Linear discriminant analysis is a widely used method for classification. However, the high dimensionality of predictors combined with small sample sizes often results in large classification errors. To address this challenge, it is crucial to leverage data from related source models to enhance the classification performance of a target model. We propose to address this problem in the framework of transfer learning.
In this paper, we present novel transfer learning methods via regularized random-effects linear discriminant analysis, where the discriminant direction is estimated as a weighted combination of ridge estimates obtained from both the target and source models. Multiple strategies for determining these weights are introduced and evaluated, including one that minimizes the estimation risk of the discriminant vector and another that minimizes the classification error. Utilizing results from random matrix theory, we explicitly derive the asymptotic values of these weights and the associated classification error rates in the high-dimensional setting, where $p/n \rightarrow γ$, with $p$ representing the predictor dimension and $n$ the sample size. We also provide geometric interpretations of various weights and a guidance on which weights to choose. Extensive numerical studies, including simulations and analysis of proteomics-based 10-year cardiovascular disease risk classification, demonstrate the effectiveness of the proposed approach.
Spectrally-Corrected and Regularized Linear Discriminant Analysis for Spiked Covariance Model
School of Science, Chang Chun University（长春大学理学院）；School of Data Sciences, Zhejiang University of Finance and Economics（浙江财经大学数据科学学院）；School of Mathematics and Statistics, Northeast Normal University（东北师范大学数学与统计学院）
COMSATS University Islamabad（COMSATS大学伊斯兰堡校区）；King Abdullah University of Science and Technology (KAUST)（阿卜杜拉国王科技大学）
Linear discriminant analysis (LDA) based classifiers tend to falter in many practical settings where the training data size is smaller than, or comparable to, the number of features. As a remedy, different regularized LDA (RLDA) methods have been proposed. These methods may still perform poorly depending on the size and quality of the available training data. In particular, the test data deviation from the training data model, for example, due to noise contamination, can cause severe performance degradation. Moreover, these methods commit further to the Gaussian assumption (upon which LDA is e…
This article carries out a large dimensional analysis of standard regularized discriminant analysis classifiers designed on the assumption that data arise from a Gaussian mixture model with different means and covariances. The analysis relies on fundamental results from random matrix theory (RMT) when both the number of features and the cardinality of the training data within each class grow large at the same pace. Under mild assumptions, we show that the asymptotic classification error approaches a deterministic quantity that depends only on the means and covariances associated with each clas…
Regularized discriminant analysis (RDA), proposed by Friedman (1989), is a widely popular classifier that lacks interpretability and is impractical for high-dimensional data sets. Here, we present an interpretable and computationally efficient classifier called high-dimensional RDA (HDRDA), designed for the small-sample, high-dimensional setting. For HDRDA, we show that each training observation, regardless of class, contributes to the class covariance matrix, resulting in an interpretable estimator that borrows from the pooled sample covariance matrix. Moreover, we show that HDRDA is equivale…
In recent years, deep learning algorithms have become increasingly more prominent for their unparalleled ability to automatically learn discriminant features from large amounts of data. However, within the field of electromyography-based gesture recognition, deep learning algorithms are seldom employed as they require an unreasonable amount of effort from a single person, to generate tens of thousands of examples. This work's hypothesis is that general, informative features can be learned from the large amounts of data generated by aggregating the signals of multiple users, thus reducing the r…
We propose a hypothesis disparity regularized mutual information maximization~(HDMI) approach to tackle unsupervised hypothesis transfer -- as an effort towards unifying hypothesis transfer learning (HTL) and unsupervised domain adaptation (UDA) -- where the knowledge from a source domain is transferred solely through hypotheses and adapted to the target domain in an unsupervised manner. In contrast to the prevalent HTL and UDA approaches that typically use a single hypothesis, HDMI employs multiple hypotheses to leverage the underlying distributions of the source and target hypotheses. To bet…
We propose a modification of linear discriminant analysis, referred to as compressive regularized discriminant analysis (CRDA), for analysis of high-dimensional datasets. CRDA is specially designed for feature elimination purpose and can be used as gene selection method in microarray studies. CRDA lends ideas from $\ell_{q,1}$ norm minimization algorithms in the multiple measurement vectors (MMV) model and utilizes joint-sparsity promoting hard thresholding for feature elimination. A regularization of the sample covariance matrix is also needed as we consider the challenging scenario where the…
Wasserstein Discriminant Analysis (WDA) is a new supervised method that can improve classification of high-dimensional data by computing a suitable linear map onto a lower dimensional subspace. Following the blueprint of classical Linear Discriminant Analysis (LDA), WDA selects the projection matrix that maximizes the ratio of two quantities: the dispersion of projected points coming from different classes, divided by the dispersion of projected points coming from the same class. To quantify dispersion, WDA uses regularized Wasserstein distances, rather than cross-variance measures which have …
Fetal alcohol syndrome (FAS) caused by prenatal alcohol exposure can result in a series of cranio-facial anomalies, and behavioral and neurocognitive problems. Current diagnosis of FAS is typically done by identifying a set of facial characteristics, which are often obtained by manual examination. Anatomical landmark detection, which provides rich geometric information, is important to detect the presence of FAS associated facial anomalies. This imaging application is characterized by large variations in data appearance and limited availability of labeled data. Current deep learning-based heat…
We propose a compressive classification framework for settings where the data dimensionality is significantly higher than the sample size. The proposed method, referred to as compressive regularized discriminant analysis (CRDA) is based on linear discriminant analysis and has the ability to select significant features by using joint-sparsity promoting hard thresholding in the discriminant rule. Since the number of features is larger than the sample size, the method also uses state-of-the-art regularized sample covariance matrix estimators. Several analysis examples on real data sets, including…
Carleton University（卡尔顿大学）；University of Ottawa（渥太华大学）
Recent advances on unsupervised domain adaptation (UDA) rely on adversarial learning to disentangle the explanatory and transferable features for domain adaptation. However, there are two issues with the existing methods. First, the discriminability of the latent space cannot be fully guaranteed without considering the class-aware information in the target domain. Second, samples from the source and target domains alone are not sufficient for domain-invariant feature extracting in the latent space. In order to alleviate the above issues, we propose a dual mixup regularized learning (DMRL) meth…
Institute of Robotics and Automatic Information System (IRAIS), College of Artificial Intelligence, Nankai University（机器人与自动信息系统研究所（IRAIS），人工智能学院，南开大学）；VisionMetric Ltd（VisionMetric有限公司）；School of Physics and Astronomy, University of Kent（物理与天文学院，肯特大学）
Regularized Linear Discriminant Analysis Using a Nonlinear Covariance Matrix Estimator
King Abdullah University of Science and Technology (KAUST)（阿卜杜拉国王科技大学）；King Abdulaziz University（阿卜杜勒阿齐兹国王大学）；Center of Excellence in Intelligent Engineering Systems (CEIES)（智能工程系统卓越中心）
King Abdullah University of Science and Technology（阿卜杜拉国王科技大学）；Vanderbilt University（范德堡大学）；Suning Commerce R&D Center USA, Inc（苏宁美国研发中心）；Harbin University of Science and Technology（哈尔滨理工大学）；New York University Abu Dhabi（纽约大学阿布扎比分校）；Michigan State University（密歇根州立大学）
In this paper, we propose a novel learning framework for the problem of domain transfer learning. We map the data of two domains to one single common space, and learn a classifier in this common space. Then we adapt the common classifier to the two domains by adding two adaptive functions to it respectively. In the common space, the target domain data points are weighted and matched to the target domain in term of distributions. The weighting terms of source domain data points and the target domain classification responses are also regularized by the local reconstruction coefficients. The nove…
Fisher discriminant analysis (FDA) is a widely used method for classification and dimensionality reduction. When the number of predictor variables greatly exceeds the number of observations, one of the alternatives for conventional FDA is regularized Fisher discriminant analysis (RFDA). In this paper, we present a simple, iterative, sketching-based algorithm for RFDA that comes with provable accuracy guarantees when compared to the conventional approach. Our analysis builds upon two simple structural results that boil down to randomized matrix multiplication, a fundamental and well-understood …
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Baidu Inc.（百度公司）
Transfer learning through fine-tuning a pre-trained neural network with an extremely large dataset, such as ImageNet, can significantly accelerate training while the accuracy is frequently bottlenecked by the limited dataset size of the new target task. To solve the problem, some regularization methods, constraining the outer layer weights of the target network using the starting point as references (SPAR), have been studied. In this paper, we propose a novel regularized transfer learning framework DELTA, namely DEep Learning Transfer using Feature Map with Attention. Instead of constraining t…
Quadratic discriminant analysis (QDA) is a widely used classification technique that generalizes the linear discriminant analysis (LDA) classifier to the case of distinct covariance matrices among classes. For the QDA classifier to yield high classification performance, an accurate estimation of the covariance matrices is required. Such a task becomes all the more challenging in high dimensional settings, wherein the number of observations is comparable with the feature dimension. A popular way to enhance the performance of QDA classifier under these circumstances is to regularize the covarian…
In many multilingual text classification problems, the documents in different languages often share the same set of categories. To reduce the labeling cost of training a classification model for each individual language, it is important to transfer the label knowledge gained from one language to another language by conducting cross language classification. In this paper we develop a novel subspace co-regularized multi-view learning method for cross language text classification. This method is built on parallel corpora produced by machine translation. It jointly minimizes the training error of …
Chongqing University（重庆大学）；School of Microelectronics and Communication Engineering（微电子与通信工程学院）
Unsupervised domain adaptation (UDA) aims to improve the classification performance on an unlabeled target domain by leveraging information from a fully labeled source domain. Recent approaches explore domain-invariant and class-discriminant representations to tackle this task. These methods, however, ignore the interaction between domain alignment learning and class discrimination learning. As a result, the missing or inadequate tradeoff between domain alignment and class discrimination are prone to the problem of negative transfer. In this paper, we propose Dynamic Weighted Learning (DWL) to…
Simple Transferability Estimation for Regression Tasks
Florida International University（佛罗里达国际大学）；VinAI Research（VinAI研究院）；MBZUAI（穆罕默德·本·扎耶德人工智能大学）；Dalhousie University（达尔豪斯大学）；University of Delaware（特拉华大学）；Meta AI
Transferring knowledge from large source datasets is an effective way to fine-tune the deep neural networks of the target task with a small sample size. A great number of algorithms have been proposed to facilitate deep transfer learning, and these techniques could be generally categorized into two groups - Regularized Learning of the target task using models that have been pre-trained from source datasets, and Multitask Learning with both source and target datasets to train a shared backbone neural network. In this work, we aim to improve the multitask paradigm for deep transfer learning via …
Shanghai Jiao Tong University（上海交通大学）；Ecole Centrale de Lyon（里昂中央理工学院）；LIRIS, CNRS（法国国家科学研究中心图像与信息系统实验室）
In leveraging manifold learning in domain adaptation (DA), graph embedding-based DA methods have shown their effectiveness in preserving data manifold through the Laplace graph. However, current graph embedding DA methods suffer from two issues: 1). they are only concerned with preservation of the underlying data structures in the embedding and ignore sub-domain adaptation, which requires taking into account intra-class similarity and inter-class dissimilarity, thereby leading to negative transfer; 2). manifold learning is proposed across different feature/label spaces separately, thereby hind…
University Medical Center Freiburg（弗莱堡大学医学中心）；Alberts-Ludwigs-University Freiburg（阿尔伯特-路德维希-弗莱堡大学）
We recorded high-density EEG in a flanker task experiment (31 subjects) and an online BCI control paradigm (4 subjects). On these datasets, we evaluated the use of transfer learning for error decoding with deep convolutional neural networks (deep ConvNets). In comparison with a regularized linear discriminant analysis (rLDA) classifier, ConvNets were significantly better in both intra- and inter-subject decoding, achieving an average accuracy of 84.1 % within subject and 81.7 % on unknown subjects (flanker task). Neither method was, however, able to generalize reliably between paradigms. Visua…
King Abdullah University of Science and Technology（阿卜杜拉国王科技大学）；Duke University（杜克大学）
The use of quadratic discriminant analysis (QDA) or its regularized version (R-QDA) for classification is often not recommended, due to its well-acknowledged high sensitivity to the estimation noise of the covariance matrix. This becomes all the more the case in unbalanced data settings for which it has been found that R-QDA becomes equivalent to the classifier that assigns all observations to the same class. In this paper, we propose an improved R-QDA that is based on the use of two regularization parameters and a modified bias, properly chosen to avoid inappropriate behaviors of R-QDA in unb…
Improving automatic endoscopic stone recognition using a multi-view fusion approach enhanced with two-step transfer learning
Tecnologico de Monterrey, School of Engineering and Sciences, Mexico（墨西哥蒙特雷科技大学工程与科学学院）；CRAN UMR 7039, Université de Lorraine and CNRS, Nancy, France（法国洛林大学CNRS CRAN UMR 7039研究中心）；CINVESTAV, Guadalajara, Mexico（墨西哥瓜达拉哈拉科学技术研究所）；CHRU Nancy, Service d’urologie de Brabois, Nancy, France（法国南锡布拉布瓦大学医院泌尿外科）
Georgia Institute of Technology（佐治亚理工学院）；Microsoft Dynamics 365 AI（微软Dynamics 365 AI）；Microsoft Research（微软研究院）
Transfer learning has fundamentally changed the landscape of natural language processing (NLP) research. Many existing state-of-the-art models are first pre-trained on a large text corpus and then fine-tuned on downstream tasks. However, due to limited data resources from downstream tasks and the extremely large capacity of pre-trained models, aggressive fine-tuning often causes the adapted model to overfit the data of downstream tasks and forget the knowledge of the pre-trained model. To address the above issue in a more principled manner, we propose a new computational framework for robust a…
DeepMind；Department of Computer Science and Engineering, POSTECH（POSTECH计算机科学与工程系）；POSTECH（POSTECH（浦项科技大学））
As reinforcement learning agents are tasked with solving more challenging and diverse tasks, the ability to incorporate prior knowledge into the learning system and to exploit reusable structure in solution space is likely to become increasingly important. The KL-regularized expected reward objective constitutes one possible tool to this end. It introduces an additional component, a default or prior behavior, which can be learned alongside the policy and as such partially transforms the reinforcement learning problem into one of behavior modelling. In this work we consider the implications of …
As a vital problem in classification-oriented transfer, unsupervised domain adaptation (UDA) has attracted widespread attention in recent years. Previous UDA methods assume the marginal distributions of different domains are shifted while ignoring the discriminant information in the label distributions. This leads to classification performance degeneration in real applications. In this work, we focus on the conditional distribution shift problem which is of great concern to current conditional invariant models. We aim to seek a kernel covariance embedding for conditional distribution which rem…
The estimation of covariance matrices of multiple classes with limited training data is a difficult problem. The sample covariance matrix (SCM) is known to perform poorly when the number of variables is large compared to the available number of samples. In order to reduce the mean squared error (MSE) of the SCM, regularized (shrinkage) SCM estimators are often used. In this work, we consider regularized SCM (RSCM) estimators for multiclass problems that couple together two different target matrices for regularization: the pooled (average) SCM of the classes and the scaled identity matrix. Regu…
We provide a unified analysis of the predictive risk of ridge regression and regularized discriminant analysis in a dense random effects model. We work in a high-dimensional asymptotic regime where $p, n \to \infty$ and $p/n \to γ\in (0, \, \infty)$, and allow for arbitrary covariance among the features. For both methods, we provide an explicit and efficiently computable expression for the limiting predictive risk, which depends only on the spectrum of the feature-covariance matrix, the signal strength, and the aspect ratio $γ$. Especially in the case of regularized discriminant analysis, we f…
As a predictor's quality is often assessed by means of its risk, it is natural to regard risk consistency as a desirable property of learning methods, and many such methods have indeed been shown to be risk consistent. The first aim of this paper is to establish the close connection between risk consistency and $L_p$-consistency for a considerably wider class of loss functions than has been done before. The attempt to transfer this connection to shifted loss functions surprisingly reveals that this shift does not reduce the assumptions needed on the underlying probability measure to the same e…
For high-dimensional classification, it is well known that naively performing the Fisher discriminant rule leads to poor results due to diverging spectra and noise accumulation. Therefore, researchers proposed independence rules to circumvent the diverse spectra, and sparse independence rules to mitigate the issue of noise accumulation. However, in biological applications, there are often a group of correlated genes responsible for clinical outcomes, and the use of the covariance information can significantly reduce misclassification rates. The extent of such error rate reductions is unveiled …
University of California, Berkeley（加州大学伯克利分校）；New York University（纽约大学）
Learning long-range behaviors on complex high-dimensional agents is a fundamental problem in robot learning. For such tasks, we argue that transferring learned information from a morphologically simpler agent can massively improve the sample efficiency of a more complex one. To this end, we propose a hierarchical decoupling of policies into two parts: an independently learned low-level policy and a transferable high-level policy. To remedy poor transfer performance due to mismatch in morphologies, we contribute two key ideas. First, we show that incentivizing a complex agent's low-level to imi…
