial stock price. In addition, we show that the convergence rate of the approximation is determined by the Hölder exponent of the payoff function. Numerical experiments on concrete examples validate the effectiveness of the proposed method.

q-fin.MF↗

arXiv2026

PiAnnotate: A Web Annotation Tool for Piano Fingering, with a Diagnostic Probe

Piano fingering shapes how a passage can be played, yet it is difficult to label after a performance. An annotator must decide which finger produced each note while reconciling the score, timing, video, and hand motion. We present PiAnnotate, a web-based pipeline for adding expert fingering annotations to the FurElise performance dataset. The tool brings together a piano-roll view, performance video, and a 3D MANO hand mesh so that reviewers can inspect each assignment in musical and physical context. Rather than storing only the final answer, PiAnnotate keeps paired rule-based and human-edited fingering tracks. These paired tracks make the annotation history auditable by showing where a geometric rule was sufficient, where experts intervened, and how labels changed across review passes. As a final diagnostic, we train a small Transformer probe on the paired tracks. The probe improves on the rule baseline on held-out pieces while remaining conservative about changing labels that were already correct, suggesting that the edited labels contain learnable structure rather than only isolated fixes.

cs.SD↗

arXiv2026

Tipiano: Cascaded Piano Hand Motion Synthesis via Fingertip Priors

Synthesizing realistic piano hand motions requires both precision and naturalness. Physics-based methods achieve precision but produce stiff motions; data-driven models learn natural dynamics but struggle with positional accuracy. Piano motion exhibits a natural hierarchy: fingertip positions are nearly deterministic given piano geometry and fingering, while wrist and intermediate joints offer stylistic freedom. We present [OURS], a four-stage framework exploiting this hierarchy: (1) statistics-based fingertip positioning, (2) FiLM-conditioned trajectory refinement, (3) wrist estimation, and (4) STGCN-based pose synthesis. We contribute expert-annotated fingerings for the FürElise dataset (153 pieces, ~10 hours). Experiments demonstrate F1 = 0.910, substantially outperforming diffusion baselines (F1 = 0.121), with user study (N=41) confirming quality approaching motion capture. Expert evaluation by professional pianists (N=5) identified anticipatory motion as the key remaining gap, providing concrete directions for future improvement.

cs.AI↗

arXiv2026

The fast rate of convergence of the smooth adapted Wasserstein distance

Estimating a $d$-dimensional distribution $μ$ by the empirical measure $\hatμ_n$ of its samples is an important task in probability theory, statistics and machine learning. It is well known that $\mathbb{E}[\mathcal{W}_p(\hatμ_n, μ)]\lesssim n^{-1/d}$ for $d>2p$, where $\mathcal{W}_p$ denotes the $p$-Wasserstein metric. An effective tool to combat this curse of dimensionality is the smooth Wasserstein distance $\mathcal{W}^{(σ)}_p$, which measures the distance between two probability measures after having convolved them with isotropic Gaussian noise $\mathcal{N}(0,σ^2\text{I})$. In this paper we apply this smoothing technique to the adapted Wasserstein distance. We show that the smooth adapted Wasserstein distance $\mathcal{A}\mathcal{W}_p^{(σ)}$ achieves the fast rate of convergence $\mathbb{E}[\mathcal{A}\mathcal{W}_p^{(σ)}(\hatμ_n, μ)]\lesssim n^{-1/2}$, if $μ$ is subgaussian. This result follows from the surprising fact, that any subgaussian measure $μ$ convolved with a Gaussian distribution has locally Lipschitz kernels.

math.PR↗

arXiv2025

On a $T_1$ Transport inequality for the adapted Wasserstein distance

The $L^1$ transport-entropy inequality (or $T_1$ inequality), which bounds the $1$-Wasserstein distance in terms of the relative entropy, is known to characterize Gaussian concentration. To extend the $T_1$ inequality to laws of discrete-time processes while preserving their temporal structure, we investigate the adapted $T_1$ inequality which relates the $1$-adapted Wasserstein distance to the relative entropy. Building on the Bolley--Villani inequality, we establish the adapted $T_1$ inequality under the same moment assumption as the classical $T_1$ inequality.

math.PR↗

arXiv2025

Designing a Multimodal Viewer for Piano Performance Analysis -- a Pedagogy-First Approach

Abstract instructions in piano education, such as "raise your wrist" and "relax your tension," lead to varying interpretations among learners, preventing instructors from effectively conveying their intended pedagogical guidance. To address this problem, this study conducted systematic interviews with a piano professor with 18 years teaching experience, and two researchers derived seven core need groups through cross-validation. Based on these findings, we developed a web-based dashboard prototype integrating video, motion capture, and musical scores, enabling instructors to provide concrete, visual feedback instead of relying solely on abstract verbal instructions. Technical feasibility was validated through 109 performance datasets.

cs.MM↗

arXiv2024

On concentration of the empirical measure for radial transport costs

Let $μ$ be a probability measure on $\mathbb{R}^d$ and $μ_N$ its empirical measure with sample size $N$. We prove a concentration inequality for the optimal transport cost between $μ$ and $μ_N$ for radial cost functions with polynomial local growth, that can have superpolynomial global growth. This result generalizes and improves upon estimates of Fournier and Guillin. The proof combines ideas from empirical process theory with known concentration rates for compactly supported $μ$. By partitioning $\mathbb{R}^d$ into annuli, we infer a global estimate from local estimates on the annuli and conclude that the global estimate can be expressed as a sum of the local estimate and a mean-deviation probability for which efficient bounds are known.

math.ST↗