The Concave-Convex Procedure

By Alan L. Yuille, Anand Rangarajan. 2003

1,286 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computational Mechanics, Control and Systems Engineering

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Citations in the corpus

Algorithms and Theory for Multiple-Source Adaptation (2018, background): “Then, (zt)t is guaranteed to converge to a local minimum of Problem (4) (Yuille and Rangarajan, 2003; Sriperumbudur and Lanckriet, 2012).”
Articulated Human Detection with Flexible Mixtures of Parts (2013, methodology): “This latent SVM problem can be solved by coordinate descent [4] or the CCP algorithm [47].”
Learning Answer-Entailing Structures for Machine Comprehension (2015, methodology): “We use a convex upper bound of the loss function (Yu and Joachims, 2009) to rewrite the objective: This problem can be solved using Concave-Convex Programming (Yuille and Rangarajan, 2003) with the cutting plane algorithm for structural SVM (Finley and Joachims, 2008).”
A Hierarchical Pose-Based Approach to Complex Action Understanding Using Dictionaries of Actionlets and Motion Poselets (2016, methodology): “We solve Equation (9) iteratively using the CCCP algorithm [40], by solving for latent labels zi and vi given model parameters W , temporal atomic action annotations (when available), and labels of complex actions occurring in training videos (see Section 3.”
Learning with Submodular Functions: A Convex Optimization Perspective (2011, neutral): “dures [210], or majorization-minimization algorithms [104].”
Multi-Stage Multi-Task Feature Learning (2012, positive): “It is closely related to the Concave Convex Procedure (CCCP) (Yuille and Rangarajan, 2003).”
A Unified Convergence Analysis of Block Successive Minimization Methods for Nonsmooth Optimization (2012, positive): “Although simple in form, the SUM algorithm is the key to many important algorithms such as the DC programming method [41] and the EM algorithm [6].”
Deep learning in medical image registration: a survey (2019, methodology): “i-metric outperformed conventional single-metric approaches. To deal with the non-convex of the aggregated similarity metric, they optimized a regularized upper bound of the loss using CCCP algorithm [180]. One limitation of this method was that segmentation masks of the source images were needed at”
Discriminative Hierarchical Modeling of Spatio-temporally Composable Human Activities (2014, methodology): “Given the loss function in Equation (15), the constrained optimization problem in Equation (13) is similar to a latent structural SVM case [39], therefore it can be solved using a Concave-Convex Procedure (CCCP) [40] which guarantees convergence to a local minimum.”
Maximum Mean Discrepancy for Class Ratio Estimation: Convergence Bounds and Kernel Selection (2014, methodology): “This makes objective (12) non-convex but since it is the difference of two convex functions, algorithms like CCCP (Yuille & Rangarajan, 2003) can give a local optimum .”
Optimization Techniques for Semi-Supervised Support Vector Machines (2008, methodology): “1 Concave Convex Procedure (CCCP) The CCCP method (Yuille and Rangarajan, 2003) has been applied to S3VMs by Fung and Mangasarian (2001), Collobert et al.”
Zero-Shot Learning via Semantic Similarity Embedding (2015, methodology): “Similarly we can perform CCCP to relax the constraint in Eq.”
Knowledge Graph and Corpus Driven Segmentation and Answer Inference for Telegraphic Entity-seeking Queries (2014, methodology): “We use the CCCP style, and augment the objective with an additional entropy term as in (Sawant and Chakrabarti, 2013).”
Action Recognition with Actons (2013, methodology): “Besides, through making relaxations on the original loss function, we can apply the concave-convex procedure (CCCP) [33] to solve the optimization problem of M4IL, which can theoretically guarantee the convergence of algorithm.”
MILEAGE: Multiple Instance LEArning with Global Embedding (2013, neutral): “It can be solved through various ways, such as constrained concave-convex procedure (CCCP) (Yuille & Rangarajan, 2003).”
Discovering discriminative action parts from mid-level video representations (2012, methodology): “The learning of the cost function that drives the matching is performed discriminatively using large-margin learning of a ranking function, while the individual part properties and the relations among them are estimated in a bootstrapped, concaveconvex procedure [35].”
Hopfield Networks is All You Need (2020, methodology): “(A20) is the Concave-Convex Procedure (CCCP) for minimizing the energy E.”