Jun Lu

Xiaofeng Liu, Fangxu Xing, Jia You et al. · cmu, harvard

Unsupervised domain adaptation (UDA) has been successfully applied to transfer knowledge from a labeled source domain to target domains without their labels. Recently introduced transferable prototypical networks (TPN) further addresses class-wise conditional alignment. In TPN, while the closeness of class centers between source and target domains is explicitly enforced in a latent space, the underlying fine-grained subtype structure and the cross-domain within-class compactness have not been fully investigated. To counter this, we propose a new approach to adaptively perform a fine-grained subtype-aware alignment to improve performance in the target domain without the subtype label in both domains. The insight of our approach is that the unlabeled subtypes in a class have the local proximity within a subtype, while exhibiting disparate characteristics, because of different conditional and label shifts. Specifically, we propose to simultaneously enforce subtype-wise compactness and class-wise separation, by utilizing intermediate pseudo-labels. In addition, we systematically investigate various scenarios with and without prior knowledge of subtype numbers, and propose to exploit the underlying subtype structure. Furthermore, a dynamic queue framework is developed to evolve the subtype cluster centroids steadily using an alternative processing scheme. Experimental results, carried out with multi-view congenital heart disease data and VisDA and DomainNet, show the effectiveness and validity of our subtype-aware UDA, compared with state-of-the-art UDA methods.

Lingsheng Kong, Bo Hu, Xiongchang Liu et al. · cmu, harvard

Deep learning is usually data starved, and the unsupervised domain adaptation (UDA) is developed to introduce the knowledge in the labeled source domain to the unlabeled target domain. Recently, deep self-training presents a powerful means for UDA, involving an iterative process of predicting the target domain and then taking the confident predictions as hard pseudo-labels for retraining. However, the pseudo-labels are usually unreliable, thus easily leading to deviated solutions with propagated errors. In this paper, we resort to the energy-based model and constrain the training of the unlabeled target sample with an energy function minimization objective. It can be achieved via a simple additional regularization or an energy-based loss. This framework allows us to gain the benefits of the energy-based model, while retaining strong discriminative performance following a plug-and-play fashion. The convergence property and its connection with classification expectation minimization are investigated. We deliver extensive experiments on the most popular and large-scale UDA benchmarks of image classification as well as semantic segmentation to demonstrate its generality and effectiveness.

Jun Lu, Zehao Sang, Haoqi Wei et al.

Cross-View Geo-Localization (CVGL) in remote sensing aims to locate a drone-view query by matching it to geo-tagged satellite images. Although supervised methods have achieved strong results on closeset benchmarks, they often fail to generalize to unconstrained, real-world scenarios due to severe viewpoint differences and dataset bias. To overcome these limitations, we present VFM-Loc, a training-free framework for zero-shot CVGL that leverages the generalizable visual representations from vision foundational models (VFMs). VFM-Loc identifies and matches discriminative visual clues across different viewpoints through a progressive alignment strategy. First, we design a hierarchical clue extraction mechanism using Generalized Mean pooling and Scale-Weighted RMAC to preserve distinctive visual clues across scales while maintaining hierarchical confidence. Second, we introduce a statistical manifold alignment pipeline based on domain-wise PCA and Orthogonal Procrustes analysis, linearly aligning heterogeneous feature distributions in a shared metric space. Experiments demonstrate that VFM-Loc exhibits strong zero-shot accuracy on standard benchmarks and surpasses supervised methods by over 20% in Recall@1 on the challenging LO-UCV dataset with large oblique angles. This work highlights that principled alignment of pre-trained features can effectively bridge the cross-view gap, establishing a robust and training-free paradigm for real-world CVGL. The relevant code is made available at: https://github.com/DingLei14/VFM-Loc.

Jun Lu

The goal of this paper is to debunk and dispel the magic behind black-box optimizers and stochastic optimizers. It aims to build a solid foundation on how and why the techniques work. This manuscript crystallizes this knowledge by deriving from simple intuitions, the mathematics behind the strategies. This tutorial doesn't shy away from addressing both the formal and informal aspects of gradient descent and stochastic optimization methods. By doing so, it hopes to provide readers with a deeper understanding of these techniques as well as the when, the how and the why of applying these algorithms. Gradient descent is one of the most popular algorithms to perform optimization and by far the most common way to optimize machine learning tasks. Its stochastic version receives attention in recent years, and this is particularly true for optimizing deep neural networks. In deep neural networks, the gradient followed by a single sample or a batch of samples is employed to save computational resources and escape from saddle points. In 1951, Robbins and Monro published \textit{A stochastic approximation method}, one of the first modern treatments on stochastic optimization that estimates local gradients with a new batch of samples. And now, stochastic optimization has become a core technology in machine learning, largely due to the development of the back propagation algorithm in fitting a neural network. The sole aim of this article is to give a self-contained introduction to concepts and mathematical tools in gradient descent and stochastic optimization.

Jun Lu, Xuanyu Ye

In this paper, we introduce a probabilistic model for learning nonnegative matrix factorization (NMF) that is commonly used for predicting missing values and finding hidden patterns in the data, in which the matrix factors are latent variables associated with each data dimension. The nonnegativity constraint for the latent factors is handled by choosing priors with support on the nonnegative subspace. Bayesian inference procedure based on Gibbs sampling is employed. We evaluate the model on several real-world datasets including MovieLens 100K and MovieLens 1M with different sizes and dimensions and show that the proposed Bayesian NMF GRRN model leads to better predictions and avoids overfitting compared to existing Bayesian NMF approaches.

Jun Lu, Shao Yi

Over the decades, the Markowitz framework has been used extensively in portfolio analysis though it puts too much emphasis on the analysis of the market uncertainty rather than on the trend prediction. While generative adversarial network (GAN) and conditional GAN (CGAN) have been explored to generate financial time series and extract features that can help portfolio analysis. The limitation of the CGAN framework stands in putting too much emphasis on generating series rather than keeping features that can help this generator. In this paper, we introduce an autoencoding CGAN (ACGAN) based on deep generative models that learns the internal trend of historical data while modeling market uncertainty and future trends. We evaluate the model on several real-world datasets from both the US and Europe markets, and show that the proposed ACGAN model leads to better portfolio allocation and generates series that are closer to true data compared to the existing Markowitz and CGAN approaches.

Jun Lu

Low-rank approximation is a fundamental technique in modern data analysis, widely utilized across various fields such as signal processing, machine learning, and natural language processing. Despite its ubiquity, the mechanics of low-rank approximation and its application in adaptation can sometimes be obscure, leaving practitioners and researchers with questions about its true capabilities and limitations. This paper seeks to clarify low-rank approximation and adaptation by offering a comprehensive guide that reveals their inner workings and explains their utility in a clear and accessible way. Our focus here is to develop a solid intuition for how low-rank approximation and adaptation operate, and why they are so effective. We begin with basic concepts and gradually build up to the mathematical underpinnings, ensuring that readers of all backgrounds can gain a deeper understanding of low-rank approximation and adaptation. We strive to strike a balance between informal explanations and rigorous mathematics, ensuring that both newcomers and experienced experts can benefit from this survey. Additionally, we introduce new low-rank decomposition and adaptation algorithms that have not yet been explored in the field, hoping that future researchers will investigate their potential applicability.

Jun Lu

In this paper, we introduce a probabilistic model for learning interpolative decomposition (ID), which is commonly used for feature selection, low-rank approximation, and identifying hidden patterns in data, where the matrix factors are latent variables associated with each data dimension. Prior densities with support on the specified subspace are used to address the constraint for the magnitude of the factored component of the observed matrix. Bayesian inference procedure based on Gibbs sampling is employed. We evaluate the model on a variety of real-world datasets including CCLE EC50, CCLE IC50, CTRP EC50,and MovieLens 100K datasets with different sizes, and dimensions, and show that the proposed Bayesian ID GBT and GBTN models lead to smaller reconstructive errors compared to existing randomized approaches.

Jun Lu, Christine P. Chai

We introduce a probabilistic model with implicit norm regularization for learning nonnegative matrix factorization (NMF) that is commonly used for predicting missing values and finding hidden patterns in the data, in which the matrix factors are latent variables associated with each data dimension. The nonnegativity constraint for the latent factors is handled by choosing priors with support on the nonnegative subspace, e.g., exponential density or distribution based on exponential function. Bayesian inference procedure based on Gibbs sampling is employed. We evaluate the model on several real-world datasets including Genomics of Drug Sensitivity in Cancer (GDSC $IC_{50}$) and Gene body methylation with different sizes and dimensions, and show that the proposed Bayesian NMF GL$_2^2$ and GL$_\infty$ models lead to robust predictions for different data values and avoid overfitting compared with competitive Bayesian NMF approaches.

Jun Lu

In this paper, we propose a probabilistic model with automatic relevance determination (ARD) for learning interpolative decomposition (ID), which is commonly used for low-rank approximation, feature selection, and identifying hidden patterns in data, where the matrix factors are latent variables associated with each data dimension. Prior densities with support on the specified subspace are used to address the constraint for the magnitude of the factored component of the observed matrix. Bayesian inference procedure based on Gibbs sampling is employed. We evaluate the model on a variety of real-world datasets including CCLE $EC50$, CCLE $IC50$, Gene Body Methylation, and Promoter Methylation datasets with different sizes, and dimensions, and show that the proposed Bayesian ID algorithms with automatic relevance determination lead to smaller reconstructive errors even compared to vanilla Bayesian ID algorithms with fixed latent dimension set to matrix rank.

Jun Lu, Shao Yi

SVR-GARCH model tends to "backward eavesdrop" when forecasting the financial time series volatility in which case it tends to simply produce the prediction by deviating the previous volatility. Though the SVR-GARCH model has achieved good performance in terms of various performance measurements, trading opportunities, peak or trough behaviors in the time series are all hampered by underestimating or overestimating the volatility. We propose a blending ARCH (BARCH) and an augmented BARCH (aBARCH) model to overcome this kind of problem and make the prediction towards better peak or trough behaviors. The method is illustrated using real data sets including SH300 and S&P500. The empirical results obtained suggest that the augmented and blending models improve the volatility forecasting ability.

Jun Lu

The sole aim of this book is to give a self-contained introduction to concepts and mathematical tools in Bayesian matrix decomposition in order to seamlessly introduce matrix decomposition techniques and their applications in subsequent sections. However, we clearly realize our inability to cover all the useful and interesting results concerning Bayesian matrix decomposition and given the paucity of scope to present this discussion, e.g., the separated analysis of variational inference for conducting the optimization. We refer the reader to literature in the field of Bayesian analysis for a more detailed introduction to the related fields. This book is primarily a summary of purpose, significance of important Bayesian matrix decomposition methods, e.g., real-valued decomposition, nonnegative matrix factorization, Bayesian interpolative decomposition, and the origin and complexity of the methods which shed light on their applications. The mathematical prerequisite is a first course in statistics and linear algebra. Other than this modest background, the development is self-contained, with rigorous proof provided throughout.

Kun Yang, Jun Lu

The proposed method in this paper proposes an end-to-end unsupervised semantic segmentation architecture DMSA based on four loss functions. The framework uses Atrous Spatial Pyramid Pooling (ASPP) module to enhance feature extraction. At the same time, a dynamic dilation strategy is designed to better capture multi-scale context information. Secondly, a Pixel-Adaptive Refinement (PAR) module is introduced, which can adaptively refine the initial pseudo labels after feature fusion to obtain high quality pseudo labels. Experiments show that the proposed DSMA framework is superior to the existing methods on the saliency dataset. On the COCO 80 dataset, the MIoU is improved by 2.0, and the accuracy is improved by 5.39. On the Pascal VOC 2012 Augmented dataset, the MIoU is improved by 4.9, and the accuracy is improved by 3.4. In addition, the convergence speed of the model is also greatly improved after the introduction of the PAR module.

Jun Lu, Joerg Osterrieder

In this paper, we propose a probabilistic model for computing an interpolative decomposition (ID) in which each column of the observed matrix has its own priority or importance, so that the end result of the decomposition finds a set of features that are representative of the entire set of features, and the selected features also have higher priority than others. This approach is commonly used for low-rank approximation, feature selection, and extracting hidden patterns in data, where the matrix factors are latent variables associated with each data dimension. Gibbs sampling for Bayesian inference is applied to carry out the optimization. We evaluate the proposed models on real-world datasets, including ten Chinese A-share stocks, and demonstrate that the proposed Bayesian ID algorithm with intervention (IID) produces comparable reconstructive errors to existing Bayesian ID algorithms while selecting features with higher scores or priority.

Jun Lu, Danny Ding

Over the decades, the Markowitz framework has been used extensively in portfolio analysis though it puts too much emphasis on the analysis of the market uncertainty rather than on the trend prediction. While generative adversarial network (GAN), conditional GAN (CGAN), and autoencoding CGAN (ACGAN) have been explored to generate financial time series and extract features that can help portfolio analysis. The limitation of the CGAN or ACGAN framework stands in putting too much emphasis on generating series and finding the internal trends of the series rather than predicting the future trends. In this paper, we introduce a hybrid approach on conditional GAN based on deep generative models that learns the internal trend of historical data while modeling market uncertainty and future trends. We evaluate the model on several real-world datasets from both the US and Europe markets, and show that the proposed HybridCGAN and HybridACGAN models lead to better portfolio allocation compared to the existing Markowitz, CGAN, and ACGAN approaches.

Lei Ding, Tong Liu, Xuanguang Liu et al.

Change detection (CD) in multitemporal remote sensing imagery presents significant challenges for fine-grained recognition, owing to heterogeneity and spatiotemporal misalignment. However, existing methodologies based on vision transformers or state-space models typically disrupt local structural consistency during temporal serialization, obscuring discriminative cues under misalignment and hindering reliable change localization. To address this, we introduce ChessMamba, a structure-aware framework leveraging interleaved state-space modeling for robust CD with multi-temporal inputs. ChessMamba integrates a SpatialMamba encoder with a lightweight cross-source interaction module, featuring two key innovations: (i) Chessboard interleaving with snake scanning order, which serializes multi-temporal features into a unified sequence within a single forward pass, thereby shortening interaction paths and enabling direct comparison for accurate change localization; and (ii) Structure-aware fusion via multi-dilated convolutions, selectively capturing center-and-corner neighborhood contexts within each mono-temporal. Comprehensive evaluations on three CD tasks, including binary CD, semantic CD and multimodal building damage assessment, demonstrate that ChessMamba effectively fuses heterogeneous features and achieves substantial accuracy improvements over state-of-the-art methods.The relevant code will be available at: github.com/DingLei14/ChessMamba.

Jun Lu, David Li, Bill Ding et al.

This paper presents an approach to improve text embedding models through contrastive fine-tuning on small datasets augmented with expert scores. It focuses on enhancing semantic textual similarity tasks and addressing text retrieval problems. The proposed method uses soft labels derived from expert-augmented scores to fine-tune embedding models, preserving their versatility and ensuring retrieval capability is improved. The paper evaluates the method using a Q\&A dataset from an online shopping website and eight expert models. Results show improved performance over a benchmark model across multiple metrics on various retrieval tasks from the massive text embedding benchmark (MTEB). The method is cost-effective and practical for real-world applications, especially when labeled data is scarce.

Lei Ding, Xibing Zuo, Danfeng Hong et al.

Unsupervised Change Detection (UCD) in multimodal Remote Sensing (RS) images remains a difficult challenge due to the inherent spatio-temporal complexity within data, and the heterogeneity arising from different imaging sensors. Inspired by recent advancements in Visual Foundation Models (VFMs) and Contrastive Learning (CL) methodologies, this research aims to develop CL methodologies to translate implicit knowledge in VFM into change representations, thus eliminating the need for explicit supervision. To this end, we introduce a Semantic-to-Change (S2C) learning framework for UCD in both homogeneous and multimodal RS images. Differently from existing CL methodologies that typically focus on learning multi-temporal similarities, we introduce a novel triplet learning strategy that explicitly models temporal differences, which are crucial to the CD task. Furthermore, random spatial and spectral perturbations are introduced during the training to enhance robustness to temporal noise. In addition, a grid sparsity regularization is defined to suppress insignificant changes, and an IoU-matching algorithm is developed to refine the CD results. Experiments on four benchmark CD datasets demonstrate that the proposed S2C learning framework achieves significant improvements in accuracy, surpassing current state-of-the-art by over 31\%, 9\%, 23\%, and 15\%, respectively. It also demonstrates robustness and sample efficiency, suitable for training and adaptation of various Visual Foundation Models (VFMs) or backbone neural networks. The relevant code will be available at: github.com/DingLei14/S2C.

Jun Lu

It is well known that we need to choose the hyper-parameters in Momentum, AdaGrad, AdaDelta, and other alternative stochastic optimizers. While in many cases, the hyper-parameters are tuned tediously based on experience becoming more of an art than science. We present a novel per-dimension learning rate method for gradient descent called AdaSmooth. The method is insensitive to hyper-parameters thus it requires no manual tuning of the hyper-parameters like Momentum, AdaGrad, and AdaDelta methods. We show promising results compared to other methods on different convolutional neural networks, multi-layer perceptron, and alternative machine learning tasks. Empirical results demonstrate that AdaSmooth works well in practice and compares favorably to other stochastic optimization methods in neural networks.

Jun Lu, Minhui Wu

In this note, we introduce how to use Volatility Index (VIX) for postprocessing quantitative strategies so as to increase the Sharpe ratio and reduce trading risks. The signal from this procedure is an indicator of trading or not on a daily basis. Finally, we analyze this procedure on SH510300 and SH510050 assets. The strategies are evaluated by measurements of Sharpe ratio, max drawdown, and Calmar ratio. However, there is always a risk of loss in trading. The results from the tests are just examples of how the method works; no claim is made on the suggestion of real market positions.

Jun Lu, Tianyi Xu, Bill Ding et al.

In this paper, we tackle the critical challenge of compressing large language models (LLMs) to facilitate their practical deployment and broader adoption. We introduce a novel post-training compression paradigm that focuses on low-rank decomposition of LLM weights. Our analysis identifies two main challenges in this task: the variability in LLM activation distributions and handling unseen activations from different datasets and models. To address these challenges, we propose a nested activation-aware framework (NSVD) for LLMs, a training-free approach designed to enhance the accuracy of low-rank decompositions by managing activation outliers through transforming the weight matrix based on activation distribution and the original weight matrix. This method allows for the absorption of outliers into the transformed weight matrix, improving decomposition accuracy. Our comprehensive evaluation across eight datasets and six models from three distinct LLM families demonstrates the superiority of NSVD over current state-of-the-art methods, especially at medium to large compression ratios or in multilingual and multitask settings.

Yang Fu, Peng Qin, Yueyue Zhang et al.

6G networks are envisioned to support on-demand AI model downloading to accommodate diverse inference requirements of end users. By proactively caching models at edge nodes, users can retrieve the requested models with low latency for on-device AI inference. However, the substantial size of contemporary AI models poses significant challenges for edge caching under limited storage capacity, as well as for the concurrent delivery of heterogeneous models over wireless channels. To address these challenges, we propose a fine-grained AI model caching and downloading system that exploits parameter reusability, stemming from the common practice of fine-tuning task-specific models from a shared pre-trained model with frozen parameters. This system selectively caches model parameter blocks (PBs) at edge nodes, eliminating redundant storage of reusable parameters across different cached models. Additionally, it incorporates coordinated multipoint (CoMP) broadcasting to simultaneously deliver reusable PBs to multiple users, thereby enhancing downlink spectrum utilization. Under this arrangement, we formulate a model downloading delay minimization problem to jointly optimize PB caching, migration (among edge nodes), and broadcasting beamforming. To tackle this intractable problem, we develop a distributed multi-agent learning framework that enables edge nodes to explicitly learn mutual influence among their actions, thereby facilitating cooperation. Furthermore, a data augmentation approach is proposed to adaptively generate synthetic training samples through a predictive model, boosting sample efficiency and accelerating policy learning. Both theoretical analysis and simulation experiments validate the superior convergence performance of the proposed learning framework.

Dezhi An, Wenqiang Liu, Kefan Wang et al.

The goal of video anomaly detection is tantamount to performing spatio-temporal localization of abnormal events in the video. The multiscale temporal dependencies, visual-semantic heterogeneity, and the scarcity of labeled data exhibited by video anomalies collectively present a challenging research problem in computer vision. This study offers a dual-path architecture called the Dual-Branch Adaptive Multiscale Spatiotemporal Framework (DAMS), which is based on multilevel feature decoupling and fusion, enabling efficient anomaly detection modeling by integrating hierarchical feature learning and complementary information. The main processing path of this framework integrates the Adaptive Multiscale Time Pyramid Network (AMTPN) with the Convolutional Block Attention Mechanism (CBAM). AMTPN enables multigrained representation and dynamically weighted reconstruction of temporal features through a three-level cascade structure (time pyramid pooling, adaptive feature fusion, and temporal context enhancement). CBAM maximizes the entropy distribution of feature channels and spatial dimensions through dual attention mapping. Simultaneously, the parallel path driven by CLIP introduces a contrastive language-visual pre-training paradigm. Cross-modal semantic alignment and a multiscale instance selection mechanism provide high-order semantic guidance for spatio-temporal features. This creates a complete inference chain from the underlying spatio-temporal features to high-level semantic concepts. The orthogonal complementarity of the two paths and the information fusion mechanism jointly construct a comprehensive representation and identification capability for anomalous events. Extensive experimental results on the UCF-Crime and XD-Violence benchmarks establish the effectiveness of the DAMS framework.

Nuoa Lei, Arman Shehabi, Jun Lu et al.

In the rapidly evolving digital era, comprehending the intricate dynamics influencing server power consumption, efficiency, and performance is crucial for sustainable data center operations. However, existing models lack the ability to provide a detailed and reliable understanding of these intricate relationships. This study employs a machine learning-based approach, using the SPECPower_ssj2008 database, to facilitate user-friendly and generalizable server modeling. The resulting models demonstrate high accuracy, with errors falling within approximately 10% on the testing dataset, showcasing their practical utility and generalizability. Through meticulous analysis, predictive features related to hardware availability date, server workload level, and specifications are identified, providing insights into optimizing energy conservation, efficiency, and performance in server deployment and operation. By systematically measuring biases and uncertainties, the study underscores the need for caution when employing historical data for prospective server modeling, considering the dynamic nature of technology landscapes. Collectively, this work offers valuable insights into the sustainable deployment and operation of servers in data centers, paving the way for enhanced resource use efficiency and more environmentally conscious practices.

Jun Lu

In an era where data-driven decision-making and computational efficiency are paramount, optimization plays a foundational role in advancing fields such as mathematics, computer science, operations research, machine learning, and beyond. From refining machine learning models to improving resource allocation and designing efficient algorithms, optimization techniques serve as essential tools for tackling complex problems. This book aims to provide both an introductory guide and a comprehensive reference, equipping readers with the necessary knowledge to understand and apply optimization methods within their respective fields. Our primary goal is to demystify the inner workings of optimization algorithms, including black-box and stochastic optimizers, by offering both formal and intuitive explanations. Starting from fundamental mathematical principles, we derive key results to ensure that readers not only learn how these techniques work but also understand when and why to apply them effectively. By striking a careful balance between theoretical depth and practical application, this book serves a broad audience, from students and researchers to practitioners seeking robust optimization strategies.

Jun Lu

The goal of this paper is to debunk and dispel the magic behind the black-box quantitative strategies. It aims to build a solid foundation on how and why the techniques work. This manuscript crystallizes this knowledge by deriving from simple intuitions, the mathematics behind the strategies. This tutorial doesn't shy away from addressing both the formal and informal aspects of quantitative strategies. By doing so, it hopes to provide readers with a deeper understanding of these techniques as well as the when, the how and the why of applying these techniques. The strategies are presented in terms of both S\&P500 and SH510300 data sets. However, the results from the tests are just examples of how the methods work; no claim is made on the suggestion of real market positions.

Jun Lu

In 1954, Alston S. Householder published Principles of Numerical Analysis, one of the first modern treatments on matrix decomposition that favored a (block) LU decomposition-the factorization of a matrix into the product of lower and upper triangular matrices. And now, matrix decomposition has become a core technology in machine learning, largely due to the development of the backpropagation algorithm in fitting a neural network. The sole aim of this survey is to give a self-contained introduction to concepts and mathematical tools in numerical linear algebra and matrix analysis in order to seamlessly introduce matrix decomposition techniques and their applications in subsequent sections. However, we clearly realize our inability to cover all the useful and interesting results concerning matrix decomposition, given the paucity of scope to present this discussion, e.g., the separated analysis of the Euclidean space, Hermitian space, Hilbert space, and things in the complex domain. We refer the reader to literature in the field of linear algebra for a more detailed introduction to the related fields.

Hui Xie, Zhuang Zhao, Jing Han et al.

We consider using the system's optical imaging process with convolutional neural networks (CNNs) to solve the snapshot hyperspectral imaging reconstruction problem, which uses a dual-camera system to capture the three-dimensional hyperspectral images (HSIs) in a compressed way. Various methods using CNNs have been developed in recent years to reconstruct HSIs, but most of the supervised deep learning methods aimed to fit a brute-force mapping relationship between the captured compressed image and standard HSIs. Thus, the learned mapping would be invalid when the observation data deviate from the training data. Especially, we usually don't have ground truth in real-life scenarios. In this paper, we present a self-supervised dual-camera equipment with an untrained physics-informed CNNs framework. Extensive simulation and experimental results show that our method without training can be adapted to a wide imaging environment with good performance. Furthermore, compared with the training-based methods, our system can be constantly fine-tuned and self-improved in real-life scenarios.

Jun Lu

Clustering has become a core technology in machine learning, largely due to its application in the field of unsupervised learning, clustering, classification, and density estimation. A frequentist approach exists to hand clustering based on mixture model which is known as the EM algorithm where the parameters of the mixture model are usually estimated into a maximum likelihood estimation framework. Bayesian approach for finite and infinite Gaussian mixture model generates point estimates for all variables as well as associated uncertainty in the form of the whole estimates' posterior distribution. The sole aim of this survey is to give a self-contained introduction to concepts and mathematical tools in Bayesian inference for finite and infinite Gaussian mixture model in order to seamlessly introduce their applications in subsequent sections. However, we clearly realize our inability to cover all the useful and interesting results concerning this field and given the paucity of scope to present this discussion, e.g., the separated analysis of the generation of Dirichlet samples by stick-breaking and Polya's Urn approaches. We refer the reader to literature in the field of the Dirichlet process mixture model for a much detailed introduction to the related fields. Some excellent examples include (Frigyik et al., 2010; Murphy, 2012; Gelman et al., 2014; Hoff, 2009). This survey is primarily a summary of purpose, significance of important background and techniques for Gaussian mixture model, e.g., Dirichlet prior, Chinese restaurant process, and most importantly the origin and complexity of the methods which shed light on their modern applications. The mathematical prerequisite is a first course in probability. Other than this modest background, the development is self-contained, with rigorous proofs provided throughout.

Jun Lu

This survey is meant to provide an introduction to the fundamental theorem of linear algebra and the theories behind them. Our goal is to give a rigorous introduction to the readers with prior exposure to linear algebra. Specifically, we provide some details and proofs of some results from (Strang, 1993). We then describe the fundamental theorem of linear algebra from different views and find the properties and relationships behind the views. The fundamental theorem of linear algebra is essential in many fields, such as electrical engineering, computer science, machine learning, and deep learning. This survey is primarily a summary of purpose, significance of important theories behind it. The sole aim of this survey is to give a self-contained introduction to concepts and mathematical tools in theory behind the fundamental theorem of linear algebra and rigorous analysis in order to seamlessly introduce its properties in four subspaces in subsequent sections. However, we clearly realize our inability to cover all the useful and interesting results and given the paucity of scope to present this discussion, e.g., the separated analysis of the (orthogonal) projection matrices. We refer the reader to literature in the field of linear algebra for a more detailed introduction to the related fields. Some excellent examples include (Rose, 1982; Strang, 2009; Trefethen and Bau III, 1997; Strang, 2019, 2021).

Xiaofeng Liu, Site Li, Yubin Ge et al.

The unsupervised domain adaptation (UDA) has been widely adopted to alleviate the data scalability issue, while the existing works usually focus on classifying independently discrete labels. However, in many tasks (e.g., medical diagnosis), the labels are discrete and successively distributed. The UDA for ordinal classification requires inducing non-trivial ordinal distribution prior to the latent space. Target for this, the partially ordered set (poset) is defined for constraining the latent vector. Instead of the typically i.i.d. Gaussian latent prior, in this work, a recursively conditional Gaussian (RCG) set is adapted for ordered constraint modeling, which admits a tractable joint distribution prior. Furthermore, we are able to control the density of content vector that violates the poset constraints by a simple "three-sigma rule". We explicitly disentangle the cross-domain images into a shared ordinal prior induced ordinal content space and two separate source/target ordinal-unrelated spaces, and the self-training is worked on the shared space exclusively for ordinal-aware domain alignment. Extensive experiments on UDA medical diagnoses and facial age estimation demonstrate its effectiveness.

Xiaofeng Liu, Bo Hu, Linghao Jin et al.

In this work, we propose a domain generalization (DG) approach to learn on several labeled source domains and transfer knowledge to a target domain that is inaccessible in training. Considering the inherent conditional and label shifts, we would expect the alignment of $p(x|y)$ and $p(y)$. However, the widely used domain invariant feature learning (IFL) methods relies on aligning the marginal concept shift w.r.t. $p(x)$, which rests on an unrealistic assumption that $p(y)$ is invariant across domains. We thereby propose a novel variational Bayesian inference framework to enforce the conditional distribution alignment w.r.t. $p(x|y)$ via the prior distribution matching in a latent space, which also takes the marginal label shift w.r.t. $p(y)$ into consideration with the posterior alignment. Extensive experiments on various benchmarks demonstrate that our framework is robust to the label shift and the cross-domain accuracy is significantly improved, thereby achieving superior performance over the conventional IFL counterparts.

Jun Lu

This book is meant to provide an introduction to linear models and the theories behind them. Our goal is to give a rigorous introduction to the readers with prior exposure to ordinary least squares. In machine learning, the output is usually a nonlinear function of the input. Deep learning even aims to find a nonlinear dependence with many layers, which require a large amount of computation. However, most of these algorithms build upon simple linear models. We then describe linear models from different perspectives and find the properties and theories behind the models. The linear model is the main technique in regression problems, and the primary tool for it is the least squares approximation, which minimizes a sum of squared errors. This is a natural choice when we're interested in finding the regression function which minimizes the corresponding expected squared error. This book is primarily a summary of purpose, significance of important theories behind linear models, e.g., distribution theory and the minimum variance estimator. We first describe ordinary least squares from three different points of view, upon which we disturb the model with random noise and Gaussian noise. Through Gaussian noise, the model gives rise to the likelihood so that we introduce a maximum likelihood estimator. It also develops some distribution theories via this Gaussian disturbance. The distribution theory of least squares will help us answer various questions and introduce related applications. We then prove least squares is the best unbiased linear model in the sense of mean squared error, and most importantly, it actually approaches the theoretical limit. We end up with linear models with the Bayesian approach and beyond.

Xiaofeng Liu, Xiongchang Liu, Bo Hu et al.

Recent advances in unsupervised domain adaptation (UDA) show that transferable prototypical learning presents a powerful means for class conditional alignment, which encourages the closeness of cross-domain class centroids. However, the cross-domain inner-class compactness and the underlying fine-grained subtype structure remained largely underexplored. In this work, we propose to adaptively carry out the fine-grained subtype-aware alignment by explicitly enforcing the class-wise separation and subtype-wise compactness with intermediate pseudo labels. Our key insight is that the unlabeled subtypes of a class can be divergent to one another with different conditional and label shifts, while inheriting the local proximity within a subtype. The cases of with or without the prior information on subtype numbers are investigated to discover the underlying subtype structure in an online fashion. The proposed subtype-aware dynamic UDA achieves promising results on medical diagnosis tasks.

Xiaofeng Liu, Linghao Jin, Xu Han et al.

This paper targets to explore the inter-subject variations eliminated facial expression representation in the compressed video domain. Most of the previous methods process the RGB images of a sequence, while the off-the-shelf and valuable expression-related muscle movement already embedded in the compression format. In the up to two orders of magnitude compressed domain, we can explicitly infer the expression from the residual frames and possible to extract identity factors from the I frame with a pre-trained face recognition network. By enforcing the marginal independent of them, the expression feature is expected to be purer for the expression and be robust to identity shifts. We do not need the identity label or multiple expression samples from the same person for identity elimination. Moreover, when the apex frame is annotated in the dataset, the complementary constraint can be further added to regularize the feature-level game. In testing, only the compressed residual frames are required to achieve expression prediction. Our solution can achieve comparable or better performance than the recent decoded image based methods on the typical FER benchmarks with about 3$\times$ faster inference with compressed data.

Xiaofeng Liu, Bo Hu, Xiongchang Liu et al.

Unsupervised domain adaptation (UDA) aims to transfer the knowledge on a labeled source domain distribution to perform well on an unlabeled target domain. Recently, the deep self-training involves an iterative process of predicting on the target domain and then taking the confident predictions as hard pseudo-labels for retraining. However, the pseudo-labels are usually unreliable, and easily leading to deviated solutions with propagated errors. In this paper, we resort to the energy-based model and constrain the training of the unlabeled target sample with the energy function minimization objective. It can be applied as a simple additional regularization. In this framework, it is possible to gain the benefits of the energy-based model, while retaining strong discriminative performance following a plug-and-play fashion. We deliver extensive experiments on the most popular and large scale UDA benchmarks of image classification as well as semantic segmentation to demonstrate its generality and effectiveness.

Jun Lu, Wei Ma, Boi Faltings

It is often the case that the performance of a neural network can be improved by adding layers. In real-world practices, we always train dozens of neural network architectures in parallel which is a wasteful process. We explored $CompNet$, in which case we morph a well-trained neural network to a deeper one where network function can be preserved and the added layer is compact. The work of the paper makes two contributions: a). The modified network can converge fast and keep the same functionality so that we do not need to train from scratch again; b). The layer size of the added layer in the neural network is controlled by removing the redundant parameters with sparse optimization. This differs from previous network morphism approaches which tend to add more neurons or channels beyond the actual requirements and result in redundance of the model. The method is illustrated using several neural network structures on different data sets including MNIST and CIFAR10.

Jun Lu, Meng Li, David Dunson

Dirichlet process mixture (DPM) models tend to produce many small clusters regardless of whether they are needed to accurately characterize the data - this is particularly true for large data sets. However, interpretability, parsimony, data storage and communication costs all are hampered by having overly many clusters. We propose a powered Chinese restaurant process to limit this kind of problem and penalize over clustering. The method is illustrated using some simulation examples and data with large and small sample size including MNIST and the Old Faithful Geyser data.

Wei Ma, Jun Lu

This article demonstrates that convolutional operation can be converted to matrix multiplication, which has the same calculation way with fully connected layer. The article is helpful for the beginners of the neural network to understand how fully connected layer and the convolutional layer work in the backend. To be concise and to make the article more readable, we only consider the linear case. It can be extended to the non-linear case easily through plugging in a non-linear encapsulation to the values like this $σ(x)$ denoted as $x^{\prime}$.

Jun Lu

In this article we introduce how to put vague hyperprior on Dirichlet distribution, and we update the parameter of it by adaptive rejection sampling (ARS). Finally we analyze this hyperprior in an over-fitted mixture model by some synthetic experiments.

Jun Lu

Machine learning has been used in all kinds of fields. In this article, we introduce how machine learning can be applied into time series problem. Especially, we use the airline ticket prediction problem as our specific problem. Airline companies use many different variables to determine the flight ticket prices: indicator whether the travel is during the holidays, the number of free seats in the plane etc. Some of the variables are observed, but some of them are hidden. Based on the data over a 103 day period, we trained our models, getting the best model - which is AdaBoost-Decision Tree Classification. This algorithm has best performance over the observed 8 routes which has 61.35$\%$ better performance than the random purchase strategy, and relatively small variance over these routes. And we also considered the situation that we cannot get too much historical datas for some routes (for example the route is new and does not have historical data) or we do not want to train historical data to predict to buy or wait quickly, in which problem, we used HMM Sequence Classification based AdaBoost-Decision Tree Classification to perform our prediction on 12 new routes. Finally, we got 31.71$\%$ better performance than the random purchase strategy.