Wasserstein-type Gaussian Process Regressions for Input Measurement Uncertainty

Gaussian process (GP) regression is widely used for uncertainty quantification, yet the standard formulation assumes noise-free covariates. When inputs are measured with error, this errors-in-variables (EIV) setting can lead to optimistically narrow posterior intervals and biased decisions. We study GP regression under input measurement uncertainty by representing each noisy input as a probability measure and defining covariance through Wasserstein distances between these measures. Building on this perspective, we instantiate a deterministic projected Wasserstein ARD (PWA) kernel whose one-dimensional components admit closed-form expressions and whose product structure yields a scalable, positive-definite kernel on distributions. Unlike latent-input GP models, PWA-based GPs (\PWAGPs) handle input noise without introducing unobserved covariates or Monte Carlo projections, making uncertainty quantification more transparent and robust.

ACMID: Automatic Curation of Musical Instrument Dataset for 7-Stem Music Source Separation

Most current music source separation (MSS) methods rely on supervised learning, limited by training data quan- tity and quality. Though web-crawling can bring abundant data, platform-level track labeling often causes metadata mismatches, impeding accurate "audio-label" pair acquisi- tion. To address this, we present ACMID: a dataset for MSS generated through web crawling of extensive raw data, fol- lowed by automatic cleaning via an instrument classifier built on a pre-trained audio encoder that filters and aggregates clean segments of target instruments from the crawled tracks, resulting in the refined ACMID-Cleaned dataset. Leverag- ing abundant data, we expand the conventional classifica- tion from 4-stem (Vocal/Bass/Drums/Others) to 7-stem (Pi- ano/Drums/Bass/Acoustic Guitar/Electric Guitar/Strings/Wind- Brass), enabling high granularity MSS systems. Experiments on SOTA MSS model demonstrates two key results: (i) MSS model trained with ACMID-Cleaned achieved a 2.39dB improvement in SDR performance compared to that with ACMID-Uncleaned, demostrating the effectiveness of our data cleaning procedure; (ii) incorporating ACMID-Cleaned to training enhances MSS model's average performance by 1.16dB, confirming the value of our dataset. Our data crawl- ing code, cleaning model code and weights are available at: https://github.com/scottishfold0621/ACMID.