111 research outputs found
Parallel decomposition methods for linearly constrained problems subject to simple bound with application to the SVMs training
We consider the convex quadratic linearly constrained problem
with bounded variables and with huge and dense Hessian matrix that arises
in many applications such as the training problem of bias support vector machines.
We propose a decomposition algorithmic scheme suitable to parallel implementations
and we prove global convergence under suitable conditions. Focusing
on support vector machines training, we outline how these assumptions
can be satisfied in practice and we suggest various specific implementations.
Extensions of the theoretical results to general linearly constrained problem
are provided. We included numerical results on support vector machines with
the aim of showing the viability and the effectiveness of the proposed scheme
A fast branch-and-bound algorithm for non-convex quadratic integer optimization subject to linear constraints using ellipsoidal relaxations
We propose two exact approaches for non-convex quadratic integer minimization subject to linear constraints where lower bounds are computed by considering ellipsoidal relaxations of the feasible set. In the first approach, we intersect the ellipsoids with the feasible linear subspace. In the second approach we penalize exactly the linear constraints. We investigate the connection between both approaches theoretically. Experimental results show that the penalty approach significantly outperforms CPLEX on problems with small or medium size variable domains. © 2015 Elsevier B.V. All rights reserved
Neural networks for small scale ORC optimization
This study concerns a thermodynamic and technical optimization of a small scale Organic Rankine Cycle system for waste heat
recovery applications. An Artificial Neural Network (ANN) has been used to develop a thermodynamic model to be used for
the maximization of the production of power while keeping the size of the heat exchangers and hence the cost of the plant at its
minimum. R1234yf has been selected as the working fluid. The results show that the use of ANN is promising in solving complex
nonlinear optimization problems that arise in the field of thermodynamics
On the convergence of a Block-Coordinate Incremental Gradient method
In this paper, we study the convergence of a block-coordinate incremental gradient method. Under some specific assumptions on the objective function, we prove that the block-coordinate incremental gradient method can be seen as a gradient method with errors and convergence can be proved by showing the error at each iteration satisfies some standard conditions. Thus, we can prove convergence towards stationary points when the block incremental gradient method is coupled with a diminishing stepsize and towards an epsilon-approximate solution when a bounded away from zero stepsize is employed
Off-the-shelf solvers for mixed-integer conic programming: insights from a computational study on congested capacitated facility location instances
This paper analyzes the performance of five well-known off-the-shelf
optimization solvers on a set of mixed-integer conic programs proposed for the
congested capacitated facility location problem. We aim to compare the
computational efficiency of the solvers and examine the solution strategies
they adopt when solving instances with different sizes and complexity.
The solvers we compare are Gurobi, Cplex, Mosek, Xpress, and Scip. We run
extensive numerical tests on a testbed of 30 instances from the literature. Our
results show that Mosek and Gurobi are the most competitive solvers, as they
achieve better time and gap performance, solving most instances within the time
limit. Mosek outperforms Gurobi in large-size problems and provides more
accurate solutions in terms of feasibility. Xpress solves to optimality about
half of the instances tested within the time limit, and in this half, it
achieves performance similar to that of Gurobi and Mosek. Cplex and Scip emerge
as the least competitive solvers. The results provide guidelines on how each
solver behaves on this class of problems and highlight the importance of
choosing a solver suited to the problem type
Margin Optimal Classification Trees
In recent years there has been growing attention to interpretable machine
learning models which can give explanatory insights on their behavior. Thanks
to their interpretability, decision trees have been intensively studied for
classification tasks, and due to the remarkable advances in mixed-integer
programming (MIP), various approaches have been proposed to formulate the
problem of training an Optimal Classification Tree (OCT) as a MIP model. We
present a novel mixed-integer quadratic formulation for the OCT problem, which
exploits the generalization capabilities of Support Vector Machines for binary
classification. Our model, denoted as Margin Optimal Classification Tree
(MARGOT), encompasses the use of maximum margin multivariate hyperplanes nested
in a binary tree structure. To enhance the interpretability of our approach, we
analyse two alternative versions of MARGOT, which include feature selection
constraints inducing local sparsity of the hyperplanes. First, MARGOT has been
tested on non-linearly separable synthetic datasets in 2-dimensional feature
space to provide a graphical representation of the maximum margin approach.
Finally, the proposed models have been tested on benchmark datasets from the
UCI repository. The MARGOT formulation turns out to be easier to solve than
other OCT approaches, and the generated tree better generalizes on new
observations. The two interpretable versions are effective in selecting the
most relevant features and maintaining good prediction quality
Machine learning use for prognostic purposes in multiple sclerosis
The course of multiple sclerosis begins with a relapsing-remitting phase, which evolves into a secondarily progressive form over an extremely variable period, depending on many factors, each with a subtle influence. To date, no prognostic factors or risk score have been validated to predict disease course in single individuals. This is increasingly frustrating, since several treatments can prevent relapses and slow progression, even for a long time, although the possible adverse effects are relevant, in particular for the more effective drugs. An early prediction of disease course would allow differentiation of the treatment based on the expected aggressiveness of the disease, reserving high-impact therapies for patients at greater risk. To increase prognostic capacity, approaches based on machine learning (ML) algorithms are being attempted, given the failure of other approaches. Here we review recent studies that have used clinical data, alone or with other types of data, to derive prognostic models. Several algorithms that have been used and compared are described. Although no study has proposed a clinically usable model, knowledge is building up and in the future strong tools are likely to emerge
Considering patient clinical history impacts performance of machine learning models in predicting course of multiple sclerosis
Multiple Sclerosis (MS) progresses at an unpredictable rate, but predictions on the disease course in each patient would be extremely useful to tailor therapy to the individual needs. We explore different machine learning (ML) approaches to predict whether a patient will shift from the initial Relapsing-Remitting (RR) to the Secondary Progressive (SP) form of the disease, using only “real world” data available in clinical routine. The clinical records of 1624 outpatients (207 in the SP phase) attending the MS service of Sant'Andrea hospital, Rome, Italy, were used. Predictions at 180, 360 or 720 days from the last visit were obtained considering either the data of the last available visit (Visit-Oriented setting), comparing four classical ML methods (Random Forest, Support Vector Machine, K-Nearest Neighbours and AdaBoost) or the whole clinical history of each patient (History-Oriented setting), using a Recurrent Neural Network model, specifically designed for historical data. Missing values were handled by removing either all clinical records presenting at least one missing parameter (Feature-saving approach) or the 3 clinical parameters which contained missing values (Record-saving approach). The performances of the classifiers were rated using common indicators, such as Recall (or Sensitivity) and Precision (or Positive predictive value). In the visit-oriented setting, the Record-saving approach yielded Recall values from 70% to 100%, but low Precision (5% to 10%), which however increased to 50% when considering only predictions for which the model returned a probability above a given “confidence threshold”. For the History-oriented setting, both indicators increased as prediction time lengthened, reaching values of 67% (Recall) and 42% (Precision) at 720 days. We show how “real world” data can be effectively used to forecast the evolution of MS, leading to high Recall values and propose innovative approaches to improve Precision towards clinically useful values
AI-based Data Preparation and Data Analytics in Healthcare: The Case of Diabetes
The Associazione Medici Diabetologi (AMD) collects and manages one of the
largest worldwide-available collections of diabetic patient records, also known
as the AMD database. This paper presents the initial results of an ongoing
project whose focus is the application of Artificial Intelligence and Machine
Learning techniques for conceptualizing, cleaning, and analyzing such an
important and valuable dataset, with the goal of providing predictive insights
to better support diabetologists in their diagnostic and therapeutic choices.Comment: The work has been presented at the conference Ital-IA 2022
(https://www.ital-ia2022.it/
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