arXiv subjects

Songcan Chen

Publications and source records attributed to Songcan Chen.

84 records · Page 5Linked to original sources

arXiv2019

Linear Convergence of Accelerated Stochastic Gradient Descent for Nonconvex Nonsmooth Optimization

In this paper, we study the stochastic gradient descent (SGD) method for the nonconvex nonsmooth optimization, and propose an accelerated SGD method by combining the variance reduction technique with Nesterov's extrapolation technique. Moreover, based on the local error bound condition, we establish the linear convergence of our method to obtain a stationary point of the nonconvex optimization. In particular, we prove that not only the sequence generated linearly converges to a stationary point of the problem, but also the corresponding sequence of objective values is linearly convergent. Finally, some numerical experiments demonstrate the effectiveness of our method. To the best of our knowledge, it is first proved that the accelerated SGD method converges linearly to the local minimum of the nonconvex optimization.

math.OC↗

arXiv2018

Multi-target Unsupervised Domain Adaptation without Exactly Shared Categories

Unsupervised domain adaptation (UDA) aims to learn the unlabeled target domain by transferring the knowledge of the labeled source domain. To date, most of the existing works focus on the scenario of one source domain and one target domain (1S1T), and just a few works concern the scenario of multiple source domains and one target domain (mS1T). While, to the best of our knowledge, almost no work concerns the scenario of one source domain and multiple target domains (1SmT), in which these unlabeled target domains may not necessarily share the same categories, therefore, contrasting to mS1T, 1SmT is more challenging. Accordingly, for such a new UDA scenario, we propose a UDA framework through the model parameter adaptation (PA-1SmT). A key ingredient of PA-1SmT is to transfer knowledge through adaptive learning of a common model parameter dictionary, which is completely different from existing popular methods for UDA, such as subspace alignment, distribution matching etc., and can also be directly used for DA of privacy protection due to the fact that the knowledge is transferred just via the model parameters rather than data itself. Finally, our experimental results on three domain adaptation benchmark datasets demonstrate the superiority of our framework.

cs.LG↗

arXiv2018

Active Feature Acquisition with Supervised Matrix Completion

Feature missing is a serious problem in many applications, which may lead to low quality of training data and further significantly degrade the learning performance. While feature acquisition usually involves special devices or complex process, it is expensive to acquire all feature values for the whole dataset. On the other hand, features may be correlated with each other, and some values may be recovered from the others. It is thus important to decide which features are most informative for recovering the other features as well as improving the learning performance. In this paper, we try to train an effective classification model with least acquisition cost by jointly performing active feature querying and supervised matrix completion. When completing the feature matrix, a novel target function is proposed to simultaneously minimize the reconstruction error on observed entries and the supervised loss on training data. When querying the feature value, the most uncertain entry is actively selected based on the variance of previous iterations. In addition, a bi-objective optimization method is presented for cost-aware active selection when features bear different acquisition costs. The effectiveness of the proposed approach is well validated by both theoretical analysis and experimental study.

cs.LG↗

arXiv2017

Stochastic Alternating Direction Method of Multipliers with Variance Reduction for Nonconvex Optimization

In the paper, we study the stochastic alternating direction method of multipliers (ADMM) for the nonconvex optimizations, and propose three classes of the nonconvex stochastic ADMM with variance reduction, based on different reduced variance stochastic gradients. Specifically, the first class called the nonconvex stochastic variance reduced gradient ADMM (SVRG-ADMM), uses a multi-stage scheme to progressively reduce the variance of stochastic gradients. The second is the nonconvex stochastic average gradient ADMM (SAG-ADMM), which additionally uses the old gradients estimated in the previous iteration. The third called SAGA-ADMM is an extension of the SAG-ADMM method. Moreover, under some mild conditions, we establish the iteration complexity bound of $O(1/ε)$ of the proposed methods to obtain an $ε$-stationary solution of the nonconvex optimizations. In particular, we provide a general framework to analyze the iteration complexity of these nonconvex stochastic ADMM methods with variance reduction. Finally, some numerical experiments demonstrate the effectiveness of our methods.

math.OC↗

arXiv2016

Joint Gender Classification and Age Estimation by Nearly Orthogonalizing Their Semantic Spaces

In human face-based biometrics, gender classification and age estimation are two typical learning tasks. Although a variety of approaches have been proposed to handle them, just a few of them are solved jointly, even so, these joint methods do not yet specifically concern the semantic difference between human gender and age, which is intuitively helpful for joint learning, consequently leaving us a room of further improving the performance. To this end, in this work we firstly propose a general learning framework for jointly estimating human gender and age by specially attempting to formulate such semantic relationships as a form of near-orthogonality regularization and then incorporate it into the objective of the joint learning framework. In order to evaluate the effectiveness of the proposed framework, we exemplify it by respectively taking the widely used binary-class SVM for gender classification, and two threshold-based ordinal regression methods (i.e., the discriminant learning for ordinal regression and support vector ordinal regression) for age estimation, and crucially coupling both through the proposed semantic formulation. Moreover, we develop its kernelized nonlinear counterpart by deriving a representer theorem for the joint learning strategy. Finally, through extensive experiments on three aging datasets FG-NET, Morph Album I and Morph Album II, we demonstrate the effectiveness and superiority of the proposed joint learning strategy.

cs.CV↗

arXiv2016

A Unified Gender-Aware Age Estimation

Human age estimation has attracted increasing researches due to its wide applicability in such as security monitoring and advertisement recommendation. Although a variety of methods have been proposed, most of them focus only on the age-specific facial appearance. However, biological researches have shown that not only gender but also the aging difference between the male and the female inevitably affect the age estimation. To our knowledge, so far there have been two methods that have concerned the gender factor. The first is a sequential method which first classifies the gender and then performs age estimation respectively for classified male and female. Although it promotes age estimation performance because of its consideration on the gender semantic difference, an accumulation risk of estimation errors is unavoidable. To overcome drawbacks of the sequential strategy, the second is to regress the age appended with the gender by concatenating their labels as two dimensional output using Partial Least Squares (PLS). Although leading to promotion of age estimation performance, such a concatenation not only likely confuses the semantics between the gender and age, but also ignores the aging discrepancy between the male and the female. In order to overcome their shortcomings, in this paper we propose a unified framework to perform gender-aware age estimation. The proposed method considers and utilizes not only the semantic relationship between the gender and the age, but also the aging discrepancy between the male and the female. Finally, experimental results demonstrate not only the superiority of our method in performance, but also its good interpretability in revealing the aging discrepancy.

cs.CV↗

arXiv2015

Tri-Subject Kinship Verification: Understanding the Core of A Family

One major challenge in computer vision is to go beyond the modeling of individual objects and to investigate the bi- (one-versus-one) or tri- (one-versus-two) relationship among multiple visual entities, answering such questions as whether a child in a photo belongs to given parents. The child-parents relationship plays a core role in a family and understanding such kin relationship would have fundamental impact on the behavior of an artificial intelligent agent working in the human world. In this work, we tackle the problem of one-versus-two (tri-subject) kinship verification and our contributions are three folds: 1) a novel relative symmetric bilinear model (RSBM) introduced to model the similarity between the child and the parents, by incorporating the prior knowledge that a child may resemble a particular parent more than the other; 2) a spatially voted method for feature selection, which jointly selects the most discriminative features for the child-parents pair, while taking local spatial information into account; 3) a large scale tri-subject kinship database characterized by over 1,000 child-parents families. Extensive experiments on KinFaceW, Family101 and our newly released kinship database show that the proposed method outperforms several previous state of the art methods, while could also be used to significantly boost the performance of one-versus-one kinship verification when the information about both parents are available.

cs.CV↗

arXiv2015

Joint Representation Classification for Collective Face Recognition

Sparse representation based classification (SRC) is popularly used in many applications such as face recognition, and implemented in two steps: representation coding and classification. For a given set of testing images, SRC codes every image over the base images as a sparse representation then classifies it to the class with the least representation error. This scheme utilizes an individual representation rather than the collective one to classify such a set of images, doing so obviously ignores the correlation among the given images. In this paper, a joint representation classification (JRC) for collective face recognition is proposed. JRC takes the correlation of multiple images as well as a single representation into account. Under the assumption that the given face images are generally related to each other, JRC codes all the testing images over the base images simultaneously to facilitate recognition. To this end, the testing inputs are aligned into a matrix and the joint representation coding is formulated to a generalized $l_{2,q}-l_{2,p}$-minimization problem. To uniformly solve the induced optimization problems for any $q\in[1,2]$ and $p\in (0,2]$, an iterative quadratic method (IQM) is developed. IQM is proved to be a strict descent algorithm with convergence to the optimal solution. Moreover, a more practical IQM is proposed for large-scale case. Experimental results on three public databases show that the JRC with practical IQM no only saves much computational cost but also achieves better performance in collective face recognition than the state-of-the-arts.

cs.CV↗

arXiv2014

Detecting Differential Expression from RNA-seq Data with Expression Measurement Uncertainty

High-throughput RNA sequencing (RNA-seq) has emerged as a revolutionary and powerful technology for expression profiling. Most proposed methods for detecting differentially expressed (DE) genes from RNA-seq are based on statistics that compare normalized read counts between conditions. However, there are few methods considering the expression measurement uncertainty into DE detection. Moreover, most methods are only capable of detecting DE genes, and few methods are available for detecting DE isoforms. In this paper, a Bayesian framework (BDSeq) is proposed to detect DE genes and isoforms with consideration of expression measurement uncertainty. This expression measurement uncertainty provides useful information which can help to improve the performance of DE detection. Three real RAN-seq data sets are used to evaluate the performance of BDSeq and results show that the inclusion of expression measurement uncertainty improves accuracy in detection of DE genes and isoforms. Finally, we develop a GamSeq-BDSeq RNA-seq analysis pipeline to facilitate users, which is freely available at the website http://parnec.nuaa.edu.cn/liux/GSBD/GamSeq-BDSeq.html.

q-bio.GN↗

arXiv2013

$l_{2,p}$ Matrix Norm and Its Application in Feature Selection

Recently, $l_{2,1}$ matrix norm has been widely applied to many areas such as computer vision, pattern recognition, biological study and etc. As an extension of $l_1$ vector norm, the mixed $l_{2,1}$ matrix norm is often used to find jointly sparse solutions. Moreover, an efficient iterative algorithm has been designed to solve $l_{2,1}$-norm involved minimizations. Actually, computational studies have showed that $l_p$-regularization ($0<p<1$) is sparser than $l_1$-regularization, but the extension to matrix norm has been seldom considered. This paper presents a definition of mixed $l_{2,p}$ $(p\in (0, 1])$ matrix pseudo norm which is thought as both generalizations of $l_p$ vector norm to matrix and $l_{2,1}$-norm to nonconvex cases $(0<p<1)$. Fortunately, an efficient unified algorithm is proposed to solve the induced $l_{2,p}$-norm $(p\in (0, 1])$ optimization problems. The convergence can also be uniformly demonstrated for all $p\in (0, 1]$. Typical $p\in (0,1]$ are applied to select features in computational biology and the experimental results show that some choices of $0<p<1$ do improve the sparse pattern of using $p=1$.

cs.LG↗

arXiv2012

Metric Learning across Heterogeneous Domains by Respectively Aligning Both Priors and Posteriors

In this paper, we attempts to learn a single metric across two heterogeneous domains where source domain is fully labeled and has many samples while target domain has only a few labeled samples but abundant unlabeled samples. To the best of our knowledge, this task is seldom touched. The proposed learning model has a simple underlying motivation: all the samples in both the source and the target domains are mapped into a common space, where both their priors P(sample)s and their posteriors P(label|sample)s are forced to be respectively aligned as much as possible. We show that the two mappings, from both the source domain and the target domain to the common space, can be reparameterized into a single positive semi-definite(PSD) matrix. Then we develop an efficient Bregman Projection algorithm to optimize the PDS matrix over which a LogDet function is used to regularize. Furthermore, we also show that this model can be easily kernelized and verify its effectiveness in crosslanguage retrieval task and cross-domain object recognition task.

cs.LG↗

arXiv2012

Margin Distribution Controlled Boosting

Schapire's margin theory provides a theoretical explanation to the success of boosting-type methods and manifests that a good margin distribution (MD) of training samples is essential for generalization. However the statement that a MD is good is vague, consequently, many recently developed algorithms try to generate a MD in their goodness senses for boosting generalization. Unlike their indirect control over MD, in this paper, we propose an alternative boosting algorithm termed Margin distribution Controlled Boosting (MCBoost) which directly controls the MD by introducing and optimizing a key adjustable margin parameter. MCBoost's optimization implementation adopts the column generation technique to ensure fast convergence and small number of weak classifiers involved in the final MCBooster. We empirically demonstrate: 1) AdaBoost is actually also a MD controlled algorithm and its iteration number acts as a parameter controlling the distribution and 2) the generalization performance of MCBoost evaluated on UCI benchmark datasets is validated better than those of AdaBoost, L2Boost, LPBoost, AdaBoost-CG and MDBoost.

cs.LG↗