arXiv subjects

Yuping Zheng

Publications and source records attributed to Yuping Zheng.

8 recordsLinked to original sources

arXiv2026

Non-Asymptotic Analysis of Classical Spectrum Estimators for $L$-mixing Time-series Data with Estimated Means

Spectral estimation is an important tool in time series analysis, with applications including economics, astronomy, and climatology. The asymptotic theory for non-parametric estimation is well-known but the development of non-asymptotic theory is still ongoing. Our recent work obtained the first non-asymptotic error bounds on the Bartlett and Welch methods with restrictive assumptions. In this work, we derive non-asymptotic error bounds for both Bartlett and Welch estimators for $L$-mixing time-series data with unknown means, and the results cover the special case with known zero means. The class of $L$-mixing processes contains common models in time series analysis, including autoregressive processes and measurements of geometrically ergodic Markov chains. Our new error bounds are of $O(\frac{1}{\sqrt{k}})$, where $k$ is the number of data segments used in the algorithm. Such bounds are the tightest among the existing work on non-asymptotic analysis of classical spectrum estimators with or without zero-mean assumptions.

math.ST↗

arXiv2026

Non-Asymptotic Error Bounds for Causally Conditioned Directed Information Rates of Gaussian Sequences

Directed information and its causally conditioned variations are often used to measure causal influences between random processes. In practice, these quantities must be measured from data. Non-asymptotic error bounds for these estimates are known for sequences over finite alphabets, but less is known for real-valued data. This paper examines the case in which the data are sequences of Gaussian vectors. We provide an explicit formula for causally conditioned directed information rate based on optimal prediction and define an estimator based on this formula. We show that our estimator gives an error of order $O\left(N^{-1/2}\log(N)\right)$ with high probability, where $N$ is the total sample size.

cs.IT↗

arXiv2025

Quantitative Convergence Analysis of Projected Stochastic Gradient Descent for Non-Convex Losses via the Goldstein Subdifferential

Stochastic gradient descent (SGD) is the main algorithm behind a large body of work in machine learning. In many cases, constraints are enforced via projections, leading to projected stochastic gradient algorithms. In recent years, a large body of work has examined the convergence properties of projected SGD for non-convex losses in asymptotic and non-asymptotic settings. Strong quantitative guarantees are available for convergence measured via Moreau envelopes. However, these results cannot be compared directly with work on unconstrained SGD, since the Moreau envelope construction changes the gradient. Other common measures based on gradient mappings have the limitation that convergence can only be guaranteed if variance reduction methods, such as mini-batching, are employed. This paper presents an analysis of projected SGD for non-convex losses over compact convex sets. Convergence is measured via the distance of the gradient to the Goldstein subdifferential generated by the constraints. Our proposed convergence criterion directly reduces to commonly used criteria in the unconstrained case, and we obtain convergence without requiring variance reduction. We obtain results for data that are independent, identically distributed (IID) or satisfy mixing conditions ($L$-mixing). In these cases, we derive asymptotic convergence and $O(N^{-1/3})$ non-asymptotic bounds in expectation, where $N$ is the number of steps. In the case of IID sub-Gaussian data, we obtain almost-sure asymptotic convergence and high-probability non-asymptotic $O(N^{-1/5})$ bounds. In particular, these are the first non-asymptotic high-probability bounds for projected SGD with non-convex losses.

math.OC↗

arXiv2025

Non-Asymptotic Analysis of Classical Spectrum Estimators with $L$-mixing Time-series Data

Spectral estimation is a fundamental problem for time series analysis, which is widely applied in economics, speech analysis, seismology, and control systems. The asymptotic convergence theory for classical, non-parametric estimators, is well-understood, but the non-asymptotic theory is still rather limited. Our recent work gave the first non-asymptotic error bounds on the well-known Bartlett and Welch methods, but under restrictive assumptions. In this paper, we derive non-asymptotic error bounds for a class of non-parametric spectral estimators, which includes the classical Bartlett and Welch methods, under the assumption that the data is an $L$-mixing stochastic process. A broad range of processes arising in time-series analysis, such as autoregressive processes and measurements of geometrically ergodic Markov chains, can be shown to be $L$-mixing. In particular, $L$-mixing processes can model a variety of nonlinear phenomena which do not satisfy the assumptions of our prior work. Our new error bounds for $L$-mixing processes match the error bounds in the restrictive settings from prior work up to logarithmic factors.

math.ST↗

arXiv2025

Efficiently Democratizing Medical LLMs for 50 Languages via a Mixture of Language Family Experts

Adapting medical Large Language Models to local languages can reduce barriers to accessing healthcare services, but data scarcity remains a significant challenge, particularly for low-resource languages. To address this, we first construct a high-quality medical dataset and conduct analysis to ensure its quality. In order to leverage the generalization capability of multilingual LLMs to efficiently scale to more resource-constrained languages, we explore the internal information flow of LLMs from a multilingual perspective using Mixture of Experts (MoE) modularity. Technically, we propose a novel MoE routing method that employs language-specific experts and cross-lingual routing. Inspired by circuit theory, our routing analysis revealed a Spread Out in the End information flow mechanism: while earlier layers concentrate cross-lingual information flow, the later layers exhibit language-specific divergence. This insight directly led to the development of the Post-MoE architecture, which applies sparse routing only in the later layers while maintaining dense others. Experimental results demonstrate that this approach enhances the generalization of multilingual models to other languages while preserving interpretability. Finally, to efficiently scale the model to 50 languages, we introduce the concept of language family experts, drawing on linguistic priors, which enables scaling the number of languages without adding additional parameters.

cs.CL↗

arXiv2023

Optimizing the Wasserstein GAN for TeV Gamma Ray Detection with VERITAS

The observation of very-high-energy (VHE, E>100 GeV) gamma rays is mediated by the imaging atmospheric Cherenkov technique (IACTs). At these energies, gamma rays interact with the atmosphere to create a cascade of electromagnetic air showers that are visible to the IACT cameras on the ground with distinct morphological and temporal features. However, hadrons with significantly higher incidence rates are also imaged with similar features, and must be distinguished with handpicked parameters extracted from the images. The advent of sophisticated deep learning models has enabled an alternative image analysis technique that has been shown to improve the detection of gamma rays, by improving background rejection. In this study, we propose an unsupervised Wasserstein Generative Adversarial Network (WGAN) framework trained on normalized, uncleaned stereoscopic shower images of real events from the VERITAS observatory to extract the landscape of their latent space and optimize against the corresponding inferred latent space of simulated gamma-ray events. We aim to develop a data driven approach to guide the understanding of the extracted features of real gamma-ray images, and will optimize the WGAN to calculate a probabilistic prediction of "gamma-ness" per event. In this poster, we present results of ongoing work toward the optimization of the WGAN, including the exploration of conditional parameters and multi-task learning.

astro-ph.HE↗

arXiv2023

Constrained Langevin Algorithms with L-mixing External Random Variables

Langevin algorithms are gradient descent methods augmented with additive noise, and are widely used in Markov Chain Monte Carlo (MCMC) sampling, optimization, and machine learning. In recent years, the non-asymptotic analysis of Langevin algorithms for non-convex learning has been extensively explored. For constrained problems with non-convex losses over a compact convex domain with IID data variables, the projected Langevin algorithm achieves a deviation of $O(T^{-1/4} (\log T)^{1/2})$ from its target distribution [27] in $1$-Wasserstein distance. In this paper, we obtain a deviation of $O(T^{-1/2} \log T)$ in $1$-Wasserstein distance for non-convex losses with $L$-mixing data variables and polyhedral constraints (which are not necessarily bounded). This improves on the previous bound for constrained problems and matches the best-known bound for unconstrained problems.

cs.LG↗

arXiv2022

From fat droplets to floating forests: cross-domain transfer learning using a PatchGAN-based segmentation model

Many scientific domains gather sufficient labels to train machine algorithms through human-in-the-loop techniques provided by the Zooniverse.org citizen science platform. As the range of projects, task types and data rates increase, acceleration of model training is of paramount concern to focus volunteer effort where most needed. The application of Transfer Learning (TL) between Zooniverse projects holds promise as a solution. However, understanding the effectiveness of TL approaches that pretrain on large-scale generic image sets vs. images with similar characteristics possibly from similar tasks is an open challenge. We apply a generative segmentation model on two Zooniverse project-based data sets: (1) to identify fat droplets in liver cells (FatChecker; FC) and (2) the identification of kelp beds in satellite images (Floating Forests; FF) through transfer learning from the first project. We compare and contrast its performance with a TL model based on the COCO image set, and subsequently with baseline counterparts. We find that both the FC and COCO TL models perform better than the baseline cases when using >75% of the original training sample size. The COCO-based TL model generally performs better than the FC-based one, likely due to its generalized features. Our investigations provide important insights into usage of TL approaches on multi-domain data hosted across different Zooniverse projects, enabling future projects to accelerate task completion.

cs.LG↗