arXiv subjects

Haixia Liu

Publications and source records attributed to Haixia Liu.

At least 19 recordsLinked to original sources

arXiv2026

The Fusion Frame Phase Retrieval

The phase retrieval problem involves reconstructing a function or signal solely from the magnitude of linear measurements. Most theoretical analyses of phase retrieval algorithms rely on i.i.d. Gaussian random measurements or sub-Gaussian random measurements. In this paper, our focus is on the fusion frame phase retrieval problem, where the sampling matrices are i.i.d. rank-$r$ orthogonal projections drawn from the Haar measure. We present concentration inequalities for functions on the set of rank-$r$ orthogonal projection matrices. These inequalities are crucial for the theoretical analysis of the fusion frame phase retrieval problem. Based on these inequalities, we demonstrate that gradient descent, combined with a two-stage initialization, achieves linear convergence to the target signal up to a global phase with a measurement complexity of $O(d\log^2 d)$ when the rank $r = O(1)$. We verify this convergence through numerical results.

cs.IT↗

arXiv2026

BlockRR: A Unified Framework of RR-type Algorithms for Label Differential Privacy

In this paper, we introduce BlockRR, a novel and unified randomized-response mechanism for label differential privacy. This framework generalizes existed RR-type mechanisms as special cases under specific parameter settings, which eliminates the need for separate, case-by-case analysis. Theoretically, we prove that BlockRR satisfies $\epsilon$-label DP. We also design a partition method for BlockRR based on a weight matrix derived from label prior information; the parallel composition principle ensures that the composition of two such mechanisms remains $\epsilon$-label DP. Empirically, we evaluate BlockRR on two variants of CIFAR-10 with varying degrees of class imbalance. Results show that in the high-privacy and moderate-privacy regimes ($\epsilon \leq 3.0$), our propsed method gets a better balance between test accuaracy and the average of per-class accuracy. In the low-privacy regime ($\epsilon \geq 4.0$), all methods reduce BlockRR to standard RR without additional performance loss.

cs.LG↗

arXiv2026

RPWithPrior: Label Differential Privacy in Regression

With the wide application of machine learning techniques in practice, privacy preservation has gained increasing attention. Protecting user privacy with minimal accuracy loss is a fundamental task in the data analysis and mining community. In this paper, we focus on regression tasks under $\epsilon$-label differential privacy guarantees. Some existing methods for regression with $\epsilon$-label differential privacy, such as the RR-On-Bins mechanism, discretized the output space into finite bins and then applied RR algorithm. To efficiently determine these finite bins, the authors rounded the original responses down to integer values. However, such operations does not align well with real-world scenarios. To overcome these limitations, we model both original and randomized responses as continuous random variables, avoiding discretization entirely. Our novel approach estimates an optimal interval for randomized responses and introduces new algorithms designed for scenarios where a prior is either known or unknown. Additionally, we prove that our algorithm, RPWithPrior, guarantees $\epsilon$-label differential privacy. Numerical results demonstrate that our approach gets better performance compared with the Gaussian, Laplace, Staircase, and RRonBins, Unbiased mechanisms on the Communities and Crime, Criteo Sponsored Search Conversion Log, California Housing datasets.

stat.ML↗

arXiv2026

Improving Classifier-Free Guidance of Flow Matching via Manifold Projection

Classifier-free guidance (CFG) is a widely used technique for controllable generation in diffusion and flow-based models. Despite its empirical success, CFG relies on a heuristic linear extrapolation that is often sensitive to the guidance scale. In this work, we provide a principled interpretation of CFG through the lens of optimization. We demonstrate that the velocity field in flow matching corresponds to the gradient of a sequence of smoothed distance functions, which guides latent variables toward the scaled target image set. This perspective reveals that the standard CFG formulation is an approximation of this gradient, where the prediction gap, the discrepancy between conditional and unconditional outputs, governs guidance sensitivity. Leveraging this insight, we reformulate the CFG sampling as a homotopy optimization with a manifold constraint. This formulation necessitates a manifold projection step, which we implement via an incremental gradient descent scheme during sampling. To improve computational efficiency and stability, we further enhance this iterative process with Anderson Acceleration without requiring additional model evaluations. Our proposed methods are training-free and consistently refine generation fidelity, prompt alignment, and robustness to the guidance scale. We validate their effectiveness across diverse benchmarks, demonstrating significant improvements on large-scale models such as DiT-XL-2-256, Flux, and Stable Diffusion 3.5.

cs.CV↗

arXiv2025

MAP-based Problem-Agnostic diffusion model for Inverse Problems

Diffusion models have indeed shown great promise in solving inverse problems in image processing. In this paper, we propose a novel, problem-agnostic diffusion model called the maximum a posteriori (MAP)-based guided term estimation method for inverse problems. To leverage unconditionally pretrained diffusion models to address conditional generation tasks, we divide the conditional score function into two terms according to Bayes' rule: an unconditional score function (approximated by a pretrained score network) and a guided term, which is estimated using a novel MAP-based method that incorporates a Gaussian-type prior of natural images. This innovation allows us to better capture the intrinsic properties of the data, leading to improved performance. Numerical results demonstrate that our method preserves contents more effectively compared to state-of-the-art methods--for example, maintaining the structure of glasses in super-resolution tasks and producing more coherent results in the neighborhood of masked regions during inpainting.

eess.IV↗

arXiv2025

The Exploration of Error Bounds in Classification with Noisy Labels

Numerous studies have shown that label noise can lead to poor generalization performance, negatively affecting classification accuracy. Therefore, understanding the effectiveness of classifiers trained using deep neural networks in the presence of noisy labels is of considerable practical significance. In this paper, we focus on the error bounds of excess risks for classification problems with noisy labels within deep learning frameworks. We derive error bounds for the excess risk, decomposing it into statistical error and approximation error. To handle statistical dependencies (e.g., mixing sequences), we employ an independent block construction to bound the error, leveraging techniques for dependent processes. For the approximation error, we establish these theoretical results to the vector-valued setting, where the output space consists of $K$-dimensional unit vectors. Finally, under the low-dimensional manifold hypothesis, we further refine the approximation error to mitigate the impact of high-dimensional input spaces.

cs.LG↗

arXiv2024

Generalized Principal Component Analysis for Large-dimensional Matrix Factor Model

Matrix factor models have been growing popular dimension reduction tools for large-dimensional matrix time series. However, the heteroscedasticity of the idiosyncratic components has barely received any attention. Starting from the pseudo likelihood function, this paper introduces a Generalized Principal Component Analysis (GPCA) method for matrix factor model which takes the heteroscedasticity into account. Theoretically, we first derive the asymptotic distributions of the GPCA estimators by assuming the separable covariance matrices are known in advance. We then propose adaptive thresholding estimators for the separable covariance matrices and derive their convergence rates, which is of independent interest. We also show that this would not alter the asymptotic distributions of the GPCA estimators under certain regular sparsity conditions in the high-dimensional covariance matrix estimation literature. The GPCA estimators are shown to be more efficient than the state-of-the-art methods under certain heteroscedasticity conditions. Thorough numerical studies are conducted to demonstrate the superiority of our method over the existing approaches. Analysis of a financial portfolio dataset illustrates the empirical usefulness of the proposed method.

math.ST↗

arXiv2024

Fairness via Independence: A (Conditional) Distance Covariance Framework

We explore fairness from a statistical perspective by selectively utilizing either conditional distance covariance or distance covariance statistics as measures to assess the independence between predictions and sensitive attributes. We boost fairness with independence by adding a distance covariance-based penalty to the model's training. Additionally, we present the matrix form of empirical (conditional) distance covariance for parallel calculations to enhance computational efficiency. Theoretically, we provide a proof for the convergence between empirical and population (conditional) distance covariance, establishing necessary guarantees for batch computations. Through experiments conducted on a range of real-world datasets, we have demonstrated that our method effectively bridges the fairness gap in machine learning. Our code is available at \url{https://github.com/liuhaixias1/Fair_dc/}.

cs.LG↗

arXiv2024

The Exploration of Neural Collapse under Imbalanced Data

Neural collapse, a newly identified characteristic, describes a property of solutions during model training. In this paper, we explore neural collapse in the context of imbalanced data. We consider the $L$-extended unconstrained feature model with a bias term and provide a theoretical analysis of global minimizer. Our findings include: (1) Features within the same class converge to their class mean, similar to both the balanced case and the imbalanced case without bias. (2) The geometric structure is mainly on the left orthonormal transformation of the product of $L$ linear classifiers and the right transformation of the class-mean matrix. (3) Some rows of the left orthonormal transformation of the product of $L$ linear classifiers collapse to zeros and others are orthogonal, which relies on the singular values of $\hat Y=(I_K-1/N\mathbf{n}1^\top_K)D$, where $K$ is class size, $\mathbf{n}$ is the vector of sample size for each class, $D$ is the diagonal matrix whose diagonal entries are given by $\sqrt{\mathbf{n}}$. Similar results are for the columns of the right orthonormal transformation of the product of class-mean matrix and $D$. (4) The $i$-th row of the left orthonormal transformation of the product of $L$ linear classifiers aligns with the $i$-th column of the right orthonormal transformation of the product of class-mean matrix and $D$. (5) We provide the estimation of singular values about $\hat Y$. Our numerical experiments support these theoretical findings.

cs.LG↗

arXiv2024

Group Projected Subspace Pursuit for Block Sparse Signal Reconstruction: Convergence Analysis and Applications

In this paper, we present a convergence analysis of the Group Projected Subspace Pursuit (GPSP) algorithm proposed by He et al. [HKL+23] (Group Projected subspace pursuit for IDENTification of variable coefficient differential equations (GP-IDENT), Journal of Computational Physics, 494, 112526) and extend its application to general tasks of block sparse signal recovery. We prove that when the sampling matrix satisfies the Block Restricted Isometry Property (BRIP) with a sufficiently small Block Restricted Isometry Constant (BRIC), GPSP exactly recovers the true block sparse signals. When the observations are noisy, this convergence property of GPSP remains valid if the magnitude of true signal is sufficiently large. GPSP selects the features by subspace projection criterion (SPC) for candidate inclusion and response magnitude criterion (RMC) for candidate exclusion. We compare these criteria with counterparts of other state-of-the-art greedy algorithms. Our theoretical analysis and numerical ablation studies reveal that SPC is critical to the superior performances of GPSP, and that RMC can enhance the robustness of feature identification when observations contain noises. We test and compare GPSP with other methods in diverse settings, including heterogeneous random block matrices, inexact observations, face recognition, and PDE identification. We find that GPSP outperforms the other algorithms in most cases for various levels of block sparsity and block sizes, justifying its effectiveness for general applications.

cs.IT↗

arXiv2024

Exploring the Unexplored: Understanding the Impact of Layer Adjustments on Image Classification

This paper investigates how adjustments to deep learning architectures impact model performance in image classification. Small-scale experiments generate initial insights although the trends observed are not consistent with the entire dataset. Filtering operations in the image processing pipeline are crucial, with image filtering before pre-processing yielding better results. The choice and order of layers as well as filter placement significantly impact model performance. This study provides valuable insights into optimizing deep learning models, with potential avenues for future research including collaborative platforms.

cs.CV↗

arXiv2024

On Cooperative Coevolution and Global Crossover

Cooperative coevolutionary algorithms (CCEAs) divide a given problem in to a number of subproblems and use an evolutionary algorithm to solve each subproblem. This short paper is concerned with the scenario under which only a single, global fitness measure exists. By removing the typically used subproblem partnering mechanism, it is suggested that such CCEAs can be viewed as making use of a generalised version of the global crossover operator introduced in early Evolution Strategies. Using the well-known NK model of fitness landscapes, the effects of varying aspects of global crossover with respect to the ruggedness of the underlying fitness landscape are explored. Results suggest improvements over the most widely used form of CCEAs, something further demonstrated using other well-known test functions.

cs.NE↗

arXiv2020

Citation Sentiment Changes Analysis

Metrics for measuring the citation sentiment changes were introduced. Citation sentiment changes can be observed from global citation sentiment sequences (GCSSs). With respect to a cited paper, the citation sentiment sequences were analysed across a collection of citing papers ordered by the published time. For analysing GCSSs, Eddy Dissipation Rate (EDR) was adopted, with the hypothesis that the GCSSs pattern differences can be spotted by EDR based method. Preliminary evidence showed that EDR based method holds the potential for analysing a publication's impact in a time series fashion.

cs.CL↗

arXiv2019

Phase retrieval for sub-Gaussian measurements

Generally, phase retrieval problem can be viewed as the reconstruction of a function/signal from only the magnitude of the linear measurements. These measurements can be, for example, the Fourier transform of the density function. Computationally the phase retrieval problem is very challenging. Many algorithms for phase retrieval are based on i.i.d. Gaussian random measurements. However, Gaussian random measurements remain one of the very few classes of measurements. In this paper, we develop an efficient phase retrieval algorithm for sub-gaussian random frames. We provide a general condition for measurements and develop a modified spectral initialization. In the algorithm, we first obtain a good approximation of the solution through the initialization, and from there we useWirtinger Flow to solve for the solution. We prove that the algorithm converges to the global minimizer linearly.

math.OC↗

arXiv2018

Optimize transfer learning for lung diseases in bronchoscopy using a new concept: sequential fine-tuning

Bronchoscopy inspection as a follow-up procedure from the radiological imaging plays a key role in lung disease diagnosis and determining treatment plans for the patients. Doctors needs to make a decision whether to biopsy the patients timely when performing bronchoscopy. However, the doctors also needs to be very selective with biopsies as biopsies may cause uncontrollable bleeding of the lung tissue which is life-threaten. To help doctors to be more selective on biopsies and provide a second opinion on diagnosis, in this work, we propose a computer-aided diagnosis (CAD) system for lung diseases including cancers and tuberculosis (TB). The system is developed based on transfer learning. We propose a novel transfer learning method: sentential fine-tuning . Compared to traditional fine-tuning methods, our methods achieves the best performance. We obtained a overall accuracy of 77.0% a dataset of 81 normal cases, 76 tuberculosis cases and 277 lung cancer cases while the other traditional transfer learning methods achieve an accuracy of 73% and 68%. . The detection accuracy of our method for cancers, TB and normal cases are 87%, 54% and 91% respectively. This indicates that the CAD system has potential to improve lung disease diagnosis accuracy in bronchoscopy and it also might be used to be more selective with biopsies.

cs.CV↗

arXiv2017

Fast Rank One Alternating Minimization Algorithm for Phase Retrieval

The phase retrieval problem is a fundamental problem in many fields, which is appealing for investigation. It is to recover the signal vector $\tilde{x}\in\mathbb{C}^d$ from a set of $N$ measurements $b_n=|f^*_n\tilde{x}|^2,\ n=1,\cdots, N$, where $\{f_n\}_{n=1}^N$ forms a frame of $\mathbb{C}^d$. %It is generally a non-convex minimization problem, which is NP-hard. Existing algorithms usually use a least squares fitting to the measurements, yielding a quartic polynomial minimization. In this paper, we employ a new strategy by splitting the variables, and we solve a bi-variate optimization problem that is quadratic in each of the variables. An alternating gradient descent algorithm is proposed, and its convergence for any initialization is provided. Since a larger step size is allowed due to the smaller Hessian, the alternating gradient descent algorithm converges faster than the gradient descent algorithm (known as the Wirtinger flow algorithm) applied to the quartic objective without splitting the variables. Numerical results illustrate that our proposed algorithm needs less iterations than Wirtinger flow to achieve the same accuracy.

math.OC↗

arXiv2017

Sentiment Analysis of Citations Using Word2vec

Citation sentiment analysis is an important task in scientific paper analysis. Existing machine learning techniques for citation sentiment analysis are focusing on labor-intensive feature engineering, which requires large annotated corpus. As an automatic feature extraction tool, word2vec has been successfully applied to sentiment analysis of short texts. In this work, I conducted empirical research with the question: how well does word2vec work on the sentiment analysis of citations? The proposed method constructed sentence vectors (sent2vec) by averaging the word embeddings, which were learned from Anthology Collections (ACL-Embeddings). I also investigated polarity-specific word embeddings (PS-Embeddings) for classifying positive and negative citations. The sentence vectors formed a feature space, to which the examined citation sentence was mapped to. Those features were input into classifiers (support vector machines) for supervised classification. Using 10-cross-validation scheme, evaluation was conducted on a set of annotated citations. The results showed that word embeddings are effective on classifying positive and negative citations. However, hand-crafted features performed better for the overall classification.

cs.CL↗

arXiv2017

Automatic Argumentative-Zoning Using Word2vec

In comparison with document summarization on the articles from social media and newswire, argumentative zoning (AZ) is an important task in scientific paper analysis. Traditional methodology to carry on this task relies on feature engineering from different levels. In this paper, three models of generating sentence vectors for the task of sentence classification were explored and compared. The proposed approach builds sentence representations using learned embeddings based on neural network. The learned word embeddings formed a feature space, to which the examined sentence is mapped to. Those features are input into the classifiers for supervised classification. Using 10-cross-validation scheme, evaluation was conducted on the Argumentative-Zoning (AZ) annotated articles. The results showed that simply averaging the word vectors in a sentence works better than the paragraph to vector algorithm and by integrating specific cuewords into the loss function of the neural network can improve the classification performance. In comparison with the hand-crafted features, the word2vec method won for most of the categories. However, the hand-crafted features showed their strength on classifying some of the categories.

cs.CL↗