1,720,960 research outputs found
Algorithms for mean-field variational inference via polyhedral optimization in the Wasserstein space
Get PDFWe develop a theory of finite-dimensional polyhedral subsets over the
Wasserstein space and optimization of functionals over them via first-order
methods. Our main application is to the problem of mean-field variational
inference, which seeks to approximate a distribution over
by a product measure . When is strongly log-concave and
log-smooth, we provide (1) approximation rates certifying that is
close to the minimizer of the KL divergence over a
\emph{polyhedral} set , and (2) an algorithm for
minimizing over with accelerated
complexity , where is
the condition number of .Comment: 47 page
Entropic estimation of optimal transport maps
Get PDFWe develop a computationally tractable method for estimating the optimal map
between two distributions over with rigorous finite-sample
guarantees. Leveraging an entropic version of Brenier's theorem, we show that
our estimator -- the \emph{barycentric projection} of the optimal entropic plan
-- is easy to compute using Sinkhorn's algorithm. As a result, unlike current
approaches for map estimation, which are slow to evaluate when the dimension or
number of samples is large, our approach is parallelizable and extremely
efficient even for massive data sets. Under smoothness assumptions on the
optimal map, we show that our estimator enjoys comparable statistical
performance to other estimators in the literature, but with much lower
computational cost. We showcase the efficacy of our proposed estimator through
numerical examples, even ones not explicitly covered by our assumptions. By
virtue of Lepski's method, we propose a modified version of our estimator that
is adaptive to the smoothness of the underlying optimal transport map. Our
proofs are based on a modified duality principle for entropic optimal transport
and on a method for approximating optimal entropic plans due to Pal (2019).Comment: 38 pages, 8 figure
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
Optimal transport map estimation in general function spaces
No full textInternational audienceWe study the problem of estimating a function T given independent samples from a distribution P and from the pushforward distribution T ♯ P . This setting is motivated by applications in the sciences, where T represents the evolution of a physical system over time, and in machine learning, where, for example, T may represent a transformation learned by a deep neural network trained for a generative modeling task. To ensure identifiability, we assume that T = ∇φ 0 is the gradient of a convex function, in which case T is known as an optimal transport map. Prior work has studied the estimation of T under the assumption that it lies in a Hölder class, but general theory is lacking. We present a unified methodology for obtaining rates of estimation of optimal transport maps in general function spaces. Our assumptions are significantly weaker than those appearing in the literature: we require only that the source measure P satisfy a Poincaré inequality and that the optimal map be the gradient of a smooth convex function that lies in a space whose metric entropy can be controlled. As a special case, we recover known estimation rates for Hölder transport maps, but also obtain nearly sharp results in many settings not covered by prior work. For example, we provide the first statistical rates of estimation when P is the normal distribution and the transport map is given by an infinite-width shallow neural network
Dispelling 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
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