arXiv subjects

Lili Pan

Publications and source records attributed to Lili Pan.

25 records · Page 2Linked to original sources

arXiv2020

Newton method for $\ell_0$-regularized optimization

As a tractable approach, regularization is frequently adopted in sparse optimization. This gives rise to the regularized optimization, aiming at minimizing the $\ell_0$ norm or its continuous surrogates that characterize the sparsity. From the continuity of surrogates to the discreteness of $\ell_0$ norm, the most challenging model is the $\ell_0$-regularized optimization. To conquer this hardness, there is a vast body of work on developing numerically effective methods. However, most of them only enjoy that either the (sub)sequence converges to a stationary point from the deterministic optimization perspective or the distance between each iterate and any given sparse reference point is bounded by an error bound in the sense of probability. In this paper, we develop a Newton-type method for the $\ell_0$-regularized optimization and prove that the generated sequence converges to a stationary point globally and quadratically under the standard assumptions, theoretically explaining that our method is able to perform surprisingly well.

math.OC↗

arXiv2020

Self-Paced Deep Regression Forests with Consideration on Underrepresented Examples

Deep discriminative models (e.g. deep regression forests, deep neural decision forests) have achieved remarkable success recently to solve problems such as facial age estimation and head pose estimation. Most existing methods pursue robust and unbiased solutions either through learning discriminative features, or reweighting samples. We argue what is more desirable is learning gradually to discriminate like our human beings, and hence we resort to self-paced learning (SPL). Then, a natural question arises: can self-paced regime lead deep discriminative models to achieve more robust and less biased solutions? To this end, this paper proposes a new deep discriminative model--self-paced deep regression forests with consideration on underrepresented examples (SPUDRFs). It tackles the fundamental ranking and selecting problem in SPL from a new perspective: fairness. This paradigm is fundamental and could be easily combined with a variety of deep discriminative models (DDMs). Extensive experiments on two computer vision tasks, i.e., facial age estimation and head pose estimation, demonstrate the efficacy of SPUDRFs, where state-of-the-art performances are achieved.

cs.CV↗

arXiv2020

Deep Embedded Multi-view Clustering with Collaborative Training

Multi-view clustering has attracted increasing attentions recently by utilizing information from multiple views. However, existing multi-view clustering methods are either with high computation and space complexities, or lack of representation capability. To address these issues, we propose deep embedded multi-view clustering with collaborative training (DEMVC) in this paper. Firstly, the embedded representations of multiple views are learned individually by deep autoencoders. Then, both consensus and complementary of multiple views are taken into account and a novel collaborative training scheme is proposed. Concretely, the feature representations and cluster assignments of all views are learned collaboratively. A new consistency strategy for cluster centers initialization is further developed to improve the multi-view clustering performance with collaborative training. Experimental results on several popular multi-view datasets show that DEMVC achieves significant improvements over state-of-the-art methods.

cs.LG↗

arXiv2020

Self-Paced Deep Regression Forests for Facial Age Estimation

Facial age estimation is an important and challenging problem in computer vision. Existing approaches usually employ deep neural networks (DNNs) to fit the mapping from facial features to age, even though there exist some noisy and confusing samples. We argue that it is more desirable to distinguish noisy and confusing facial images from regular ones, and alleviate the interference arising from them. To this end, we propose self-paced deep regression forests (SP-DRFs) -- a gradual learning DNNs framework for age estimation. As the model is learned gradually, from simplicity to complexity, it tends to emphasize more on reliable samples and avoid bad local minima. Moreover, the proposed capped-likelihood function helps to exclude noisy samples in training, rendering our SP-DRFs significantly more robust. We demonstrate the efficacy of SP-DRFs on Morph II and FG-NET datasets, where our model achieves state-of-the-art performance.

cs.CV↗

arXiv2020

Newton Hard Thresholding Pursuit for Sparse LCP via A New Merit Function

Solutions to the linear complementarity problem (LCP) are naturally sparse in many applications such as bimatrix games and portfolio section problems. Despite that it gives rise to the hardness, sparsity makes optimization faster and enables relatively large scale computation. Motivated by this, we take the sparse LCP into consideration, investigating the existence and boundedness of its solution set as well as introducing a new merit function, which allows us to convert the problem into a sparsity constrained optimization. The function turns out to be continuously differentiable and twice continuously differentiable for some chosen parameters. Interestingly, it is also convex if the involved matrix is positive semidefinite. We then explore the relationship between the solution set to the sparse LCP and stationary points of the sparsity constrained optimization. Finally, Newton hard thresholding pursuit is adopted to solve the sparsity constrained model. Numerical experiments demonstrate that the problem can be efficiently solved through the new merit function.

math.OC↗

arXiv2019

Latent Dirichlet Allocation in Generative Adversarial Networks

We study the problem of multimodal generative modelling of images based on generative adversarial networks (GANs). Despite the success of existing methods, they often ignore the underlying structure of vision data or its multimodal generation characteristics. To address this problem, we introduce the Dirichlet prior for multimodal image generation, which leads to a new Latent Dirichlet Allocation based GAN (LDAGAN). In detail, for the generative process modelling, LDAGAN defines a generative mode for each sample, determining which generative sub-process it belongs to. For the adversarial training, LDAGAN derives a variational expectation-maximization (VEM) algorithm to estimate model parameters. Experimental results on real-world datasets have demonstrated the outstanding performance of LDAGAN over other existing GANs.

cs.LG↗

arXiv2014

Gradient Support Projection Algorithm for Affine Feasibility Problem with Sparsity and Nonnegativity

Let $A$ be a real $M \times N$ measurement matrix and $b\in \mathbb{R}^M$ be an observations vector. The affine feasibility problem with sparsity and nonnegativity ($AFP_{SN}$ for short) is to find a sparse and nonnegative vector $x\in \mathbb{R}^N$ with $Ax=b$ if such $x$ exists. In this paper, we focus on establishment of optimization approach to solving the $AFP_{SN}$. By discussing tangent cone and normal cone of sparse constraint, we give the first necessary optimality conditions, $α$-Stability, T-Stability and N-Stability, and the second necessary and sufficient optimality conditions for the related minimization problems with the $AFP_{SN}$. By adopting Armijo-type stepsize rule, we present a framework of gradient support projection algorithm for the $AFP_{SN}$ and prove its full convergence when matrix $A$ is $s$-regular. By doing some numerical experiments, we show the excellent performance of the new algorithm for the $AFP_{SN}$ without and with noise.

math.OC↗