Hongyu Zhao

Hongyu Zhao, Hao Tan, Hongyuan Mei

Adapter-tuning is a paradigm that transfers a pretrained language model to downstream tasks by adding and tuning a small number of new parameters. Previously proposed adapter architectures are all feed-forward neural networks. In this paper, we investigate the effectiveness of using tiny-attention -- i.e., attention with extremely small per-head dimensionality -- as adapters. Our tiny-attention adapter learns to modify the hidden states at each position directly conditioned on the hidden states at all the other positions, which is missed by the previously proposed adapters. Moreover, we view its multiple attention heads as a mixture of experts and propose to average their weights during deployment, which further reduces its inference computation cost. On the GLUE benchmark, our tiny-attention adapter outperforms the other parameter-efficient transfer learning methods as well as full fine-tuning while only updating 0.05% of the parameters. On the FewGLUE benchmark, its performance is comparable to that of GPT-3 and PET.

Jiasheng Gu, Hongyu Zhao, Hanzi Xu et al.

Traditional supervised learning mostly works on individual tasks and requires training on a large set of task-specific examples. This paradigm seriously hinders the development of task generalization since preparing a task-specific example set is costly. To build a system that can quickly and easily generalize to new tasks, task instructions have been adopted as an emerging trend of supervision recently. These instructions give the model the definition of the task and allow the model to output the appropriate answer based on the instructions and inputs. However, task instructions are often expressed in different forms, which can be interpreted from two threads: first, some instructions are short sentences and are pretrained language model (PLM) oriented, such as prompts, while other instructions are paragraphs and are human-oriented, such as those in Amazon MTurk; second, different end-users very likely explain the same task with instructions of different textual expressions. A robust system for task generalization should be able to handle any new tasks regardless of the variability of instructions. However, the system robustness in dealing with instruction-driven task generalization is still unexplored. This work investigates the system robustness when the instructions of new tasks are (i) manipulated, (ii) paraphrased, or (iii) from different levels of conciseness. To our knowledge, this is the first work that systematically studies how robust a PLM is when it is supervised by instructions with different factors of variability.

Siqiao Xue, Fan Zhou, Yi Xu et al.

We present WeaverBird, an intelligent dialogue system designed specifically for the finance domain. Our system harnesses a large language model of GPT architecture that has been tuned using extensive corpora of finance-related text. As a result, our system possesses the capability to understand complex financial queries, such as "How should I manage my investments during inflation?", and provide informed responses. Furthermore, our system incorporates a local knowledge base and a search engine to retrieve relevant information. The final responses are conditioned on the search results and include proper citations to the sources, thus enjoying an enhanced credibility. Through a range of finance-related questions, we have demonstrated the superior performance of our system compared to other models. To experience our system firsthand, users can interact with our live demo at https://weaverbird.ttic.edu, as well as watch our 2-min video illustration at https://www.youtube.com/watch?v=yofgeqnlrMc.

Hongyu Zhao, Kangrui Wang, Mo Yu et al.

Language models have been shown to perform remarkably well on a wide range of natural language processing tasks. In this paper, we propose LEAP, a novel system that uses language models to perform multi-step logical reasoning and incorporates explicit planning into the inference procedure. Explicit planning enables the system to make more informed reasoning decisions at each step by looking ahead into their future effects. Moreover, we propose a training strategy that safeguards the planning process from being led astray by spurious features. Our full system significantly outperforms other competing methods on multiple standard datasets. When using small T5 models as its core selection and deduction components, our system performs competitively compared to GPT-3 despite having only about 1B parameters (i.e., 175 times smaller than GPT-3). When using GPT-3.5, it significantly outperforms chain-of-thought prompting on the challenging PrOntoQA dataset. We have conducted extensive empirical studies to demonstrate that explicit planning plays a crucial role in the system's performance.

Fangxu Yu, Xingang Guo, Lingzhi Yuan et al.

Time series data is ubiquitous in real-world scenarios and crucial for critical applications ranging from energy management to traffic control. Consequently, the ability to reason over time series is a fundamental skill for generalist models to solve practical problems. However, this dimension is notably absent from existing benchmarks of generalist models. To bridge this gap, we introduce TSRBench, a comprehensive multi-modal benchmark designed to stress-test the full spectrum of time series reasoning capabilities. TSRBench features: i) a diverse set of 4125 problems from 14 domains, and is categorized into 4 major dimensions: Perception, Reasoning, Prediction, and Decision-Making. ii) 15 tasks from the 4 dimensions evaluating essential reasoning capabilities (e.g., numerical reasoning). Through extensive experiments, we evaluated over 30 leading proprietary and open-source LLMs, VLMs, and TSLLMs within TSRBench. Our findings reveal that: i) scaling laws hold for perception and reasoning but break down for prediction; ii) strong reasoning does not guarantee accurate context-aware forecasting, indicating a decoupling between semantic understanding and numerical prediction; and iii) despite the complementary nature of textual and visual represenations of time series as inputs, current multimodal models fail to effectively fuse them for reciprocal performance gains. TSRBench provides a standardized evaluation platform that not only highlights existing challenges but also offers valuable insights to advance generalist models. Our code and dataset are available at https://tsrbench.github.io/.

Tianyu Liu, Yuge Wang, Rex Ying et al.

Discovering genes with similar functions across diverse biomedical contexts poses a significant challenge in gene representation learning due to data heterogeneity. In this study, we resolve this problem by introducing a novel model called Multimodal Similarity Learning Graph Neural Network, which combines Multimodal Machine Learning and Deep Graph Neural Networks to learn gene representations from single-cell sequencing and spatial transcriptomic data. Leveraging 82 training datasets from 10 tissues, three sequencing techniques, and three species, we create informative graph structures for model training and gene representations generation, while incorporating regularization with weighted similarity learning and contrastive learning to learn cross-data gene-gene relationships. This novel design ensures that we can offer gene representations containing functional similarity across different contexts in a joint space. Comprehensive benchmarking analysis shows our model's capacity to effectively capture gene function similarity across multiple modalities, outperforming state-of-the-art methods in gene representation learning by up to 97.5%. Moreover, we employ bioinformatics tools in conjunction with gene representations to uncover pathway enrichment, regulation causal networks, and functions of disease-associated or dosage-sensitive genes. Therefore, our model efficiently produces unified gene representations for the analysis of gene functions, tissue functions, diseases, and species evolution.

Tianyu Liu, Weihao Xuan, Hao Wu et al.

Advances in AI have introduced several strong models in computational pathology to usher it into the era of multi-modal diagnosis, analysis, and interpretation. However, the current pathology-specific visual language models still lack capacities in making the diagnosis with rigorous reasoning paths as well as handling divergent tasks, and thus, challenges of building AI Copilots for real scenarios still exist. Here we introduce TeamPath, an AI system powered by reinforcement learning and router-enhanced solutions based on large-scale histopathology multimodal datasets, to work as a virtual assistant for expert-level disease diagnosis, patch-level information summarization, and cross-modality generation to integrate transcriptomic information for clinical usage. We also collaborate with pathologists from Yale School of Medicine to demonstrate that TeamPath can assist them in working more efficiently by identifying and correcting expert conclusions and reasoning paths. We also discuss the human evaluation results to support the reasoning quality from TeamPath. Overall, TeamPath can flexibly choose the best settings according to the needs, and serve as an innovative and reliable system for information communication across different modalities and experts.

Hongyu Zhao, Gongming Wei, Yang Xiao et al.

Multi-ship tracking (MST) as a core technology has been proven to be applied to situational awareness at sea and the development of a navigational system for autonomous ships. Despite impressive tracking outcomes achieved by multi-object tracking (MOT) algorithms for pedestrian and vehicle datasets, these models and techniques exhibit poor performance when applied to ship datasets. Intersection of Union (IoU) is the most popular metric for computing similarity used in object tracking. The low frame rates and severe image shake caused by wave turbulence in ship datasets often result in minimal, or even zero, Intersection of Union (IoU) between the predicted and detected bounding boxes. This issue contributes to frequent identity switches of tracked objects, undermining the tracking performance. In this paper, we address the weaknesses of IoU by incorporating the smallest convex shapes that enclose both the predicted and detected bounding boxes. The calculation of the tracking version of IoU (TIoU) metric considers not only the size of the overlapping area between the detection bounding box and the prediction box, but also the similarity of their shapes. Through the integration of the TIoU into state-of-the-art object tracking frameworks, such as DeepSort and ByteTrack, we consistently achieve improvements in the tracking performance of these frameworks.

Yuanqi Du, Botao Yu, Tianyu Liu et al.

There has been unprecedented interest in developing agents that expand the boundary of scientific discovery, primarily by optimizing quantitative objective functions specified by scientists. However, for grand challenges in science , these objectives are only imperfect proxies. We argue that automating objective function design is a central, yet unmet requirement for scientific discovery agents. In this work, we introduce the Scientific Autonomous Goal-evolving Agent (SAGA) to amend this challenge. SAGA employs a bi-level architecture in which an outer loop of LLM agents analyzes optimization outcomes, proposes new objectives, and converts them into computable scoring functions, while an inner loop performs solution optimization under the current objectives. This bi-level design enables systematic exploration of the space of objectives and their trade-offs, rather than treating them as fixed inputs. We demonstrate the framework through a broad spectrum of applications, including antibiotic design, inorganic materials design, functional DNA sequence design, and chemical process design, showing that automating objective formulation can substantially improve the effectiveness of scientific discovery agents.

Ming Li, Pei Chen, Chenguang Wang et al.

Finetuning large language models with a variety of instruction-response pairs has enhanced their capability to understand and follow instructions. Current instruction tuning primarily relies on teacher models or human intervention to generate and refine the instructions and responses for training, which are costly, non-sustainable, and may lack diversity. In this paper, we introduce Mosaic Instruction Tuning (Mosaic-IT), a human/model-free compositional data synthesis method that can efficiently create rich and diverse augmentations from existing instruction tuning data to enhance the LLMs. Mosaic-IT randomly concatenates multiple instruction data into one and trains the model to produce the corresponding responses with predefined higher-level meta-instructions to strengthen its multi-step instruction-following and format-following skills. Our extensive evaluations demonstrate a superior performance and training efficiency of Mosaic-IT, which achieves consistent performance improvements over various benchmarks and an 80% reduction in training costs compared with original instruction tuning. Our codes and data are available at https://github.com/tianyi-lab/Mosaic-IT.

Tianyu Liu, Simeng Han, Xiao Luo et al.

Large language models (LLMs) and large multimodal models (LMMs) promise to accelerate biomedical discovery, yet their reliability remains unclear. We introduce ARIEL (AI Research Assistant for Expert-in-the-Loop Learning), an open-source evaluation and optimization framework that pairs a curated multimodal biomedical corpus with expert-vetted tasks to probe two capabilities: full-length article summarization and fine-grained figure interpretation. Using uniform protocols and blinded PhD-level evaluation, we find that state-of-the-art models generate fluent but incomplete summaries, whereas LMMs struggle with detailed visual reasoning. We later observe that prompt engineering and lightweight fine-tuning substantially improve textual coverage, and a compute-scaled inference strategy enhances visual question answering. We build an ARIEL agent that integrates textual and visual cues, and we show it can propose testable mechanistic hypotheses. ARIEL delineates current strengths and limitations of foundation models, and provides a reproducible platform for advancing trustworthy AI in biomedicine.

Tianyu Liu, Sihan Jiang, Fan Zhang et al.

Large language models (LLMs) are in the ascendancy for research in drug discovery, offering unprecedented opportunities to reshape drug research by accelerating hypothesis generation, optimizing candidate prioritization, and enabling more scalable and cost-effective drug discovery pipelines. However there is currently a lack of objective assessments of LLM performance to ascertain their advantages and limitations over traditional drug discovery platforms. To tackle this emergent problem, we have developed DrugPlayGround, a framework to evaluate and benchmark LLM performance for generating meaningful text-based descriptions of physiochemical drug characteristics, drug synergism, drug-protein interactions, and the physiological response to perturbations introduced by drug molecules. Moreover, DrugPlayGround is designed to work with domain experts to provide detailed explanations for justifying the predictions of LLMs, thereby testing LLMs for chemical and biological reasoning capabilities to push their greater use at the frontier of drug discovery at all of its stages.

Ming Li, Yong Zhang, Shwai He et al.

Instruction tuning is critical to improve LLMs but usually suffers from low-quality and redundant data. Data filtering for instruction tuning has proved important in improving both the efficiency and performance of the tuning process. But it also leads to extra cost and computation due to the involvement of LLMs in this process. To reduce the filtering cost, we study Superfiltering: Can we use a smaller and weaker model to select data for finetuning a larger and stronger model? Despite the performance gap between weak and strong language models, we find their highly consistent capability to perceive instruction difficulty and data selection results. This enables us to use a much smaller and more efficient model to filter the instruction data used to train a larger language model. Not only does it largely speed up the data filtering, but the filtered-data-finetuned LLM achieves even better performance on standard benchmarks. Extensive experiments validate the efficacy and efficiency of our approach.

Tianyu Liu, Yijia Xiao, Xiao Luo et al.

The applications of large language models (LLMs) are promising for biomedical and healthcare research. Despite the availability of open-source LLMs trained using a wide range of biomedical data, current research on the applications of LLMs to genomics and proteomics is still limited. To fill this gap, we propose a collection of finetuned LLMs and multimodal LLMs (MLLMs), known as Geneverse, for three novel tasks in genomic and proteomic research. The models in Geneverse are trained and evaluated based on domain-specific datasets, and we use advanced parameter-efficient finetuning techniques to achieve the model adaptation for tasks including the generation of descriptions for gene functions, protein function inference from its structure, and marker gene selection from spatial transcriptomic data. We demonstrate that adapted LLMs and MLLMs perform well for these tasks and may outperform closed-source large-scale models based on our evaluations focusing on both truthfulness and structural correctness. All of the training strategies and base models we used are freely accessible.

Brian Lu, Hongyu Zhao, Shuo Sun et al.

Reinforcement learning with verifiable rewards (RLVR) has emerged as a promising paradigm for post-training large language models (LLMs) on complex reasoning tasks. Yet, the conditions under which RLVR yields robust generalization remain poorly understood. This paper provides an empirical study of RLVR generalization in the setting of probabilistic inference over causal graphical models. This setting offers two natural axes along which to examine generalization: (i) the level of the probabilistic query -- associational, interventional, or counterfactual -- and (ii) the structural complexity of the query, measured by the size of its relevant subgraph. We construct datasets of causal graphs and queries spanning these difficulty axes and fine-tune Qwen-2.5-Instruct models using RLVR or supervised fine-tuning (SFT). We vary both the model scale (3B-32B) and the query level included in training. We find that RLVR yields stronger within-level and across-level generalization than SFT, but only for specific combinations of model size and training query level. Further analysis shows that RLVR's effectiveness depends on the model's initial reasoning competence. With sufficient initial competence, RLVR improves an LLM's marginalization strategy and reduces errors in intermediate probability calculations, producing substantial accuracy gains, particularly on more complex queries. These findings show that RLVR can improve specific causal reasoning subskills, with its benefits emerging only when the model has sufficient initial competence.

Tianyu Liu, Wangjie Zheng, Rui Yang et al.

Accurate and timely diagnosis is essential for effective treatment, particularly in the context of rare diseases. However, current diagnostic workflows often lead to prolonged assessment times and low accuracy. To address these limitations, we introduce Hygieia, a multi-modal AI agent system designed to support precision disease diagnosis by integrating diverse data sources, including phenotypic features, genetic profiles, and clinical records. Hygieia features a router-based and knowledge-enhanced framework that mitigates hallucination and tailors diagnostic strategies to different disease categories. Notably, it prioritizes risk-related genomic factors for rare diseases and provides confidence scores to assist clinical decision-making. We conducted a comprehensive evaluation demonstrating that Hygieia achieves state-of-the-art performance across multiple diagnostic benchmarks. In collaboration with clinical experts from Yale School of Medicine and Duke-NUS Medical School, we further validated its practical utility by showing (1) Hygieia's superior diagnostic performance compared to physicians with an improvement from 12%-60% and (2) its effectiveness in assisting clinicians with medical records for handling real-world cases. Our findings indicate that Hygieia not only enhances diagnostic accuracy and interpretability but also significantly reduces clinician workload, highlighting its potential as a valuable tool in clinical decision support systems.

Hongyu Zhao, Siyu Zhou, Haolin Yang et al.

Large language models (LLMs) exhibit strong general-purpose reasoning capabilities, yet they frequently hallucinate when used as world models (WMs), where strict compliance with deterministic transition rules--particularly in corner cases--is essential. In contrast, Symbolic WMs provide logical consistency but lack semantic expressivity. To bridge this gap, we propose Neuro-Symbolic Synergy (NeSyS), a framework that integrates the probabilistic semantic priors of LLMs with executable symbolic rules to achieve both expressivity and robustness. NeSyS alternates training between the two models using trajectories inadequately explained by the other. Unlike rule-based prompting, the symbolic WM directly constrains the LLM by modifying its output probability distribution. The neural WM is fine-tuned only on trajectories not covered by symbolic rules, reducing training data by 50% without loss of accuracy. Extensive experiments on three distinct interactive environments, i.e., ScienceWorld, Webshop, and Plancraft, demonstrate NeSyS's consistent advantages over baselines in both WM prediction accuracy and data efficiency.

Hongyu Zhao, Zezhi Tang, Zhenhong Li et al.

The optimisation of crop harvesting processes for commonly cultivated crops is of great importance in the aim of agricultural industrialisation. Nowadays, the utilisation of machine vision has enabled the automated identification of crops, leading to the enhancement of harvesting efficiency, but challenges still exist. This study presents a new framework that combines two separate architectures of convolutional neural networks (CNNs) in order to simultaneously accomplish the tasks of crop detection and harvesting (robotic manipulation) inside a simulated environment. Crop images in the simulated environment are subjected to random rotations, cropping, brightness, and contrast adjustments to create augmented images for dataset generation. The you only look once algorithmic framework is employed with traditional rectangular bounding boxes for crop localization. The proposed method subsequently utilises the acquired image data via a visual geometry group model in order to reveal the grasping positions for the robotic manipulation.

Hongyu Zhao, Ming Li, Lichao Sun et al.

Evaluating large language models (LLMs) is costly: it requires the generation and examination of LLM outputs on a large-scale benchmark of various tasks. This paper investigates how to efficiently reduce the tasks used to benchmark LLMs without affecting the evaluation quality. Our study reveals that task transferability and relevance provide critical information to identify the most representative subset of tasks via optimizing a facility location function. We propose a practically efficient metric for estimating the transferability between two tasks via in-context learning (ICL). By analyzing the pairwise transferability, we can reduce tasks in a modern LLM benchmark (e.g., MMLU or FLAN) to 5% while inducing only a <4% difference to the evaluation on the original benchmark. Compared to prior works, our method is training-free, gradient-free, and highly efficient requiring ICL only.

Can Wang, Hongyu Zhao, Yiqun Chen

Causal inference is central to scientific discovery, yet choosing appropriate methods remains challenging because of the complexity of both statistical methodology and real-world data. Inspired by the success of artificial intelligence in accelerating scientific discovery, we introduce InferenceEvolve, an evolutionary framework that uses large language models to discover and iteratively refine causal methods. Across widely used benchmarks, InferenceEvolve yields estimators that consistently outperform established baselines: against 58 human submissions in a recent community competition, our best evolved estimator lay on the Pareto frontier across two evaluation metrics. We also developed robust proxy objectives for settings without semi-synthetic outcomes, with competitive results. Analysis of the evolutionary trajectories shows that agents progressively discover sophisticated strategies tailored to unrevealed data-generating mechanisms. These findings suggest that language-model-guided evolution can optimize structured scientific programs such as causal inference, even when outcomes are only partially observed.

Fangxu Yu, Hongyu Zhao, Tianyi Zhou

Time series reasoning is crucial to decision-making in diverse domains, including finance, energy usage, traffic, weather, and scientific discovery. While existing time series foundation models (TSFMs) can capture low-level dynamic patterns and provide accurate forecasting, further analysis usually requires additional background knowledge and sophisticated reasoning, which are lacking in most TSFMs but can be achieved through large language models (LLMs). On the other hand, without expensive post-training, LLMs often struggle with the numerical understanding of time series data. Although it is intuitive to integrate the two types of models, developing effective training recipes that align the two modalities for reasoning tasks is still an open challenge. To this end, we propose TS-Reasoner that aligns the latent representations of TSFMs with the textual inputs of LLMs for downstream understanding/reasoning tasks. Specifically, we propose a simple yet effective method to curate diverse, synthetic pairs of time series and textual captions for alignment training. We then develop a two-stage training recipe that applies instruction finetuning after the alignment pretraining. Unlike existing works that train an LLM to take time series as inputs, we leverage a pretrained TSFM and freeze it during training. Extensive experiments on several benchmarks demonstrate that TS-Reasoner not only outperforms a wide range of prevailing LLMs, Vision Language Models (VLMs), and Time Series LLMs, but also achieves this with remarkable data efficiency, e.g., using less than half the training data.

Li Zeng, Zhaolong Yu, Yiliang Zhang et al.

Predictive modeling based on genomic data has gained popularity in biomedical research and clinical practice by allowing researchers and clinicians to identify biomarkers and tailor treatment decisions more efficiently. Analysis incorporating pathway information can boost discovery power and better connect new findings with biological mechanisms. In this article, we propose a general framework, Pathway-based Kernel Boosting (PKB), which incorporates clinical information and prior knowledge about pathways for prediction of binary, continuous and survival outcomes. We introduce appropriate loss functions and optimization procedures for different outcome types. Our prediction algorithm incorporates pathway knowledge by constructing kernel function spaces from the pathways and use them as base learners in the boosting procedure. Through extensive simulations and case studies in drug response and cancer survival datasets, we demonstrate that PKB can substantially outperform other competing methods, better identify biological pathways related to drug response and patient survival, and provide novel insights into cancer pathogenesis and treatment response.

Zhongruo Wang, Bingyuan Liu, Shixiang Chen et al.

Spectral clustering is one of the fundamental unsupervised learning methods widely used in data analysis. Sparse spectral clustering (SSC) imposes sparsity to the spectral clustering and it improves the interpretability of the model. This paper considers a widely adopted model for SSC, which can be formulated as an optimization problem over the Stiefel manifold with nonsmooth and nonconvex objective. Such an optimization problem is very challenging to solve. Existing methods usually solve its convex relaxation or need to smooth its nonsmooth part using certain smoothing techniques. In this paper, we propose a manifold proximal linear method (ManPL) that solves the original SSC formulation. We also extend the algorithm to solve the multiple-kernel SSC problems, for which an alternating ManPL algorithm is proposed. Convergence and iteration complexity results of the proposed methods are established. We demonstrate the advantage of our proposed methods over existing methods via the single-cell RNA sequencing data analysis.

Xiaochen Wang, Arash Pakbin, Bobak J. Mortazavi et al.

The proliferation of medical monitoring devices makes it possible to track health vitals at high frequency, enabling the development of dynamic health risk scores that change with the underlying readings. Survival analysis, in particular hazard estimation, is well-suited to analyzing this stream of data to predict disease onset as a function of the time-varying vitals. This paper introduces the software package BoXHED (pronounced 'box-head') for nonparametrically estimating hazard functions via gradient boosting. BoXHED 1.0 is a novel tree-based implementation of the generic estimator proposed in Lee, Chen, Ishwaran (2017), which was designed for handling time-dependent covariates in a fully nonparametric manner. BoXHED is also the first publicly available software implementation for Lee, Chen, Ishwaran (2017). Applying BoXHED to cardiovascular disease onset data from the Framingham Heart Study reveals novel interaction effects among known risk factors, potentially resolving an open question in clinical literature.

Li Zeng, Zhaolong Yu, Hongyu Zhao

The analysis of cancer genomic data has long suffered "the curse of dimensionality". Sample sizes for most cancer genomic studies are a few hundreds at most while there are tens of thousands of genomic features studied. Various methods have been proposed to leverage prior biological knowledge, such as pathways, to more effectively analyze cancer genomic data. Most of the methods focus on testing marginal significance of the associations between pathways and clinical phenotypes. They can identify relevant pathways, but do not involve predictive modeling. In this article, we propose a Pathway-based Kernel Boosting (PKB) method for integrating gene pathway information for sample classification, where we use kernel functions calculated from each pathway as base learners and learn the weights through iterative optimization of the classification loss function. We apply PKB and several competing methods to three cancer studies with pathological and clinical information, including tumor grade, stage, tumor sites, and metastasis status. Our results show that PKB outperforms other methods, and identifies pathways relevant to the outcome variables.

Xiaowei Zhou, Can Yang, Hongyu Zhao et al.

Low-rank modeling generally refers to a class of methods that solve problems by representing variables of interest as low-rank matrices. It has achieved great success in various fields including computer vision, data mining, signal processing and bioinformatics. Recently, much progress has been made in theories, algorithms and applications of low-rank modeling, such as exact low-rank matrix recovery via convex programming and matrix completion applied to collaborative filtering. These advances have brought more and more attentions to this topic. In this paper, we review the recent advance of low-rank modeling, the state-of-the-art algorithms, and related applications in image analysis. We first give an overview to the concept of low-rank modeling and challenging problems in this area. Then, we summarize the models and algorithms for low-rank matrix recovery and illustrate their advantages and limitations with numerical experiments. Next, we introduce a few applications of low-rank modeling in the context of image analysis. Finally, we conclude this paper with some discussions.

Mengjie Chen, Chao Gao, Hongyu Zhao

By expressing prior distributions as general stochastic processes, nonparametric Bayesian methods provide a flexible way to incorporate prior knowledge and constrain the latent structure in statistical inference. The Indian buffet process (IBP) is such an example that can be used to define a prior distribution on infinite binary features, where the exchangeability among subjects is assumed. The phylogenetic Indian buffet process (pIBP), a derivative of IBP, enables the modeling of non-exchangeability among subjects through a stochastic process on a rooted tree, which is similar to that used in phylogenetics, to describe relationships among the subjects. In this paper, we study the theoretical properties of IBP and pIBP under a binary factor model. We establish the posterior contraction rates for both IBP and pIBP and substantiate the theoretical results through simulation studies. This is the first work addressing the frequentist property of the posterior behaviors of IBP and pIBP. We also demonstrated its practical usefulness by applying pIBP prior to a real data example arising in the field of cancer genomics where the exchangeability among subjects is violated.