In this paper, we consider the learning problem of multilayer perceptrons (MLPs) formulated as the problem of minimizing a smooth error function. As well known, the learning problem of MLPs can be a difficult nonlinear nonconvex optimization problem. Typical difficulties can be the presence of extensive flat regions and steep sided valleys in the error surface, and the possible large number of training data and of free network parameters. We define a wide class of batch learning algorithms for MLP, based on the use of block decomposition techniques in the minimization of the error function. The learning problem is decomposed into a sequence of smaller and structured minimization problems in order to advantageously exploit the structure of the objective function. Theoretical convergence results are established, and a specific algorithm is constructed and evaluated through an extensive numerical experimentation. The comparisons with the state-of-the-art learning algorithms show the effectiveness of the proposed techniques.
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.
The Support Vector Machines (SVMs) dual formulation has a non-separable structure that makes the design of a convergent distributed algorithm a very difficult task. Recently some separable and distributable reformulations of the SVM training problem have been obtained by fixing one primal variable. While this strategy seems effective for some applications, in certain cases it could be weak since it drastically reduces the overall final performance. In this work we present the first fully distributable algorithm for SVMs training that globally converges to a solution of the original (non-separable) SVMs dual formulation. Besides a detailed convergence analysis, we provide a simple demonstrative example showing the advantages of the original SVMs dual formulation with respect to the weak separable one and highlights the practical effectiveness of our method. We report further tests to show practical convergence of the proposed method on real-world datasets
This paper is aimed at developing a workable model for the identification of key-cost drivers in the Italian Local Public Bus Transport (LPBT) sector. Disaggregated information about costs, technical characteristics and environmental characteristics have been collected by means of questionnaires sent to LPBT companies producing more than 500 million bus revenue kilometres in Italy in 2011. A supervised regression model is built by training a regularized Artificial Neural Network in order to determine the quantitative and qualitative characteristics that contribute to explaining the variability of the driving personnel and the unit cost of the fleet (which usually covers more than 50% of the total economic cost) and the remaining portion of the unit cost. The proposed models could be an effective and simple tool for local authorities to validate reserve prices in tender procedures. Keywords: standard costs, local public transport, fiscal federalism, cost drivers, machine learning. INTRODUCTIONIn Italy, the Local Public Transport (LPT) industry reform bill (1997) touched upon two dimensions: the allocation of public funds to Regions -and, in turns, to Local Authorities (LAs) -as well as the definition of an upper bound to public compensations to LPT firms. Although the reform bill stated that all subsidized LPT services should have been tendered off by January 2004, later legislative interventions left discretion to local governments about whether tendering out concessions or adopting in-house provision. Some competitive tendering took place after 1998 [1]. However, at present, the amount of LPT services that are tendered off is negligible with respect to in house provision that still prevails, especially in large cities [2]. In recent years, a number of policy interventions reaffirmed the political aim to improve market-oriented mechanisms in the allotment of LPT services; moreover, several parliamentary acts established that the maximum economic compensation to LPT firms should be based on standard costs (Law number 135/2012). The standard cost is defined as the cost of a LPT service provided by a reasonably efficient operator given a pre-specified level of service quality. However, at present, the Italian policy makers have not yet promulgated an appropriate methodology for the calculation of unit standard costs.Our paper contributes to the literature since we develop two Top-Down cost models, based on recent advancements of machine learning approaches [3], in order to identify key cost drivers with respect to different cost items. The proposed models could be an effective and simple tool for LAs to validate reserve prices in tender procedures. Detailed information about costs has been gathered in order to fairly compute the total economic costs of the LPBT services; the collected economic and transport data relates to LPBT companies producing more than 500 million of bus revenue kilometers (BRK) in Italy in 2011 (approximately 30% of the overall amount of BRK offered in Italy for bus LPT services).Thi...
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