Parallel decomposition methods for linearly constrained problems subject to simple bound with application to the SVMs training

Manno, Andrea; Palagi, Laura; Sagratella, Simone

doi:10.1007/s10589-018-9987-0

Cited by 9 publications

(9 citation statements)

References 26 publications

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“…Different working set selection rules, based on sufficient predicted descent, have also been studied in [30]. Moreover, a Jacobi-type algorithm has been devised in [15] and a class of parallel decomposition methods for quadratic objective functions has been proposed in [18].…”

Section: Introductionmentioning

confidence: 99%

An almost cyclic 2-coordinate descent method for singly linearly constrained problems

Cristofari

2019

Comput Optim Appl

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A block decomposition method is proposed for minimizing a (possibly nonconvex) continuously differentiable function subject to one linear equality constraint and simple bounds on the variables. The proposed method iteratively selects a pair of coordinates according to an almost cyclic strategy that does not use first-order information, allowing us not to compute the whole gradient of the objective function during the algorithm. Using firstorder search directions to update each pair of coordinates, global convergence to stationary points is established for different choices of the stepsize under an appropriate assumption on the level set. In particular, both inexact and exact line search strategies are analyzed. Further, linear convergence rate is proved under standard additional assumptions. Numerical results are finally provided to show the effectiveness of the proposed method.Keywords. Block coordinate descent methods. Block decomposition methods. Linear convergence rate. SVM.MSC2000 subject classifications. 90C06. 90C30. 65K05.

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Section: Introductionmentioning

confidence: 99%

An almost cyclic 2-coordinate descent method for singly linearly constrained problems

Cristofari

2019

Comput Optim Appl

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“…This plays a fundamental role in applications where either different pieces of information are available only to different processes or if the knowledge of such data requires significant computational burdens. The latter is the case of support vector machines training, because in its dual quadratic formulation a column of the matrix Q requires in general O(n 2 ) nonlinear calculations [28,30]. Nonetheless, we underline that the above scheme is not directly applicable to the support vector machines quadratic formulation due to the presence of a coupling linear constraint (m = 1) [31].…”

Section: Motivationmentioning

confidence: 99%

“…In particular, in the dual formulation of the training problem of support vector machines the presence of a linear equality constraint (i.e. a coupling constraint) over all the variables makes the distribution of the data uneasy [26,28,30,31,33].…”

Section: Introductionmentioning

confidence: 99%

Distributed algorithms for convex problems with linear coupling constraints

Colombo

Sagratella

2019

J Glob Optim

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Distributed and parallel algorithms have been frequently investigated in the recent years, in particular in applications like machine learning. Nonetheless, only a small subclass of the optimization algorithms in the literature can be easily distributed, for the presence, e.g., of coupling constraints that make all the variables dependent from each other with respect to the feasible set. Augmented Lagrangian methods are among the most used techniques to get rid of the coupling constraints issue, namely by moving such constraints to the objective function in a structured, well-studied manner. Unfortunately, standard augmented Lagrangian methods need the solution of a nested problem by needing to (at least inexactly) solve a subproblem at each iteration, therefore leading to potential inefficiency of the algorithm. To fill this gap, we propose an augmented Lagrangian method to solve convex problems with linear coupling constraints that can be distributed and requires a single gradient projection step at every iteration. We give a formal convergence proof to at least ε-approximate solutions of the problem and a detailed analysis of how the parameters of the algorithm influence the value of the approximating parameter ε. Furthermore, we introduce a distributed version of the algorithm allowing to partition the data and perform the distribution of the computation in a parallel fashion.

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“…A proper prediction model trained for classification should be able to reconstruct the unknown class membership (output) for any given sample (input). The most commonly used ML techniques for classifications are Decision Trees 47 , Support Vector Machines (SVMs) 9,35,36 , ANNs 7,20,23 , and recently Deep Neural Networks (DNNs) 31 . Even if all the above methods have been often applied to classification task in healthcare domains 21,27,34,53 , the Neural Networks based ones seem to be the more suited to capture the complicated and hidden nonlinear relationship between the input and the output, and are therefore the most used in this kind of applications.…”

Section: Introductionmentioning

confidence: 99%

The New SUMPOT to Predict Postoperative Complications Using an Artificial Neural Network

Chelazzi

Villa

Manno

et al. 2021

Preprint

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An accurate assessment of preoperative risk may improve use of hospital resources and reduce morbidity and mortality inhigh-risk surgical patients. This study aims at implementing an automated surgical risk calculator based on Artificial NeuralNetwork technology to identify patients at risk for postoperative complications. We developed the new SUMPOT based on risk factors previously used in other scoring systems and tested it in a cohortof 560 surgical patients undergoing elective or emergency procedures and subsequently admitted to intensive care units,high-dependency units or standard wards. The whole dataset was divided into a training set, to train the predictive model, anda testing set, to assess generalization performance. The effectiveness of the Artificial Neural Network is a measure of theaccuracy in detecting those patients who will develop postoperative complications.A total of 560 surgical patients entered the analysis. Among them, 77 patients (13.7%) suffered from one or more postoperativecomplications (PoCs), while 483 patients (86.3%) did not. The trained Artificial Neural Network returned an average classificationaccuracy of 90% in the testing set. Specifically, classification accuracy was 90.2% in the control group (46 patients out of 51were correctly classified) and 88.9% in the PoC group (8 patients out of 9 were correctly classified).The Artificial Neural Network showed good performance in predicting presence/absence of postoperative complications,suggesting its potential value for perioperative management of surgical patients. Further clinical studies are required to confirmits applicability in routine clinical practice.

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Parallel decomposition methods for linearly constrained problems subject to simple bound with application to the SVMs training

Cited by 9 publications

References 26 publications

An almost cyclic 2-coordinate descent method for singly linearly constrained problems

An almost cyclic 2-coordinate descent method for singly linearly constrained problems

Distributed algorithms for convex problems with linear coupling constraints

The New SUMPOT to Predict Postoperative Complications Using an Artificial Neural Network

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