Smoothing proximal gradient method for general structured sparse regression

Chen, Xi; Lin, Qihang; Kim, Seyoung; Carbonell, Jaime G.; Xing, Eric P.

doi:10.1214/11-aoas514

Cited by 217 publications

(286 citation statements)

References 36 publications

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“…To further demonstrate the advantages of FEGA-MTL, we compare it with the other graph-guided MTL methods [6,26]. Fig.4 shows that higher accuracy is obtained with our approach for different training set sizes.…”

Section: Resultsmentioning

confidence: 95%

“…Fig.4 shows that higher accuracy is obtained with our approach for different training set sizes. A main difference between FEGA-MTL and these methods [6,26] is that they do not decompose w t,c as s t,c + θ t,c , and due to the non-consideration of task-specific components θ t,c , they have less flexibility. Moreover, in [26] (due to the use of 2 norm) and [6] (due to smoothing) task-clustering is encouraged but not enforced, i.e.…”

Section: Resultsmentioning

confidence: 99%

“…in the form of a graph) defining task dependencies [6] or learn the task relationships simultaneously with task-specific parameters [11,24,10,25,9]. Among these, the work most similar to ours is [6]. Similar to [6], our algorithm adopts a graph to specify a-priori task dependencies.…”

Section: Related Workmentioning

confidence: 99%

“…Among these, the work most similar to ours is [6]. Similar to [6], our algorithm adopts a graph to specify a-priori task dependencies. We also overcome the limitations of [6] as FEGA-MTL automatically discovers task relationships and refines the initial graph structure.…”

Section: Related Workmentioning

confidence: 99%

“…Similar to [6], our algorithm adopts a graph to specify a-priori task dependencies. We also overcome the limitations of [6] as FEGA-MTL automatically discovers task relationships and refines the initial graph structure. For multi-view head pose estimation under motion, the graph structure is very useful as it reflects interregion facial appearance similarity as derived from the camera geometry.…”

Section: Related Workmentioning

confidence: 99%

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No Matter Where You Are: Flexible Graph-Guided Multi-task Learning for Multi-view Head Pose Classification under Target Motion

Yan

Ricci

Subramanian

et al. 2013

2013 IEEE International Conference on Computer Vision

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We propose a novel Multi-Task Learning framework (FEGA-MTL) for classifying the head pose of a person who moves freely in an environment monitored by multiple, large field-of-view surveillance cameras. As the target (person) moves, distortions in facial appearance owing to camera perspective and scale severely impede performance of traditional head pose classification methods. FEGA-MTL operates on a dense uniform spatial grid and learns appearance relationships across partitions as well as partition-specific appearance variations for a given head pose to build region-specific classifiers. Guided by two graphs which a-priori model appearance similarity among (i) grid partitions based on camera geometry and (ii) head pose classes, the learner efficiently clusters appearancewise related grid partitions to derive the optimal partitioning. For pose classification, upon determining the target's position using a person tracker, the appropriate regionspecific classifier is invoked. Experiments confirm that FEGA-MTL achieves state-of-the-art classification with few training data.

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Section: Resultsmentioning

confidence: 95%

Section: Resultsmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

See 3 more Smart Citations

No Matter Where You Are: Flexible Graph-Guided Multi-task Learning for Multi-view Head Pose Classification under Target Motion

Yan

Ricci

Subramanian

et al. 2013

2013 IEEE International Conference on Computer Vision

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Quantile Regression in Risk Calibration

Chao

Härdle

Wang

2014

Handbook of Financial Econometrics and Statistics

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Quantile regression studies the conditional quantile function Q Y |X (τ ) on X at level τ which satisfies F Y |X  Q Y |X (τ )  = τ , where F Y |X is the conditional CDF of Y given X, ∀τ ∈ (0, 1). Quantile regression allows for a closer inspection of the conditional distribution beyond the conditional moments. This technique is particularly useful in, for example, the Value-at-Risk (VaR) which the Basel accords (2011) require all banks to report, or the "quantile treatment effect" and "conditional stochastic dominance (CSD)" which are economic concepts in measuring the effectiveness of a government policy or a medical treatment.Given its value of applicability, to develop the technique of quantile regression is, however, more challenging than mean regression. It is necessary to be adept with general regression problems and M -estimators; additionally one needs to deal with non-smooth loss functions. In this dissertation, chapter 2 is devoted to empirical risk management during financial crises using quantile regression. Chapter 3 and 4 address the issue of high-dimensionality and the nonparametric technique of quantile regression.Chapter 2 applies nonparametric confidence bands for quantile functions to investigate the tail dependence of stock returns. It is shown that strong nonlinear correlation exists when stock prices drop, confirming the fact that in financial crises, firms are more dependent on each other than when the market is booming. This sheds light on the risk management of counterparty risk.In Chapter 3, motivated by applications in economics like quantile treatment effects, or conditional stochastic dominance, we focus on the construction of confidence corridors for nonparametric multivariate kernel quantile and expectile regression functions. Through an uniform kernel Bahadur representation for M -estimators, strong Gaussian approximation and asymptotic extreme value theory we derive the asymptotic confidence corridor for the nonparametric kernel conditional quantile/expectile functions. We find that the bands for quantile/expectile functions are wide when τ is close to 0 and 1 due to the variance of the estimator. The coverage ratios given by the asymptotic confidence corridors are meager. To deal with this issue, we propose a novel smoothing bootstrap which gives satisfactory coverage ratios while keeping the size of the confidence corridors in a reasonable range. Our method contributes to the differentiation between the "risk reduction CSD" and "potential enhancement CSD", which is not possible by using techniques based on previous research in CSD like Delgado and Escanciano (2013). This differentiation is crucial as the two types of CSD may induce different utility to the government and citizens. After applying our method to the data set from National Supported Work Demonstration, a temporary internship program offered to disadvantaged workers, it is found that this program tends to be "potential enhancement CSD" and it may not help foster the employment of less capable people as much...

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