scholarly journals AUC Optimization with a Reject Option

2020 ◽  
Vol 34 (04) ◽  
pp. 5684-5691
Author(s):  
Song-Qing Shen ◽  
Bin-Bin Yang ◽  
Wei Gao
Keyword(s):  
Online Algorithm ◽  
Lower Cost ◽  
Convex Relaxation ◽  
Class Imbalance ◽  
Optimal Solution ◽  
Score Function ◽  
Reject Option ◽  
Erroneous Decision ◽  
Auc Optimization ◽  
Mission Critical

Making an erroneous decision may cause serious results in diverse mission-critical tasks such as medical diagnosis and bioinformatics. Previous work focuses on classification with a reject option, i.e., abstain rather than classify an instance of low confidence. Most mission-critical tasks are always accompanied with class imbalance and cost sensitivity, where AUC has been shown a preferable measure than accuracy in classification. In this work, we propose the framework of AUC optimization with a reject option, and the basic idea is to withhold the decision of ranking a pair of positive and negative instances with a lower cost, rather than mis-ranking. We obtain the Bayes optimal solution for ranking, and learn the reject function and score function for ranking, simultaneously. An online algorithm has been developed for AUC optimization with a reject option, by considering the convex relaxation and plug-in rule. We verify, both theoretically and empirically, the effectiveness of the proposed algorithm.

scholarly journals Online Clique Clustering

Algorithmica ◽  
2019 ◽  
Vol 82 (4) ◽  
pp. 938-965
Author(s):  
Marek Chrobak ◽  
Christoph Dürr ◽  
Aleksander Fabijan ◽  
Bengt J. Nilsson
Keyword(s):  
Objective Function ◽  
Competitive Ratio ◽  
Online Algorithm ◽  
Optimal Solution ◽  
Deterministic Algorithm ◽  
Input Graph ◽  
Online Clustering ◽  
Objective Value ◽  
Asymptotic Competitive Ratio ◽  
Better Than

Abstract Clique clustering is the problem of partitioning the vertices of a graph into disjoint clusters, where each cluster forms a clique in the graph, while optimizing some objective function. In online clustering, the input graph is given one vertex at a time, and any vertices that have previously been clustered together are not allowed to be separated. The goal is to maintain a clustering with an objective value close to the optimal solution. For the variant where we want to maximize the number of edges in the clusters, we propose an online algorithm based on the doubling technique. It has an asymptotic competitive ratio at most 15.646 and a strict competitive ratio at most 22.641. We also show that no deterministic algorithm can have an asymptotic competitive ratio better than 6. For the variant where we want to minimize the number of edges between clusters, we show that the deterministic competitive ratio of the problem is $$n-\omega (1)$$n-ω(1), where n is the number of vertices in the graph.

scholarly journals Converting existing transmission corridors to HVDC is an overlooked option for increasing transmission capacity

2019 ◽  
Vol 116 (28) ◽  
pp. 13879-13884 ◽  
Author(s):  
Liza Reed ◽  
M. Granger Morgan ◽  
Parth Vaishnav ◽  
Daniel Erian Armanios
Keyword(s):  
High Voltage ◽  
Lower Cost ◽  
Optimal Solution ◽  
High Voltage Direct Current ◽  
Right Of Way ◽  
Electricity System ◽  
And Topology ◽  
Cost Strategy ◽  
And Performance ◽  
The Cost

A changing generation mix and growing demand for carbon-free electricity will almost certainly require dramatic changes in the infrastructure and topology of the electricity system. Rather than build new lines, one way to minimize social opposition and regulatory obstacles is to increase the capacity of existing transmission corridors. In addition to upgrading the capacity of high-voltage alternating current (HVAC) lines, we identify a number of situations in which conversion from HVAC to high-voltage direct current (HVDC) is the least-cost strategy to increase the capacity of the corridor. If restricted to the existing right-of-way (ROW), we find DC conversion to be the least-cost, and in some cases the only, option for distances of >200 km or for increases of >50% capacity. Across all configurations analyzed, we assess HVDC conversion to be the lower-cost option at >350 km and >50% capacity increases. While we recognize that capacity expansion through HVDC conversion may be the optimal solution in only some situations, with future improvements in the cost and performance of solid-state power electronics, conversion to HVDC could be attractive in a growing set of circumstances.

A Decision-Making Tool for the Optimization of Empty Containers' Return in the Liner Shipping: Optimization by Using the Genetic Algorithm

2018 ◽  
Vol 10 (3) ◽  
pp. 39-56
Author(s):  
Naima Belayachi ◽  
Fouzia Amrani ◽  
Karim Bouamrane
Keyword(s):  
Decision Making ◽  
Lower Cost ◽  
Optimal Solution ◽  
Maritime Transportation ◽  
Initial Population ◽  
Transportation Sector ◽  
Empty Containers ◽  
Feasible Solutions ◽  
The Cost ◽  
Decision Making Tool

This article describes how in the maritime transportation sector, containerization represents one of the most remarkable improvements. In fact, the different shipping companies provide great efforts, whose purpose is to reduce the cost of this transport. However, these companies are facing a problem of empty containers, which are not available at some ports of Maritime Transport Network (MTN) to meet the clients' demands. This problem is simply a consequence of the imbalance in the distribution of containers through the MTN due to the set of containers that do not return to the origin port. This work offers a decision-making tool to this problem by proposing an optimal return of empty containers. The proposed application is based on evolutionary heuristics. Its principle is to find an optimal solution from a set of several feasible solutions generated during an initial population in order to enable the search of empty containers at lower cost.

scholarly journals Quadruply Stochastic Gradient Method for Large Scale Nonlinear Semi-Supervised Ordinal Regression AUC Optimization

2020 ◽  
Vol 34 (04) ◽  
pp. 5734-5741
Author(s):  
Wanli Shi ◽  
Bin Gu ◽  
Xiang Li ◽  
Heng Huang
Keyword(s):  
Real World ◽  
Large Scale ◽  
Optimal Solution ◽  
Ordinal Regression ◽  
Data Sampling ◽  
Decomposition Approach ◽  
Scalable Algorithm ◽  
Auc Optimization ◽  
Stochastic Data ◽  
Real World Datasets

Semi-supervised ordinal regression (S2OR) problems are ubiquitous in real-world applications, where only a few ordered instances are labeled and massive instances remain unlabeled. Recent researches have shown that directly optimizing concordance index or AUC can impose a better ranking on the data than optimizing the traditional error rate in ordinal regression (OR) problems. In this paper, we propose an unbiased objective function for S2OR AUC optimization based on ordinal binary decomposition approach. Besides, to handle the large-scale kernelized learning problems, we propose a scalable algorithm called QS3ORAO using the doubly stochastic gradients (DSG) framework for functional optimization. Theoretically, we prove that our method can converge to the optimal solution at the rate of O(1/t), where t is the number of iterations for stochastic data sampling. Extensive experimental results on various benchmark and real-world datasets also demonstrate that our method is efficient and effective while retaining similar generalization performance.

Approach to Energy Optimization Axiomatic Design Based on Design Unite

2011 ◽  
Vol 130-134 ◽  
pp. 1582-1585
Author(s):  
Dan Zhou ◽  
Guang Fu Liu ◽  
Ping He
Keyword(s):  
Energy Efficiency ◽  
Lower Cost ◽  
Energy Optimization ◽  
Optimal Solution ◽  
Axiomatic Design ◽  
Design Stage ◽  
Independence Axiom ◽  
Information Axiom ◽  
Cost Of Energy ◽  
Model C

Under the control of energy efficiency model C, design unite (DU) changes function F to state S through design progress P. Thus, the target of energy optimization is achieved by gain the F in a lower cost of energy. In order to make energy efficiency model C used in design progress more easily, the EDF’s optimization target T and energy consumption influence modulus M is added to C. In the process of energy optimization axiomatic design, DU changes the initial customer’s requests to product’s physical modules in a decomposing process and its content is transformed from asthenia to sthenia. DU’s function F is decomposed and defined at the guidance of independence axiom. And the optimal solution is selected at the operation of information axiom and energy efficiency model C. By the end of this paper, the contrast of energy optimization degree in each design stage is detailed.

scholarly journals Block-Sparse Recovery with Optimal Block Partition

2021 ◽  
Author(s):  
Hiroki Kuroda ◽  
Daichi Kitahara
Keyword(s):  
Penalty Function ◽  
A Priori ◽  
Convex Relaxation ◽  
Optimal Solution ◽  
Sparse Recovery ◽  
Sparse Signals ◽  
L1 Norm ◽  
Recovery Method ◽  
Block Partition ◽  
L2 Norm

This paper presents a convex recovery method for block-sparse signals whose block partitions are unknown a priori. We first introduce a nonconvex penalty function, where the block partition is adapted for the signal of interest by minimizing the mixed l2/l1 norm over all possible block partitions. Then, by exploiting a variational representation of the l2 norm, we derive the proposed penalty function as a suitable convex relaxation of the nonconvex one. For a block-sparse recovery model designed with the proposed penalty, we develop an iterative algorithm which is guaranteed to converge to a globally optimal solution. Numerical experiments demonstrate the effectiveness of the proposed method.

scholarly journals Quadruply Stochastic Gradients for Large Scale Nonlinear Semi-Supervised AUC Optimization

2019 ◽  
Author(s):  
Wanli Shi ◽  
Bin Gu ◽  
Xiang Li ◽  
Xiang Geng ◽  
Heng Huang
Keyword(s):  
Learning Community ◽  
Supervised Learning ◽  
Large Scale ◽  
Optimal Solution ◽  
Stochastic Gradient ◽  
Gradient Algorithm ◽  
Maximization Problem ◽  
Classification Problems ◽  
Auc Maximization ◽  
Auc Optimization

Semi-supervised learning is pervasive in real-world applications, where only a few labeled data are available and large amounts of instances remain unlabeled. Since AUC is an important model evaluation metric in classification, directly optimizing AUC in semi-supervised learning scenario has drawn much attention in the machine learning community. Recently, it has been shown that one could find an unbiased solution for the semi-supervised AUC maximization problem without knowing the class prior distribution. However, this method is hardly scalable for nonlinear classification problems with kernels. To address this problem, in this paper, we propose a novel scalable quadruply stochastic gradient algorithm (QSG-S2AUC) for nonlinear semi-supervised AUC optimization. In each iteration of the stochastic optimization process, our method randomly samples a positive instance, a negative instance, an unlabeled instance and their random features to compute the gradient and then update the model by using this quadruply stochastic gradient to approach the optimal solution. More importantly, we prove that QSG-S2AUC can converge to the optimal solution in O(1/t), where t is the iteration number. Extensive experimental results on  a variety of benchmark datasets show that QSG-S2AUC is far more efficient than the existing state-of-the-art algorithms for semi-supervised AUC maximization, while retaining the similar generalization performance.

scholarly journals Block-Sparse Recovery with Optimal Block Partition

2021 ◽  
Author(s):  
Hiroki Kuroda ◽  
Daichi Kitahara
Keyword(s):  
Penalty Function ◽  
A Priori ◽  
Convex Relaxation ◽  
Optimal Solution ◽  
Sparse Recovery ◽  
Sparse Signals ◽  
L1 Norm ◽  
Recovery Method ◽  
Block Partition ◽  
L2 Norm

This paper presents a convex recovery method for block-sparse signals whose block partitions are unknown a priori. We first introduce a nonconvex penalty function, where the block partition is adapted for the signal of interest by minimizing the mixed l2/l1 norm over all possible block partitions. Then, by exploiting a variational representation of the l2 norm, we derive the proposed penalty function as a suitable convex relaxation of the nonconvex one. For a block-sparse recovery model designed with the proposed penalty, we develop an iterative algorithm which is guaranteed to converge to a globally optimal solution. Numerical experiments demonstrate the effectiveness of the proposed method.

Online Minimum Spanning Tree with Advice

2018 ◽  
Vol 29 (04) ◽  
pp. 505-527
Author(s):  
Maria Paola Bianchi ◽  
Hans-Joachim Böckenhauer ◽  
Tatjana Brülisauer ◽  
Dennis Komm ◽  
Beatrice Palano
Keyword(s):  
Lower Bound ◽  
Weight Function ◽  
Competitive Ratio ◽  
Spanning Tree ◽  
Online Algorithm ◽  
Minimum Spanning Tree ◽  
Optimal Solution ◽  
Bounded Degree ◽  
Advice Complexity ◽  
Graph Classes

In the online minimum spanning tree problem, a graph is revealed vertex by vertex; together with every vertex, all edges to vertices that are already known are given, and an online algorithm must irrevocably choose a subset of them as a part of its solution. The advice complexity of an online problem is a means to quantify the information that needs to be extracted from the input to achieve good results. For a graph of size [Formula: see text], we show an asymptotically tight bound of [Formula: see text] on the number of advice bits to produce an optimal solution for any given graph. For particular graph classes, e.g., with bounded degree or a restricted edge weight function, we prove that the upper bound can be drastically reduced; e.g., [Formula: see text] advice bits allow to compute an optimal result if the weight function equals the Euclidean distance; if the graph is complete and has two different edge weights, even a logarithmic number suffices. Some of these results make use of the optimality of Kruskal’s algorithm for the offline setting. We also study the trade-off between the number of advice bits and the achievable competitive ratio. To this end, we perform a reduction from another online problem to obtain a linear lower bound on the advice complexity for any near-optimal solution. Using our results finally allows us to give a lower bound on the expected competitive ratio of any randomized online algorithm for the problem, even on graphs with three different edge weights.

scholarly journals Distributed Learning Algorithms and Lossless Convex Relaxation for Economic Dispatch with Transmission Losses and Capacity Limits

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Kwang-Ki K. Kim
Keyword(s):  
Power Generation ◽  
Learning Algorithm ◽  
Convex Relaxation ◽  
Economic Dispatch ◽  
Optimal Solution ◽  
Necessary Optimality Conditions ◽  
Distributed Learning ◽  
Coefficient Matrix ◽  
Test Case ◽  
Capacity Limits

This paper considers problems of economic dispatch in power networks that contain independent power generation units and loads. For efficient distributed economic dispatch, we present a mechanism of multiagent learning in which each agent corresponding to a generation unit updates the power generation based on the received information from the neighborhood. The convergence of the proposed distributed learning algorithm to the global optimal solution is analyzed. Another method of distributed economic dispatch we propose is a decentralized iterative linear projection method in which the necessary optimality conditions are solved without considering the generation capacities and the obtained solutions are iteratively projected onto the convex set corresponding to the generation capacities. A centralized method based on semidefinite programming for economic dispatch with a loss coefficient matrix is also presented for comparisons. For demonstration, the proposed methods of distributed economic dispatch are applied to a 6-generator test case and the three different methods of economic dispatch give the same solutions. We also analyze parametric dependence of the optimal power generation profiles on varying power demands in economic dispatch.

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