arXiv subjects

Huiping Chen

Publications and source records attributed to Huiping Chen.

11 recordsLinked to original sources

arXiv2026

Optimal Sobolev Rate for Gaussian Density Approximation of Wiener Chaos Vectors

Let $(F_n)$ be a sequence of random vectors with identity covariance matrix whose components belong to the same fixed Wiener chaos, and assume that $F_n$ converges in law to a standard Gaussian vector. We prove that, for every integer $m\geq0$ and every $p\in[1,\infty]$, the optimal rate of convergence of the densities in the Sobolev space $W^{m,p}$ is given by the maximum of the absolute third-order cumulants and the diagonal fourth-order cumulants. The same quantity also gives the optimal rates in total variation, Kolmogorov and $1$-Wasserstein distances. Our proof first derives, by Gaussian interpolation and Gaussian convolution, a cumulant expansion in the space of tempered distributions without imposing Malliavin nondegeneracy at the endpoint. Finite-order Malliavin density estimates then upgrade this identity to Sobolev spaces. Matching lower bounds follow from a finite-dimensional argument in which parity separates the third-order and fourth-order Gaussian corrections, while norm equivalence rules out cancellations among mixed cumulants. A superconvergence theorem supplies the required finite negative moments of the Malliavin determinant along a sufficiently far tail of the approximating sequence, so that no Malliavin nondegeneracy assumption is required.

math.PR↗

arXiv2026

FairReL: Deepfake Detection using Fairness-Aware Representation Learning

Although recent deepfake detectors achieve high overall accuracy, their errors remain unevenly distributed across demographic subgroups, with real faces from certain groups more often misclassified as fake. Existing fairness-aware detectors typically regularise the entire feature representation, without identifying or controlling the specific components that drive unfair predictions. Such coarse intervention can over-suppress useful forgery cues while leaving demographic structure in component-specific subspaces. To address this, we identify two subgroup-sensitive components: multi-scale spatial features, which encode local facial and forgery patterns, and fine-tuning-induced residual features, which adapt the backbone to the unfair training distribution. We propose FairReL, a fairness-aware representation-learning framework that targets both components with dedicated demographic supervision. FairReL uses an SVD-decomposed foundation-model backbone to isolate the fine-tuning-induced residual representation, and introduces two complementary losses. Group-Conditional Wavelet Decorrelation (GCWD) suppresses subgroup-imbalanced structure across spatial wavelet sub-bands, while Subspace-Localised Mean Alignment (SLMA) aligns subgroup means within each real/fake class in the residual representation. Experiments on FF++, Celeb-DF, DFD and DFDC show that, against the state-of-the-art fairness-aware detector, FairReL improves unseen-dataset AUC by 3.9% while reducing subgroup FPR disparity by 10.2%. Code is available at https://github.com/xiaoman89/FairReL .

cs.CV↗

arXiv2025

Towards Robust Protective Perturbation against DeepFake Face Swapping

DeepFake face swapping enables highly realistic identity forgeries, posing serious privacy and security risks. A common defence embeds invisible perturbations into images, but these are fragile and often destroyed by basic transformations such as compression or resizing. In this paper, we first conduct a systematic analysis of 30 transformations across six categories and show that protection robustness is highly sensitive to the choice of training transformations, making the standard Expectation over Transformation (EOT) with uniform sampling fundamentally suboptimal. Motivated by this, we propose Expectation Over Learned distribution of Transformation (EOLT), the framework to treat transformation distribution as a learnable component rather than a fixed design choice. Specifically, EOLT employs a policy network that learns to automatically prioritize critical transformations and adaptively generate instance-specific perturbations via reinforcement learning, enabling explicit modeling of defensive bottlenecks while maintaining broad transferability. Extensive experiments demonstrate that our method achieves substantial improvements over state-of-the-art approaches, with 26% higher average robustness and up to 30% gains on challenging transformation categories.

cs.CV↗

arXiv2025

Indexing Strings with Utilities

Applications in domains ranging from bioinformatics to advertising feature strings that come with numerical scores (utilities). The utilities quantify the importance, interest, profit, or risk of the letters occurring at every position of a string. Motivated by the ever-increasing rate of generating such data, as well as by their importance in several domains, we introduce Useful String Indexing (USI), a natural generalization of the classic String Indexing problem. Given a string $S$ (the text) of length $n$, USI asks for preprocessing $S$ into a compact data structure supporting the following queries efficiently: given a shorter string $P$ (the pattern), return the global utility $U(P)$ of $P$ in $S$, where $U$ is a function that maps any string $P$ to a utility score based on the utilities of the letters of every occurrence of $P$ in $S$. Our work also makes the following contributions: (1) We propose a novel and efficient data structure for USI based on finding the top-$K$ frequent substrings of $S$. (2) We propose a linear-space data structure that can be used to mine the top-$K$ frequent substrings of $S$ or to tune the parameters of the USI data structure. (3) We propose a novel space-efficient algorithm for estimating the set of the top-$K$ frequent substrings of $S$, thus improving the construction space of the data structure for USI. (4) We show that popular space-efficient top-$K$ frequent item mining strategies employed by state-of-the-art algorithms do not smoothly translate from items to substrings. (5) Using billion-letter datasets, we experimentally demonstrate that: (i) our top-$K$ frequent substring mining algorithms are accurate and scalable, unlike two state-of-the-art methods; and (ii) our USI data structures are up to $15$ times faster in querying than $4$ nontrivial baselines while occupying the same space with them.

cs.DS↗

arXiv2024

Ergodicity for Ginzburg-Landau equation with complex-valued space-time white noise on two-dimensional torus

We investigate the global well-posedness and ergodicity of the complex Ginzburg-Landau equation with a general nonlinear term on the two-dimensional torus, driven by complex-valued space-time white noise. Due to the roughness of noise, the solution to this singular equation is a distribution-valued stochastic process. As a result, the nonlinear term is ill-defined and requires renormalization. We establish global well-posedness by combining the fixed point theorem with an estimate that decays over time. Moreover, we prove ergodicity by applying the Krylov-Bogoliubov theorem along with an asymptotic coupling argument. A crucial tool in our proof is the theory of complex multiple Wiener-Ito integrals, which enables direct estimates for random distributions themselves and provides a systematic framework for estimating complex Wick products.

math.PR↗

arXiv2024

Berry-Esséen bound for complex Wiener-Itô integral

For complex multiple Wiener-Itô integral, we present Berry-Esséen upper and lower bounds in terms of moments and kernel contractions under the Wasserstein distance. As a corollary, we simplify the previously known contraction condition of the complex Fourth Moment Theorem. Additionally, as an application, we explore the optimal Berry-Esséen bound for a statistic associated with the complex-valued Ornstein-Uhlenbeck process.

math.PR↗

arXiv2024

Pattern Masking for Dictionary Matching

In the Pattern Masking for Dictionary Matching (PMDM) problem, we are given a dictionary $\mathcal{D}$ of $d$ strings, each of length $\ell$, a query string $q$ of length $\ell$, and a positive integer $z$, and we are asked to compute a smallest set $K\subseteq\{1,\ldots,\ell\}$, so that if $q[i]$, for all $i\in K$, is replaced by a wildcard, then $q$ matches at least $z$ strings from $\mathcal{D}$. The PMDM problem lies at the heart of two important applications featured in large-scale real-world systems: record linkage of databases that contain sensitive information, and query term dropping. In both applications, solving PMDM allows for providing data utility guarantees as opposed to existing approaches. We first show, through a reduction from the well-known $k$-Clique problem, that a decision version of the PMDM problem is NP-complete, even for strings over a binary alphabet. We present a data structure for PMDM that answers queries over $\mathcal{D}$ in time $\mathcal{O}(2^{\ell/2}(2^{\ell/2}+τ)\ell)$ and requires space $\mathcal{O}(2^{\ell}d^2/τ^2+2^{\ell/2}d)$, for any parameter $τ\in[1,d]$. We also approach the problem from a more practical perspective. We show an $\mathcal{O}((d\ell)^{k/3}+d\ell)$-time and $\mathcal{O}(d\ell)$-space algorithm for PMDM if $k=|K|=\mathcal{O}(1)$. We generalize our exact algorithm to mask multiple query strings simultaneously. We complement our results by showing a two-way polynomial-time reduction between PMDM and the Minimum Union problem [Chlamtáč et al., SODA 2017]. This gives a polynomial-time $\mathcal{O}(d^{1/4+ε})$-approximation algorithm for PMDM, which is tight under plausible complexity conjectures.

cs.DS↗

arXiv2023

An improved complex fourth moment theorem

For a series of univariate or multivariate complex multiple Wiener-Itô integrals, we appreciably improve the previously known contractions condition of complex Fourth Moment Theorem (FMT) and present a fourth moment type Berry-Esséen bound under Wasserstein distance. Note that in some special cases of univariate complex multiple Wiener-Itô integral, the Berry-Esséen bound we acquired is optimal. A remarkable fact is that the Berry-Esséen bound of multivariate complex multiple Wiener-Itô integral is related to the partially order of the index of the complex multiple Wiener-Itô integral, which has no real counterparts as far as we know. As an application, we explore the asymptotic property for the numerator of a ratio process which originates from the classical Chandler wobble model.

math.PR↗

arXiv2023

Optimal Rate of Convergence for Vector-valued Wiener-Ito Integral

We investigate the optimal rate of convergence in the multidimensional normal approximation of vector-valued Wiener-Ito integrals of which components all belong to the same fixed Wiener chaos. Combining Malliavin calculus, Stein's method for normal approximation and method of cumulants, we obtain the optimal rate of convergence with respect to a suitable smooth distance. As applications, we derive the optimal rates of convergences for complex Wiener-Ito integrals, vector-valued Wiener-Ito integrals with kernels of step functions and vector-valued Toeplitz quadratic functionals.

math.PR↗

arXiv2022

Kernel representation formula from complex to real Wiener-Ito integrals and vice versa

We clearly characterize the relation between real and complex Wiener-Ito integrals. Given a complex multiple Wiener-Ito integral, we get explicit expressions for two kernels of its real and imaginary parts. Conversely, consider a two-dimensional real Wiener-Ito integral, we obtain the representation formula by a finite sum of complex Wiener-Ito integrals. The main tools are a recursion technique and Malliavin derivative operators. We build a bridge between real and complex Wiener-Ito integrals.

math.PR↗

arXiv2019

Combinatorial Algorithms for String Sanitization

String data are often disseminated to support applications such as location-based service provision or DNA sequence analysis. This dissemination, however, may expose sensitive patterns that model confidential knowledge. In this paper, we consider the problem of sanitizing a string by concealing the occurrences of sensitive patterns, while maintaining data utility, in two settings that are relevant to many common string processing tasks. In the first setting, we aim to generate the minimal-length string that preserves the order of appearance and frequency of all non-sensitive patterns. Such a string allows accurately performing tasks based on the sequential nature and pattern frequencies of the string. To construct such a string, we propose a time-optimal algorithm, TFS-ALGO. We also propose another time-optimal algorithm, PFS-ALGO, which preserves a partial order of appearance of non-sensitive patterns but produces a much shorter string that can be analyzed more efficiently. The strings produced by either of these algorithms are constructed by concatenating non-sensitive parts of the input string. However, it is possible to detect the sensitive patterns by ``reversing'' the concatenation operations. In response, we propose a heuristic, MCSR-ALGO, which replaces letters in the strings output by the algorithms with carefully selected letters, so that sensitive patterns are not reinstated, implausible patterns are not introduced, and occurrences of spurious patterns are prevented. In the second setting, we aim to generate a string that is at minimal edit distance from the original string, in addition to preserving the order of appearance and frequency of all non-sensitive patterns. To construct such a string, we propose an algorithm, ETFS-ALGO, based on solving specific instances of approximate regular expression matching.

cs.DS↗