Jiaxin Zhang

Zhuohang Li, Jiaxin Zhang, Luyang Liu et al.

Federated Learning (FL) framework brings privacy benefits to distributed learning systems by allowing multiple clients to participate in a learning task under the coordination of a central server without exchanging their private data. However, recent studies have revealed that private information can still be leaked through shared gradient information. To further protect user's privacy, several defense mechanisms have been proposed to prevent privacy leakage via gradient information degradation methods, such as using additive noise or gradient compression before sharing it with the server. In this work, we validate that the private training data can still be leaked under certain defense settings with a new type of leakage, i.e., Generative Gradient Leakage (GGL). Unlike existing methods that only rely on gradient information to reconstruct data, our method leverages the latent space of generative adversarial networks (GAN) learned from public image datasets as a prior to compensate for the informational loss during gradient degradation. To address the nonlinearity caused by the gradient operator and the GAN model, we explore various gradient-free optimization methods (e.g., evolution strategies and Bayesian optimization) and empirically show their superiority in reconstructing high-quality images from gradients compared to gradient-based optimizers. We hope the proposed method can serve as a tool for empirically measuring the amount of privacy leakage to facilitate the design of more robust defense mechanisms.

Bo Shen, Jiaxin Zhang, Taihong Chen et al.

Large Language Models for Code (Code LLM) are flourishing. New and powerful models are released on a weekly basis, demonstrating remarkable performance on the code generation task. Various approaches have been proposed to boost the code generation performance of pre-trained Code LLMs, such as supervised fine-tuning, instruction tuning, reinforcement learning, etc. In this paper, we propose a novel RRTF (Rank Responses to align Test&Teacher Feedback) framework, which can effectively and efficiently boost pre-trained large language models for code generation. Under this framework, we present PanGu-Coder2, which achieves 62.20% pass@1 on the OpenAI HumanEval benchmark. Furthermore, through an extensive evaluation on CoderEval and LeetCode benchmarks, we show that PanGu-Coder2 consistently outperforms all previous Code LLMs.

Jiaxin Zhang, Zhuohang Li, Kamalika Das et al.

Hallucination detection is a critical step toward understanding the trustworthiness of modern language models (LMs). To achieve this goal, we re-examine existing detection approaches based on the self-consistency of LMs and uncover two types of hallucinations resulting from 1) question-level and 2) model-level, which cannot be effectively identified through self-consistency check alone. Building upon this discovery, we propose a novel sampling-based method, i.e., semantic-aware cross-check consistency (SAC3) that expands on the principle of self-consistency checking. Our SAC3 approach incorporates additional mechanisms to detect both question-level and model-level hallucinations by leveraging advances including semantically equivalent question perturbation and cross-model response consistency checking. Through extensive and systematic empirical analysis, we demonstrate that SAC3 outperforms the state of the art in detecting both non-factual and factual statements across multiple question-answering and open-domain generation benchmarks.

Jiaxin Zhang, Zhuohang Li, Kamalika Das et al.

Large language models (LLMs) have demonstrated remarkable capabilities in various tasks. However, their suitability for domain-specific tasks, is limited due to their immense scale at deployment, susceptibility to misinformation, and more importantly, high data annotation costs. We propose a novel Interactive Multi-Fidelity Learning (IMFL) framework for the cost-effective development of small domain-specific LMs under limited annotation budgets. Our approach formulates the domain-specific fine-tuning process as a multi-fidelity learning problem, focusing on identifying the optimal acquisition strategy that balances between low-fidelity automatic LLM annotations and high-fidelity human annotations to maximize model performance. We further propose an exploration-exploitation query strategy that enhances annotation diversity and informativeness, incorporating two innovative designs: 1) prompt retrieval that selects in-context examples from human-annotated samples to improve LLM annotation, and 2) variable batch size that controls the order for choosing each fidelity to facilitate knowledge distillation, ultimately enhancing annotation quality. Extensive experiments on financial and medical tasks demonstrate that IMFL achieves superior performance compared with single fidelity annotations. Given a limited budget of human annotation, IMFL significantly outperforms the human annotation baselines in all four tasks and achieves very close performance as human annotations on two of the tasks. These promising results suggest that the high human annotation costs in domain-specific tasks can be significantly reduced by employing IMFL, which utilizes fewer human annotations, supplemented with cheaper and faster LLM (e.g., GPT-3.5) annotations to achieve comparable performance.

Yue Cui, Syed Irfan Ali Meerza, Zhuohang Li et al.

Federated learning (FL) provides a variety of privacy advantages by allowing clients to collaboratively train a model without sharing their private data. However, recent studies have shown that private information can still be leaked through shared gradients. To further minimize the risk of privacy leakage, existing defenses usually require clients to locally modify their gradients (e.g., differential privacy) prior to sharing with the server. While these approaches are effective in certain cases, they regard the entire data as a single entity to protect, which usually comes at a large cost in model utility. In this paper, we seek to reconcile utility and privacy in FL by proposing a user-configurable privacy defense, RecUP-FL, that can better focus on the user-specified sensitive attributes while obtaining significant improvements in utility over traditional defenses. Moreover, we observe that existing inference attacks often rely on a machine learning model to extract the private information (e.g., attributes). We thus formulate such a privacy defense as an adversarial learning problem, where RecUP-FL generates slight perturbations that can be added to the gradients before sharing to fool adversary models. To improve the transferability to un-queryable black-box adversary models, inspired by the idea of meta-learning, RecUP-FL forms a model zoo containing a set of substitute models and iteratively alternates between simulations of the white-box and the black-box adversarial attack scenarios to generate perturbations. Extensive experiments on four datasets under various adversarial settings (both attribute inference attack and data reconstruction attack) show that RecUP-FL can meet user-specified privacy constraints over the sensitive attributes while significantly improving the model utility compared with state-of-the-art privacy defenses.

Sirui Bi, Victor Fung, Jiaxin Zhang

Computational imaging plays a pivotal role in determining hidden information from sparse measurements. A robust inverse solver is crucial to fully characterize the uncertainty induced by these measurements, as it allows for the estimation of the complete posterior of unrecoverable targets. This, in turn, facilitates a probabilistic interpretation of observational data for decision-making. In this study, we propose a deep variational framework that leverages a deep generative model to learn an approximate posterior distribution to effectively quantify image reconstruction uncertainty without the need for training data. We parameterize the target posterior using a flow-based model and minimize their Kullback-Leibler (KL) divergence to achieve accurate uncertainty estimation. To bolster stability, we introduce a robust flow-based model with bi-directional regularization and enhance expressivity through gradient boosting. Additionally, we incorporate a space-filling design to achieve substantial variance reduction on both latent prior space and target posterior space. We validate our method on several benchmark tasks and two real-world applications, namely fastMRI and black hole image reconstruction. Our results indicate that our method provides reliable and high-quality image reconstruction with robust uncertainty estimation.

Zhong-Zhi Li, Ming-Liang Zhang, Fei Yin et al.

Due to the rapid advancements in multimodal large language models, evaluating their multimodal mathematical capabilities continues to receive wide attention. Despite the datasets like MathVista proposed benchmarks for assessing mathematical capabilities in multimodal scenarios, there is still a lack of corresponding evaluation tools and datasets for fine-grained assessment in the context of K12 education in Chinese language. To systematically evaluate the capability of multimodal large models in solving Chinese multimodal mathematical problems, we propose a Chinese Multi-modal Math Skill Evaluation Benchmark, named CMMaTH, contraining 23k multimodal K12 math related questions, forming the largest Chinese multimodal mathematical problem benchmark to date. CMMaTH questions from elementary to high school levels, provide increased diversity in problem types, solution objectives, visual elements, detailed knowledge points, and standard solution annotations. We have constructed an open-source tool GradeGPT integrated with the CMMaTH dataset, facilitating stable, rapid, and cost-free model evaluation. Our data and code are available.

Xiang Gao, Jiaxin Zhang, Lalla Mouatadid et al.

In recent years, large language models (LLMs) have become increasingly prevalent, offering remarkable text generation capabilities. However, a pressing challenge is their tendency to make confidently wrong predictions, highlighting the critical need for uncertainty quantification (UQ) in LLMs. While previous works have mainly focused on addressing aleatoric uncertainty, the full spectrum of uncertainties, including epistemic, remains inadequately explored. Motivated by this gap, we introduce a novel UQ method, sampling with perturbation for UQ (SPUQ), designed to tackle both aleatoric and epistemic uncertainties. The method entails generating a set of perturbations for LLM inputs, sampling outputs for each perturbation, and incorporating an aggregation module that generalizes the sampling uncertainty approach for text generation tasks. Through extensive experiments on various datasets, we investigated different perturbation and aggregation techniques. Our findings show a substantial improvement in model uncertainty calibration, with a reduction in Expected Calibration Error (ECE) by 50\% on average. Our findings suggest that our proposed UQ method offers promising steps toward enhancing the reliability and trustworthiness of LLMs.

Wendi Cui, Zhuohang Li, Hao Sun et al.

Designing optimal prompts for Large Language Models (LLMs) is a complicated and resource-intensive task, often requiring substantial human expertise and effort. Existing approaches typically separate the optimization of prompt instructions and in-context learning examples, leading to incohesive prompts that are defined and represented by suboptimal task performance. To overcome these challenges, we propose a novel Cohesive In-Context Prompt Optimization framework that refines both prompt instructions and examples. However, formulating such an optimization in the discrete and high-dimensional space of natural language poses significant challenges in both convergence and computational efficiency. To address these issues, we introduce SEE, a scalable and efficient prompt optimization framework that adopts metaheuristic optimization principles and strategically balances exploration and exploitation to enhance optimization performance and achieve efficient convergence. SEE features a quad-phased design that alternates between global traversal (exploration) and local optimization (exploitation) and adaptively chooses LLM operators during the optimization process. We have conducted a comprehensive evaluation across 35 benchmark tasks, and SEE significantly outperforms state-of-the-art baseline methods by a large margin, achieving an average performance gain of 13.94 while reducing computational costs by 58.67.

Wendi Cui, Zhuohang Li, Hao Sun et al.

Recent advances in Large Language Models have led to remarkable achievements across a variety of Natural Language Processing tasks, making prompt engineering increasingly central to guiding model outputs. While manual methods can be effective, they typically rely on intuition and do not automatically refine prompts over time. In contrast, automatic prompt optimization employing heuristic-based search algorithms can systematically explore and improve prompts with minimal human oversight. This survey proposes a comprehensive taxonomy of these methods, categorizing them by where optimization occurs, what is optimized, what criteria drive the optimization, which operators generate new prompts, and which iterative search algorithms are applied. We further highlight specialized datasets and tools that support and accelerate automated prompt refinement. We conclude by discussing key open challenges pointing toward future opportunities for more robust and versatile LLM applications.

Syed Irfan Ali Meerza, Luyang Liu, Jiaxin Zhang et al.

Federated learning (FL) has emerged as a prospective solution for collaboratively learning a shared model across clients without sacrificing their data privacy. However, the federated learned model tends to be biased against certain demographic groups (e.g., racial and gender groups) due to the inherent FL properties, such as data heterogeneity and party selection. Unlike centralized learning, mitigating bias in FL is particularly challenging as private training datasets and their sensitive attributes are typically not directly accessible. Most prior research in this field only focuses on global fairness while overlooking the local fairness of individual clients. Moreover, existing methods often require sensitive information about the client's local datasets to be shared, which is not desirable. To address these issues, we propose GLOCALFAIR, a client-server co-design fairness framework that can jointly improve global and local group fairness in FL without the need for sensitive statistics about the client's private datasets. Specifically, we utilize constrained optimization to enforce local fairness on the client side and adopt a fairness-aware clustering-based aggregation on the server to further ensure the global model fairness across different sensitive groups while maintaining high utility. Experiments on two image datasets and one tabular dataset with various state-of-the-art fairness baselines show that GLOCALFAIR can achieve enhanced fairness under both global and local data distributions while maintaining a good level of utility and client fairness.

Jiaxin Zhang, Kamalika Das, Sricharan Kumar

Uncertainty estimation is a crucial aspect of deploying dependable deep learning models in safety-critical systems. In this study, we introduce a novel and efficient method for deterministic uncertainty estimation called Discriminant Distance-Awareness Representation (DDAR). Our approach involves constructing a DNN model that incorporates a set of prototypes in its latent representations, enabling us to analyze valuable feature information from the input data. By leveraging a distinction maximization layer over optimal trainable prototypes, DDAR can learn a discriminant distance-awareness representation. We demonstrate that DDAR overcomes feature collapse by relaxing the Lipschitz constraint that hinders the practicality of deterministic uncertainty methods (DUMs) architectures. Our experiments show that DDAR is a flexible and architecture-agnostic method that can be easily integrated as a pluggable layer with distance-sensitive metrics, outperforming state-of-the-art uncertainty estimation methods on multiple benchmark problems.

Wendi Cui, Jiaxin Zhang, Zhuohang Li et al.

Evaluating the quality and variability of text generated by Large Language Models (LLMs) poses a significant, yet unresolved research challenge. Traditional evaluation methods, such as ROUGE and BERTScore, which measure token similarity, often fail to capture the holistic semantic equivalence. This results in a low correlation with human judgments and intuition, which is especially problematic in high-stakes applications like healthcare and finance where reliability, safety, and robust decision-making are highly critical. This work proposes DCR, an automated framework for evaluating and improving the consistency of LLM-generated texts using a divide-conquer-reasoning approach. Unlike existing LLM-based evaluators that operate at the paragraph level, our method employs a divide-and-conquer evaluator (DCE) that breaks down the paragraph-to-paragraph comparison between two generated responses into individual sentence-to-paragraph comparisons, each evaluated based on predefined criteria. To facilitate this approach, we introduce an automatic metric converter (AMC) that translates the output from DCE into an interpretable numeric score. Beyond the consistency evaluation, we further present a reason-assisted improver (RAI) that leverages the analytical reasons with explanations identified by DCE to generate new responses aimed at reducing these inconsistencies. Through comprehensive and systematic empirical analysis, we show that our approach outperforms state-of-the-art methods by a large margin (e.g., +19.3% and +24.3% on the SummEval dataset) in evaluating the consistency of LLM generation across multiple benchmarks in semantic, factual, and summarization consistency tasks. Our approach also substantially reduces nearly 90% of output inconsistencies, showing promise for effective hallucination mitigation.

Jiaxin Zhang, Zhuohang Li, Wendi Cui et al.

Large language models (LLMs) have demonstrated remarkable performance, yet their diverse strengths and weaknesses prevent any single LLM from achieving dominance across all tasks. Ensembling multiple LLMs is a promising approach to generate reliable responses but conventional ensembling frameworks suffer from high computational overheads. This work introduces Scalable Consistency Ensemble (SCE), an efficient framework for ensembling LLMs by prompting consistent outputs. The SCE framework systematically evaluates and integrates outputs to produce a cohesive result through two core components: SCE-CHECK, a mechanism that gauges the consistency between response pairs via semantic equivalence; and SCE-FUSION, which adeptly merges the highest-ranked consistent responses from SCE-CHECK, to optimize collective strengths and mitigating potential weaknesses. To improve the scalability with multiple inference queries, we further propose ``{You Only Prompt Once}'' (YOPO), a novel technique that reduces the inference complexity of pairwise comparison from quadratic to constant time. We perform extensive empirical evaluations on diverse benchmark datasets to demonstrate \methodName's effectiveness. Notably, the \saccheckcomponent outperforms conventional baselines with enhanced performance and a significant reduction in computational overhead.

Jingbo Sun, Li Yang, Jiaxin Zhang et al.

Novelty detection aims to automatically identify out-of-distribution (OOD) data, without any prior knowledge of them. It is a critical step in data monitoring, behavior analysis and other applications, helping enable continual learning in the field. Conventional methods of OOD detection perform multi-variate analysis on an ensemble of data or features, and usually resort to the supervision with OOD data to improve the accuracy. In reality, such supervision is impractical as one cannot anticipate the anomalous data. In this paper, we propose a novel, self-supervised approach that does not rely on any pre-defined OOD data: (1) The new method evaluates the Mahalanobis distance of the gradients between the in-distribution and OOD data. (2) It is assisted by a self-supervised binary classifier to guide the label selection to generate the gradients, and maximize the Mahalanobis distance. In the evaluation with multiple datasets, such as CIFAR-10, CIFAR-100, SVHN and TinyImageNet, the proposed approach consistently outperforms state-of-the-art supervised and unsupervised methods in the area under the receiver operating characteristic (AUROC) and area under the precision-recall curve (AUPR) metrics. We further demonstrate that this detector is able to accurately learn one OOD class in continual learning.

Ján Drgoňa, Sayak Mukherjee, Jiaxin Zhang et al.

Deep Markov models (DMM) are generative models that are scalable and expressive generalization of Markov models for representation, learning, and inference problems. However, the fundamental stochastic stability guarantees of such models have not been thoroughly investigated. In this paper, we provide sufficient conditions of DMM's stochastic stability as defined in the context of dynamical systems and propose a stability analysis method based on the contraction of probabilistic maps modeled by deep neural networks. We make connections between the spectral properties of neural network's weights and different types of used activation functions on the stability and overall dynamic behavior of DMMs with Gaussian distributions. Based on the theory, we propose a few practical methods for designing constrained DMMs with guaranteed stability. We empirically substantiate our theoretical results via intuitive numerical experiments using the proposed stability constraints.

Zhuohang Li, Luyang Liu, Jiaxin Zhang et al.

Federated Learning (FL) enables multiple distributed clients (e.g., mobile devices) to collaboratively train a centralized model while keeping the training data locally on the client. Compared to traditional centralized machine learning, FL offers many favorable features such as offloading operations which would usually be performed by a central server and reducing risks of serious privacy leakage. However, Byzantine clients that send incorrect or disruptive updates due to system failures or adversarial attacks may disturb the joint learning process, consequently degrading the performance of the resulting model. In this paper, we propose to mitigate these failures and attacks from a spatial-temporal perspective. Specifically, we use a clustering-based method to detect and exclude incorrect updates by leveraging their geometric properties in the parameter space. Moreover, to further handle malicious clients with time-varying behaviors, we propose to adaptively adjust the learning rate according to momentum-based update speculation. Extensive experiments on 4 public datasets demonstrate that our algorithm achieves enhanced robustness comparing to existing methods under both cross-silo and cross-device FL settings with faulty/malicious clients.

Jiaxin Zhang, Sirui Bi, Guannan Zhang

Bayesian experimental design (BED) aims at designing an experiment to maximize the information gathering from the collected data. The optimal design is usually achieved by maximizing the mutual information (MI) between the data and the model parameters. When the analytical expression of the MI is unavailable, e.g., having implicit models with intractable data distributions, a neural network-based lower bound of the MI was recently proposed and a gradient ascent method was used to maximize the lower bound. However, the approach in Kleinegesse et al., 2020 requires a pathwise sampling path to compute the gradient of the MI lower bound with respect to the design variables, and such a pathwise sampling path is usually inaccessible for implicit models. In this work, we propose a hybrid gradient approach that leverages recent advances in variational MI estimator and evolution strategies (ES) combined with black-box stochastic gradient ascent (SGA) to maximize the MI lower bound. This allows the design process to be achieved through a unified scalable procedure for implicit models without sampling path gradients. Several experiments demonstrate that our approach significantly improves the scalability of BED for implicit models in high-dimensional design space.

Jiaxin Zhang, Sirui Bi, Guannan Zhang

Bayesian experimental design (BED) is to answer the question that how to choose designs that maximize the information gathering. For implicit models, where the likelihood is intractable but sampling is possible, conventional BED methods have difficulties in efficiently estimating the posterior distribution and maximizing the mutual information (MI) between data and parameters. Recent work proposed the use of gradient ascent to maximize a lower bound on MI to deal with these issues. However, the approach requires a sampling path to compute the pathwise gradient of the MI lower bound with respect to the design variables, and such a pathwise gradient is usually inaccessible for implicit models. In this paper, we propose a novel approach that leverages recent advances in stochastic approximate gradient ascent incorporated with a smoothed variational MI estimator for efficient and robust BED. Without the necessity of pathwise gradients, our approach allows the design process to be achieved through a unified procedure with an approximate gradient for implicit models. Several experiments show that our approach outperforms baseline methods, and significantly improves the scalability of BED in high-dimensional problems.

Sirui Bi, Jiaxin Zhang, Guannan Zhang

Topology optimization (TO) is a popular and powerful computational approach for designing novel structures, materials, and devices. Two computational challenges have limited the applicability of TO to a variety of industrial applications. First, a TO problem often involves a large number of design variables to guarantee sufficient expressive power. Second, many TO problems require a large number of expensive physical model simulations, and those simulations cannot be parallelized. To address these issues, we propose a general scalable deep-learning (DL) based TO framework, referred to as SDL-TO, which utilizes parallel schemes in high performance computing (HPC) to accelerate the TO process for designing additively manufactured (AM) materials. Unlike the existing studies of DL for TO, our framework accelerates TO by learning the iterative history data and simultaneously training on the mapping between the given design and its gradient. The surrogate gradient is learned by utilizing parallel computing on multiple CPUs incorporated with a distributed DL training on multiple GPUs. The learned TO gradient enables a fast online update scheme instead of an expensive update based on the physical simulator or solver. Using a local sampling strategy, we achieve to reduce the intrinsic high dimensionality of the design space and improve the training accuracy and the scalability of the SDL-TO framework. The method is demonstrated by benchmark examples and AM materials design for heat conduction. The proposed SDL-TO framework shows competitive performance compared to the baseline methods but significantly reduces the computational cost by a speed up of around 8.6x over the standard TO implementation.

Jiaxin Zhang, Congjie Wei, Chenglin Wu

For multilayer materials in thin substrate systems, interfacial failure is one of the most challenges. The traction-separation relations (TSR) quantitatively describe the mechanical behavior of a material interface undergoing openings, which is critical to understand and predict interfacial failures under complex loadings. However, existing theoretical models have limitations on enough complexity and flexibility to well learn the real-world TSR from experimental observations. A neural network can fit well along with the loading paths but often fails to obey the laws of physics, due to a lack of experimental data and understanding of the hidden physical mechanism. In this paper, we propose a thermodynamic consistent neural network (TCNN) approach to build a data-driven model of the TSR with sparse experimental data. The TCNN leverages recent advances in physics-informed neural networks (PINN) that encode prior physical information into the loss function and efficiently train the neural networks using automatic differentiation. We investigate three thermodynamic consistent principles, i.e., positive energy dissipation, steepest energy dissipation gradient, and energy conservative loading path. All of them are mathematically formulated and embedded into a neural network model with a novel defined loss function. A real-world experiment demonstrates the superior performance of TCNN, and we find that TCNN provides an accurate prediction of the whole TSR surface and significantly reduces the violated prediction against the laws of physics.

Jiaxin Zhang, Hoang Tran, Dan Lu et al.

We propose an improved evolution strategy (ES) using a novel nonlocal gradient operator for high-dimensional black-box optimization. Standard ES methods with $d$-dimensional Gaussian smoothing suffer from the curse of dimensionality due to the high variance of Monte Carlo (MC) based gradient estimators. To control the variance, Gaussian smoothing is usually limited in a small region, so existing ES methods lack nonlocal exploration ability required for escaping from local minima. We develop a nonlocal gradient operator with directional Gaussian smoothing (DGS) to address this challenge. The DGS conducts 1D nonlocal explorations along $d$ orthogonal directions in $\mathbb{R}^d$, each of which defines a nonlocal directional derivative as a 1D integral. We then use Gauss-Hermite quadrature, instead of MC sampling, to estimate the $d$ 1D integrals to ensure high accuracy (i.e., small variance). Our method enables effective nonlocal exploration to facilitate the global search in high-dimensional optimization. We demonstrate the superior performance of our method in three sets of examples, including benchmark functions for global optimization, and real-world science and engineering applications.

Jiaxin Zhang, Xianglin Liu, Sirui Bi et al.

High entropy alloys (HEAs) have been increasingly attractive as promising next-generation materials due to their various excellent properties. It's necessary to essentially characterize the degree of chemical ordering and identify order-disorder transitions through efficient simulation and modeling of thermodynamics. In this study, a robust data-driven framework based on Bayesian approaches is proposed and demonstrated on the accurate and efficient prediction of configurational energy of high entropy alloys. The proposed effective pair interaction (EPI) model with ensemble sampling is used to map the configuration and its corresponding energy. Given limited data calculated by first-principles calculations, Bayesian regularized regression not only offers an accurate and stable prediction but also effectively quantifies the uncertainties associated with EPI parameters. Compared with the arbitrary determination of model complexity, we further conduct a physical feature selection to identify the truncation of coordination shells in EPI model using Bayesian information criterion. The results achieve efficient and robust performance in predicting the configurational energy, particularly given small data. The developed methodology is applied to study a series of refractory HEAs, i.e. NbMoTaW, NbMoTaWV and NbMoTaWTi where it is demonstrated how dataset size affects the confidence we can place in statistical estimates of configurational energy when data are sparse.

Xiangyang Zhou, Jiaxin Zhang, Brian Kulis

Algorithms based on spectral graph cut objectives such as normalized cuts, ratio cuts and ratio association have become popular in recent years because they are widely applicable and simple to implement via standard eigenvector computations. Despite strong performance for a number of clustering tasks, spectral graph cut algorithms still suffer from several limitations: first, they require the number of clusters to be known in advance, but this information is often unknown a priori; second, they tend to produce clusters with uniform sizes. In some cases, the true clusters exhibit a known size distribution; in image segmentation, for instance, human-segmented images tend to yield segment sizes that follow a power-law distribution. In this paper, we propose a general framework of power-law graph cut algorithms that produce clusters whose sizes are power-law distributed, and also does not fix the number of clusters upfront. To achieve our goals, we treat the Pitman-Yor exchangeable partition probability function (EPPF) as a regularizer to graph cut objectives. Because the resulting objectives cannot be solved by relaxing via eigenvectors, we derive a simple iterative algorithm to locally optimize the objectives. Moreover, we show that our proposed algorithm can be viewed as performing MAP inference on a particular Pitman-Yor mixture model. Our experiments on various data sets show the effectiveness of our algorithms.