arXiv subjects

Yilun Wang

Publications and source records attributed to Yilun Wang.

44 records · Page 3Linked to original sources

arXiv2015

Randomized Structural Sparsity based Support Identification with Applications to Locating Activated or Discriminative Brain Areas: A Multi-center Reproducibility Study

In this paper, we focus on how to locate the relevant or discriminative brain regions related with external stimulus or certain mental decease, which is also called support identification, based on the neuroimaging data. The main difficulty lies in the extremely high dimensional voxel space and relatively few training samples, easily resulting in an unstable brain region discovery (or called feature selection in context of pattern recognition). When the training samples are from different centers and have betweencenter variations, it will be even harder to obtain a reliable and consistent result. Corresponding, we revisit our recently proposed algorithm based on stability selection and structural sparsity. It is applied to the multi-center MRI data analysis for the first time. A consistent and stable result is achieved across different centers despite the between-center data variation while many other state-of-the-art methods such as two sample t-test fail. Moreover, we have empirically showed that the performance of this algorithm is robust and insensitive to several of its key parameters. In addition, the support identification results on both functional MRI and structural MRI are interpretable and can be the potential biomarkers.

cs.CV↗

arXiv2015

Multi-stage Multi-task feature learning via adaptive threshold

Multi-task feature learning aims to identity the shared features among tasks to improve generalization. It has been shown that by minimizing non-convex learning models, a better solution than the convex alternatives can be obtained. Therefore, a non-convex model based on the capped-$\ell_{1},\ell_{1}$ regularization was proposed in \cite{Gong2013}, and a corresponding efficient multi-stage multi-task feature learning algorithm (MSMTFL) was presented. However, this algorithm harnesses a prescribed fixed threshold in the definition of the capped-$\ell_{1},\ell_{1}$ regularization and the lack of adaptivity might result in suboptimal performance. In this paper we propose to employ an adaptive threshold in the capped-$\ell_{1},\ell_{1}$ regularized formulation, where the corresponding variant of MSMTFL will incorporate an additional component to adaptively determine the threshold value. This variant is expected to achieve a better feature selection performance over the original MSMTFL algorithm. In particular, the embedded adaptive threshold component comes from our previously proposed iterative support detection (ISD) method \cite{Wang2010}. Empirical studies on both synthetic and real-world data sets demonstrate the effectiveness of this new variant over the original MSMTFL.

cs.LG↗

arXiv2015

Linear Spatial Pyramid Matching Using Non-convex and non-negative Sparse Coding for Image Classification

Recently sparse coding have been highly successful in image classification mainly due to its capability of incorporating the sparsity of image representation. In this paper, we propose an improved sparse coding model based on linear spatial pyramid matching(SPM) and Scale Invariant Feature Transform (SIFT ) descriptors. The novelty is the simultaneous non-convex and non-negative characters added to the sparse coding model. Our numerical experiments show that the improved approach using non-convex and non-negative sparse coding is superior than the original ScSPM[1] on several typical databases.

cs.CV↗

arXiv2015

Sensitivity Analysis for Computationally Expensive Models using Optimization and Objective-oriented Surrogate Approximations

In this paper, we focus on developing efficient sensitivity analysis methods for a computationally expensive objective function $f(x)$ in the case that the minimization of it has just been performed. Here "computationally expensive" means that each of its evaluation takes significant amount of time, and therefore our main goal to use a small number of function evaluations of $f(x)$ to further infer the sensitivity information of these different parameters. Correspondingly, we consider the optimization procedure as an adaptive experimental design and re-use its available function evaluations as the initial design points to establish a surrogate model $s(x)$ (or called response surface). The sensitivity analysis is performed on $s(x)$, which is an lieu of $f(x)$. Furthermore, we propose a new local multivariate sensitivity measure, for example, around the optimal solution, for high dimensional problems. Then a corresponding "objective-oriented experimental design" is proposed in order to make the generated surrogate $s(x)$ better suitable for the accurate calculation of the proposed specific local sensitivity quantities. In addition, we demonstrate the better performance of the Gaussian radial basis function interpolator over Kriging in our cases, which are of relatively high dimensionality and few experimental design points. Numerical experiments demonstrate that the optimization procedure and the "objective-oriented experimental design" behavior much better than the classical Latin Hypercube Design. In addition, the performance of Kriging is not as good as Gaussian RBF, especially in the case of high dimensional problems.

stat.ML↗

arXiv2014

A General Stochastic Algorithmic Framework for Minimizing Expensive Black Box Objective Functions Based on Surrogate Models and Sensitivity Analysis

We are focusing on bound constrained global optimization problems, whose objective functions are computationally expensive black-box functions and have multiple local minima. The recently popular Metric Stochastic Response Surface (MSRS) algorithm proposed by \cite{Regis2007SRBF} based on adaptive or sequential learning based on response surfaces is revisited and further extended for better performance in case of higher dimensional problems. Specifically, we propose a new way to generate the candidate points which the next function evaluation point is picked from according to the metric criteria, based on a new definition of distance, and prove the global convergence of the corresponding. Correspondingly, a more adaptive implementation of MSRS, named "SO-SA", is presented. "SO-SA" is is more likely to perturb those most sensitive coordinates when generating the candidate points, instead of perturbing all coordinates simultaneously. Numerical experiments on both synthetic problems and real problems demonstrate the advantages of our new algorithm, compared with many state of the art alternatives.}

stat.ML↗

arXiv2014

Truncated Nuclear Norm Minimization for Image Restoration Based On Iterative Support Detection

Recovering a large matrix from limited measurements is a challenging task arising in many real applications, such as image inpainting, compressive sensing and medical imaging, and this kind of problems are mostly formulated as low-rank matrix approximation problems. Due to the rank operator being non-convex and discontinuous, most of the recent theoretical studies use the nuclear norm as a convex relaxation and the low-rank matrix recovery problem is solved through minimization of the nuclear norm regularized problem. However, a major limitation of nuclear norm minimization is that all the singular values are simultaneously minimized and the rank may not be well approximated \cite{hu2012fast}. Correspondingly, in this paper, we propose a new multi-stage algorithm, which makes use of the concept of Truncated Nuclear Norm Regularization (TNNR) proposed in \citep{hu2012fast} and Iterative Support Detection (ISD) proposed in \citep{wang2010sparse} to overcome the above limitation. Besides matrix completion problems considered in \citep{hu2012fast}, the proposed method can be also extended to the general low-rank matrix recovery problems. Extensive experiments well validate the superiority of our new algorithms over other state-of-the-art methods.

cs.CV↗

arXiv2014

FTVd is beyond Fast Total Variation regularized Deconvolution

In this paper, we revisit the "FTVd" algorithm for Fast Total Variation Regularized Deconvolution, which has been widely used in the past few years. Both its original version implemented in the MATLAB software FTVd 3.0 and its related variant implemented in the latter version FTVd 4.0 are considered \cite{Wang08FTVdsoftware}. We propose that the intermediate results during the iterations are the solutions of a series of combined Tikhonov and total variation regularized image deconvolution models and therefore some of them often have even better image quality than the final solution, which is corresponding to the pure total variation regularized model.

cs.CV↗

arXiv2010

Sparse Signal Reconstruction via Iterative Support Detection

We present a novel sparse signal reconstruction method "ISD", aiming to achieve fast reconstruction and a reduced requirement on the number of measurements compared to the classical l_1 minimization approach. ISD addresses failed reconstructions of l_1 minimization due to insufficient measurements. It estimates a support set I from a current reconstruction and obtains a new reconstruction by solving the minimization problem \min{\sum_{i\not\in I}|x_i|:Ax=b}, and it iterates these two steps for a small number of times. ISD differs from the orthogonal matching pursuit (OMP) method, as well as its variants, because (i) the index set I in ISD is not necessarily nested or increasing and (ii) the minimization problem above updates all the components of x at the same time. We generalize the Null Space Property to Truncated Null Space Property and present our analysis of ISD based on the latter. We introduce an efficient implementation of ISD, called threshold--ISD, for recovering signals with fast decaying distributions of nonzeros from compressive sensing measurements. Numerical experiments show that threshold--ISD has significant advantages over the classical l_1 minimization approach, as well as two state--of--the--art algorithms: the iterative reweighted l_1 minimization algorithm (IRL1) and the iterative reweighted least--squares algorithm (IRLS). MATLAB code is available for download from http://www.caam.rice.edu/~optimization/L1/ISD/.

cs.IT↗