arXiv subjects

Lujia Bai

Publications and source records attributed to Lujia Bai.

11 recordsLinked to original sources

arXiv2026

EMPURPLE: A Free Lunch for Diffusion Distillation based on the Information Bottleneck

Diffusion models achieve impressive image-generation quality but remain expensive at inference time. Diffusion distillation reduces sampling steps, yet many distilled models, including SDXL-Lightning and distribution matching distillation methods, suffer from degraded Fr\'echet Inception Distance (FID). We analyze this phenomenon through a PAC-style generalization bound. Our analysis suggests that aggressive early-step redirection of the velocity field makes the distillation target harder to learn, enlarging the train-test gap. As a result, early-step output distributions differ between training and inference, causing distribution mismatch in the intermediate noisy latent used as next-step inputs. We empirically validate this mechanism by showing reduced diversity in both intermediate features and final outputs. To address this issue, we propose EMPURPLE, a simple training-free method that recycles intermediate latents sampled from the original model. EMPURPLE is model-agnostic and improves FID by 7\% to 20\% across DMD2, Hyper-SD, FlashSD, and SDXL-Lightning. The repo is: https://github.com/TheLovesOfLadyPurple/Empurple-Training-Free-Algorithm-To-enhance-Diversity-of-The-Diffusion-Distillation-Model

cs.CV↗

arXiv2026

Validating spatial-temporal separability for stationary processes

A crucial assumption to reduce computational complexity in spatial-temporal data analysis is separability, which factors the covariance structure into a purely spatial and a purely temporal component. In this paper, we develop statistical inference tools for validating this assumption for a second-order stationary process under both domain-expanding-infill asymptotics and domain-expanding asymptotics. In contrast to previous work on this subject, the methodology neither requires the assumption of normally distributed data, nor uses spectral methods. Our approach is based on nonparametric estimates of measures for the deviation between the covariance matrix and separable approximations, which vanish if and only if the assumption of separability is satisfied. We derive the asymptotic distributions of appropriate estimators for these measures with non-standard limiting distributions and use these results to develop inference tools for validating the assumption of separability. More specifically, we derive confidence intervals for the deviation measures, tests for the hypothesis of exact separability, and for the hypothesis that the deviation from separability is smaller than a prespecified threshold.

math.ST↗

arXiv2025

Asymptotic Uniform False Discovery Rate Control for Inference of Time-varying Correlations

Inference for locally stationary time series is challenging because the associated hypotheses form an uncountable collection over a continuous time interval, making pointwise false discovery rate (FDR) control inadequate for simultaneous statistical guarantees. We introduce a novel asymptotically uniform false discovery rate (AuFDR), defined as the expectation of the $L_r$-norm of the false discovery proportion (FDP) process where $r$ is allowed to diverge, to quantify and control false discoveries uniformly over time. To operationalize AuFDR control, we develop an inferential framework for time-varying correlations in high-dimensional nonstationary time series that allows for non-Gaussianity, nonlinearity and possible jumps in mean functions. The proposed approach combines robust difference-based estimators with a multiplier-bootstrap procedure to construct uniformly valid time-varying $P$-values. Based on these $P$-values, we propose a time-varying Benjamini--Yekutieli procedure for controlling the AuFDR under arbitrary dependence and establish its asymptotic validity. Extensive simulations demonstrate the finite-sample performance of the proposed method in controlling the AuFDR. Applications to EEG data and financial time-series data illustrate its practical utility.

stat.ME↗

arXiv2025

Measuring deviations from spherical symmetry

Most of the work on checking spherical symmetry assumptions on the distribution of the $p$-dimensional random vector $Y$ has its focus on statistical tests for the null hypothesis of exact spherical symmetry. In this paper, we take a different point of view and propose a measure for the deviation from spherical symmetry, which is based on the minimum distance between the distribution of the vector $\big (\|Y\|, Y/ \|Y\| )^\top $ and its best approximation by a distribution of a vector $\big (\|Y_s\|, Y_s/ \|Y_s \| )^\top $ corresponding to a random vector $Y_s$ with a spherical distribution. We develop estimators for the minimum distance with corresponding statistical guarantees (provided by asymptotic theory) and demonstrate the applicability of our approach by means of a simulation study and a real data example.

stat.ME↗

arXiv2025

F-scheduler: illuminating the free-lunch design space for fast sampling of diffusion models

Diffusion models are the state-of-the-art generative models for high-resolution images, but sampling from pretrained models is computationally expensive, motivating interest in fast sampling. Although Free-U Net is a training-free enhancement for improving image quality, we find it ineffective under few-step ($<10$) sampling. We analyze the discrete diffusion ODE and propose F-scheduler, a scheduler designed for ODE solvers with Free-U Net. Our proposed scheduler consists of a special time schedule that does not fully denoise the feature to enable the use of the KL-term in the $\beta$-VAE decoder, and the schedule of a proper inference stage for modifying the U-Net skip-connection via Free-U Net. Via information theory, we provide insights into how the better scheduled ODE solvers for the diffusion model can outperform the training-based diffusion distillation model. The newly proposed scheduler is compatible with most of the few-step ODE solvers and can sample a 1024 x 1024-resolution image in 6 steps and a 512 x 512-resolution image in 5 steps when it applies to DPM++ 2m and UniPC, with an FID result that outperforms the SOTA distillation models and the 20-step DPM++ 2m solver, respectively. Codebase: https://github.com/TheLovesOfLadyPurple/F-scheduler

cs.GR↗

arXiv2024

A portmanteau test for multivariate non-stationary functional time series with an increasing number of lags

Multivariate locally stationary functional time series provide a flexible framework for modeling functional data exhibiting both temporal and spatial dependencies while allowing for a time-varying data generating mechanism. In this paper, we introduce a portmanteau-type test for assessing white noise assumptions tailored for multivariate locally stationary functional time series without dimension reduction. A simple bootstrap procedure is proposed to implement the test, because it is not clear if the limiting distribution of the test statistic exists. Our approach is based on a Gaussian approximation result for a degenerate $U$-statistic of second-order functional time series involving an increasing number of lags, which is of independent interest. Through theoretical analysis, simulation studies, and real data analysis of energy consumptions, we demonstrate the efficacy and adaptability of the proposed method in detecting departures from white noise assumptions in multivariate locally stationary functional time series. Finally, the R package corresponding to our method can be downloaded from https://github.com/Lujia-Bai/nftsport.

stat.ME↗

arXiv2024

Complex trend inference for high-dimensional piecewise locally stationary time series

This paper studies high-dimensional trend inference for piecewise smooth signals under nonstationary noise and asynchronous structural breaks by first detecting asynchronous changes without assuming stationarity and then further exploiting latent group structures to estimate trend functions. In the first step, we propose AJDN (Asynchronous Jump Detection under Nonstationary Noise), a multiscale framework for the identification and localization of jumps in high-dimensional time series. We show that AJDN consistently recovers the number of jumps with a prescribed asymptotic probability and achieves nearly optimal localization rates in the presence of asynchronicity and nonstationarity, both of which often violate the assumptions of existing high-dimensional change point methods and thereby deteriorate their performance. In the second step, we augment AJDN with a homogeneity pursuit step and obtain AJDN-H, which identifies latent groups of dimensions that share common jump structures and trend parameters given the detected jumps. This allows for efficient information pooling and improves the accuracy of trend estimation under both asynchronicity and nonstationarity. The robustness and finite-sample performance of the proposed methodology are examined by extensive simulation studies. An application to financial data demonstrates the practical utility of the AJDN-H framework in complex, high-dimensional settings.

stat.ME↗

arXiv2023

Difference-based covariance matrix estimate in time series nonparametric regression with applications to specification tests

Long-run covariance matrix estimation is the building block of time series inference. The corresponding difference-based estimator, which avoids detrending, has attracted considerable interest due to its robustness to both smooth and abrupt structural breaks and its competitive finite sample performance. However, existing methods mainly focus on estimators for the univariate process while their direct and multivariate extensions for most linear models are asymptotically biased. We propose a novel difference-based and debiased long-run covariance matrix estimator for functional linear models with time-varying regression coefficients, allowing time series non-stationarity, long-range dependence, state-heteroscedasticity and their mixtures. We apply the new estimator to (i) the structural stability test, overcoming the notorious non-monotonic power phenomena caused by piecewise smooth alternatives for regression coefficients, and (ii) the nonparametric residual-based tests for long memory, improving the performance via the residual-free formula of the proposed estimator. The effectiveness of the proposed method is justified theoretically and demonstrated by superior performance in simulation studies, while its usefulness is elaborated via real data analysis. Our method is implemented in the R package mlrv.

stat.ME↗

arXiv2023

Time-varying correlation network analysis of non-stationary multivariate time series with complex trends

This paper proposes a flexible framework for inferring large-scale time-varying and time-lagged correlation networks from multivariate or high-dimensional non-stationary time series with piecewise smooth trends. Built on a novel and unified multiple-testing procedure of time-lagged cross-correlation functions with a fixed or diverging number of lags, our method can accurately disclose flexible time-varying network structures associated with complex functional structures at all time points. We broaden the applicability of our method to the structure breaks by developing difference-based nonparametric estimators of cross-correlations, achieve accurate family-wise error control via a bootstrap-assisted procedure adaptive to the complex temporal dynamics, and enhance the probability of recovering the time-varying network structures using a new uniform variance reduction technique. We prove the asymptotic validity of the proposed method and demonstrate its effectiveness in finite samples through simulation studies and empirical applications.

stat.ME↗

arXiv2023

UniPC: A Unified Predictor-Corrector Framework for Fast Sampling of Diffusion Models

Diffusion probabilistic models (DPMs) have demonstrated a very promising ability in high-resolution image synthesis. However, sampling from a pre-trained DPM is time-consuming due to the multiple evaluations of the denoising network, making it more and more important to accelerate the sampling of DPMs. Despite recent progress in designing fast samplers, existing methods still cannot generate satisfying images in many applications where fewer steps (e.g., $<$10) are favored. In this paper, we develop a unified corrector (UniC) that can be applied after any existing DPM sampler to increase the order of accuracy without extra model evaluations, and derive a unified predictor (UniP) that supports arbitrary order as a byproduct. Combining UniP and UniC, we propose a unified predictor-corrector framework called UniPC for the fast sampling of DPMs, which has a unified analytical form for any order and can significantly improve the sampling quality over previous methods, especially in extremely few steps. We evaluate our methods through extensive experiments including both unconditional and conditional sampling using pixel-space and latent-space DPMs. Our UniPC can achieve 3.87 FID on CIFAR10 (unconditional) and 7.51 FID on ImageNet 256$\times$256 (conditional) with only 10 function evaluations. Code is available at https://github.com/wl-zhao/UniPC.

cs.LG↗

arXiv2021

Detecting long-range dependence for time-varying linear models

We consider the problem of testing for long-range dependence in time-varying coefficient regression models, where the covariates and errors are locally stationary, allowing complex temporal dynamics and heteroscedasticity. We develop KPSS, R/S, V/S, and K/S-type statistics based on the nonparametric residuals. Under the null hypothesis, the local alternatives as well as the fixed alternatives, we derive the limiting distributions of the test statistics. As the four types of test statistics could degenerate when the time-varying mean, variance, long-run variance of errors, covariates, and the intercept lie in certain hyperplanes, we show the bootstrap-assisted tests are consistent under both degenerate and non-degenerate scenarios. In particular, in the presence of covariates the exact local asymptotic power of the bootstrap-assisted tests can enjoy the same order as that of the classical KPSS test of long memory for strictly stationary series. The asymptotic theory is built on a new Gaussian approximation technique for locally stationary long-memory processes with short-memory covariates, which is of independent interest. The effectiveness of our tests is demonstrated by extensive simulation studies and real data analysis.

math.ST↗