1,721,026 research outputs found
Optimization techniques for large scale finite sum problems
Get PDFWith the explosion of machine learning and artificial intelligence applications, the need for optimization methods specialized in the training of such models has been steadily growing for the last 10-20 years. Indeed, given the big data regime and the special structure of the optimization problems to be solved in these settings, a number of new, efficient optimization methods have been developed. A large amount of these new methods strongly rely on the finite sum structure of the objective function to be minimized, where the indices i=1,...,N often refer to the availability of N input-output pairs on which the model should be trained, i.e. the training set. Nevertheless, this is not the only application where a finite sum structure of the objective function appears. Indeed, beyond the training of Neural Networks (NN) and Support Vector Machines (SVM), which depend by definition on a dataset of input-output pairs, a finite sum structure can also be recognized in Reinforcement Learning (RL) applications, due to the need of estimating expected values by sample approximation. In all these cases, N is usually huge, in the order of millions, or even billions, therefore making the exact computation of the function and gradient infeasible for many real life applications. This is one of the reasons why the field has seen a flourishing of publications from the most diverse communities, beyond the operations research one, for example the dynamical control, computer science, stochastic optimization ones. Many new methods have been developed by these communities, both deterministic and stochastic algorithms, although their comparison is made difficult by the different approaches coming from the different communities the new algorithms belong to. Due to the above considerations, the focus of this dissertation is on how to solve optimization problems where the function is structured as a finite sum of component functions. In this finite sum setting, a function fi can be referred to as a component function, and its gradient Ñfi as a component gradient. In particular, a deep investigation of the algorithms developed so far to solve such problems is carried on, with a specific interest in showing the similarities and differences of the convergence analysis when it is developed in the deterministic vs stochastic cases. The target of the investigation is the case when the component gradients are continuously differentiable, and easily computable, like in many machine learning settings (e.g., neural networks training). In this framework, dynamic minibatching schemes are addressed. These are employed to determine the size of the sample to be used during the optimization process, especially in gradient-based methods, when the gradient is estimated by subsampling the component gradients, namely, when it is estimated based on a subset of the indices 1,...,N. The aim of dynamic minibatching schemes is to dynamically test the quality of the gradient approximation, and consequently suggest if the sample size should grow or not. A new technique is proposed, based on statistical analysis of the gradient estimates. The new technique is based on the well-known Analysis of Variance (ANOVA) test, and the convergence of a subsampled gradient-based method is proved when such technique is employed. Numerical experiments are reported on standard machine learning tasks, like (nonlinear) regression and binary classification. Then, the derivative free setting is explored, i.e. the setting where the component functions come from a black-box-like process and the component gradients are not directly available. An example of such setting is policy optimization for reinforcement learning, where only sample approximations of the stochastic reward function are available. Therefore, in literature, Derivative Free Optimization (DFO) methods have been applied to solve this problem, in particular by trying to estimate the gradient by computing only sample approximations of the function. An analysis of the convergence guaran4 tees of stochastic optimization methods in this setting is performed, showing that approximating the gradient by only computing sample-based estimates of the function brings a further approximation error, leading to poorer theoretical results. The special case of policy optimization for reinforcement learning is analysed, showing that such application is even harder, since the sample approximation of the function, in general, does not have continuity guarantees. Finally, a new class of distributed algorithms is introduced to solve linearly constrained, convex problems, with potential application to the dual formulation of the support vector machines training problem. This employs augmented Lagrangian and primal-dual theory to develop a simple, distributable and parallelizable class of algorithms to solve convex problems with simple bound and hard (i.e. coupling all the variables), linear constraints. Such class of algorithms is of particular interest for training support vector machines, since it allows to fully distribute the data, i.e. the input-output pairs, to the available parallel processes, simplifying the (often infeasible) storage of such large amount of data
Advances in large scale unconstrained optimization: novel preconditioning strategies for Nonlinear Conjugate Gradient methods and new developments in Newton-Krylov methods
Get PDFIn this thesis we propose new iteratively constructed preconditioners, to be paired with Conjugate Gradient-type algorithms, in order to efficiently solve large scale unconstrained optimization problems. On this guideline, the central thread of this thesis is the use of conjugate directions given by Conjugate Gradient or SYMMBK algorithms. To this aim, in Chapter 1 we recall some results about iterative methods for solving linear systems. In particular, we introduce both the Conjugate Gradient method and the Lanczos process. Finally, the idea of preconditioning is given and the well known Preconditioned Conjugate Gradient method is provided. In Chapter 2 we deal with large scale unconstrained optimization problems, recalling the Nonlinear Conjugate Gradient (NCG) method and its preconditioned version, the quasi-Newton methods, including the damped techniques, and finally the linesearch-based Inexact Newton methods. The main contribution in this thesis is given by Chapters 3-7. In particular, Chapter 3 provides new preconditioners to be used within the NCG method. This class of preconditioners draws inspiration from quasi-Newton updates, in order to obtain a good approximation of the inverse of the Hessian matrix. On detail, at the current iteration of the NCG we consider some preconditioners based on new low-rank quasi-Newton symmetric updating formulae, obtained as by-product of the NCG method at the previous steps. In particular, we propose five classes of preconditioners: in the first three classes the major drawback is that preconditioner might not be positive definite. In the fourth class, a preconditoner that is positive definite and satisfies the secant equation at the current iteration is given. Finally, in the last class, a preconditoner that is positive definite and satisfies the modified secant equation at each iteration is provided. However, in general, the search direction pk we compute at iteration k of NCG could be not well scaled, which may introduce some ill-conditioning when applying Preconditioned Nonlinear Conjugate Gradient (PNCG). In order to reduce the scaling problem, in Chapter 4 we focus on the use of damped techniques within NCG methods. Damped techniques were introduced by Powell and recently reproposed by Al-Baali, in the framework of quasi-Newton methods. New damped techniques are proposed and are embedded within a class of preconditioners described in Chapter 3 (see Section 3.3.4). In Chapter 5, by referring to the Polak-Ribière (PR) method, we firstly give theoretical results on the global convergence for an effective PNCG algorithm. Secondly, we investigate the use of a damped vector in the definition of the scalar k, hence affecting the definition of the search direction and producing a modified NCG/PNCG method. On this purpose, we prove that some global convergence properties still hold for the modified damped Polak-Ribière (D-PR-PNCG) method, while substantially preserving numerical performance. In Chapters 6-7 we focus on linesearch-based Newton-Krylov methods for solving large scale unconstrained optimization problems. In particular, in Chapter 6 we try to improve the efficiency of Newton-Krylov methods by proposing an adaptive truncation rule, for deciding the maximum number of inner iterations allowed at each outer iteration. The adaptive truncation rule is tested both within the unpreconditioned and the preconditioned framework proposed in [48]. Finally, Chapter 7 represents a work in progress: on detail, starting from [48] we deal with a class of preconditioners specifically suited for large indefinite linear systems, and may be obtained as by-product of Krylov subspace solvers, as well as by applying L-BFGS updates. In particular, in Chapter 7, only some preliminaries and the structure of our class of preconditioners, namely AINVK, are provided. At the end, conclusions are given
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Get PDFWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
To the special issue dedicated to the 3rd international conference "Numerical Computations: Theory and Algorithms-NUMTA 2019" June 15-21, 2019, Isola Capo Rizzuto, Italy
No full textDispelling the Myths Behind First-author Citation Counts
Get PDFWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
koamabayili/VECTRON-author-checklist: VECTRON author checklist
No full textWe have done our best to complete the author checklist relating to the use of animals in the hut study. Note that the objective for the hut study was to evaluate the IRS treatment applications for residual efficacy against Anopheles mosquitoes, including the local An. coluzzii mosquito population. Cows were only used to attract mosquitoes into the huts and no tests were carried out directly on the cows. The author checklist is intended for use with studies where experiments are carried out on animals, which is why we have had such difficulty in completing this for the hut study, as many of the questions do not relate to how the cows were used
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