Jun Lü

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

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

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

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

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

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.

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.