1,720,973 research outputs found
The Data-Driven Schrödinger Bridge
Full text linkErwin Schrödinger posed—and to a large extent solved—in 1931/32 the problem of finding the most likely random evolution between two continuous probability distributions. This article considers this problem in the case when only samples of the two distributions are available. A novel iterative procedure is proposed, inspired by Fortet-IPF-Sinkhorn type algorithms. Since only samples of the marginals are available, the new approach features constrained maximum likelihood estimation in place of the nonlinear boundary couplings, and importance sampling to propagate the functions φ and (Formula presented.) solving the Schrödinger system. This method mitigates the curse of dimensionality, compared to the introduction of grids, which in high dimensions lead to numerically unfeasible methods. The methodology is illustrated in two applications: entropic interpolation of two-dimensional Gaussian mixtures, and the estimation of integrals through a variation of importance sampling. © 2020 Wiley Periodicals LLC
Stochastic control liaisons: Richard Sinkhorn meets gaspard monge on a schrödinger bridge
Full text linkIn 1931-1932, Erwin Schrödinger studied a hot gas Gedankenexperiment (an instance of large deviations of the empirical distribution). Schrödinger's problem represents an early example of a fundamental inference method, the so-called maximum entropy method, having roots in Boltzmann's work and being developed in subsequent years by Jaynes, Burg, Dempster, and Csiszár. The problem, known as the Schrödinger bridge problem (SBP) with "uniform"prior, was more recently recognized as a regularization of the Monge-Kantorovich optimal mass transport (OMT) problem, leading to effective computational schemes for the latter. Specifically, OMT with quadratic cost may be viewed as a zerotemperature limit of the problem posed by Schrödinger in the early 1930s. The latter amounts to minimization of Helmholtz's free energy over probability distributions that are constrained to possess two given marginals. The problem features a delicate compromise, mediated by a temperature parameter, between minimizing the internal energy and maximizing the entropy. These concepts are central to a rapidly expanding area of modern science dealing with the so-called Sinkhorn algorithm, which appears as a special case of an algorithm first studied in the more challenging continuous space setting by the French analyst Robert Fortet in 1938-1940 specifically for Schrödinger bridges. Due to the constraint on end-point distributions, dynamic programming is not a suitable tool to attack these problems. Instead, Fortet's iterative algorithm and its discrete counterpart, the Sinkhorn iteration, permit computation of the optimal solution by iteratively solving the so-called Schrödinger system. Convergence of the iteration is guaranteed by contraction along the steps in suitable metrics, such as Hilbert's projective metric. In both the continuous as well as the discrete time and space settings, stochastic control provides a reformulation of and a context for the dynamic versions of general Schrödinger bridge problems and of their zero-temperature limit, the OMT problem. These problems, in turn, naturally lead to steering problems for flows of one-time marginals which represent a new paradigm for controlling uncertainty. The zero-temperature problem in the continuous-time and space setting turns out to be the celebrated Benamou-Brenier characterization of the McCann displacement interpolation flow in OMT. The formalism and techniques behind these control problems on flows of probability distributions have attracted significant attention in recent years as they lead to a variety of new applications in spacecraft guidance, control of robot or biological swarms, sensing, active cooling, and network routing as well as in computer and data science. This multifaceted and versatile framework, intertwining SBP and OMT, provides the substrate for the historical and technical overview of the field given in this paper. A key motivation has been to highlight links between the classical early work in both topics and the more recent stochastic control viewpoint, which naturally lends itself to efficient computational schemes and interesting generalizations
Controlling Uncertainty
Full text linkOur account begins in 1931/1932, when one of the fathers of quantum theory, Erwin Schroedinger, proposed a Gedankenexperiment to comprehend the propagation of a cloud of Brownian particles. He proposed [1], [2] the inference problem to identify the most likely evolution of a large collection of particles as they traverse between two endpoints in timeâ their distribution being measured and available at the two endpoints. This random evolution, now known as the Schroedinger bridge, entails a flow of one-time distributions that interpolate the known initial and final marginals
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe 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
Relaxed schrödinger bridges and robust network routing
No full textWe seek network routing towards a desired final distribution that can mediate possible random link failures. In other words, we seek a routing plan that utilizes alternative routes so as to be relatively robust to link failures. To this end, we provide a mathematical formulation of a relaxed transport problem where the final distribution only needs to be close to the desired one. The problem is cast as a maximum entropy problem for probability distributions on paths with added terminal cost. The entropic regularizing penalty aims at distributing the choice of paths amongst possible alternatives. We prove that the unique solution may be obtained by solving a generalized Schrödinger system of equations. An iterative algorithm to compute the solution is provided. Each iteration of the algorithm contracts the distance (in the Hilbert metric) to the optimal solution by more than 1/2, leading to extremely fast convergence
Regularized transport between singular covariance matrices
Full text linkWe consider the problem of steering a linear stochastic system between two end-point degenerate Gaussian distributions in finite time. This accounts for those situations in which some but not all of the state entries are uncertain at the initial, t = 0, and final time, t = T. This problem entails non-trivial technical challenges as the singularity of terminal state-covariance causes the control to grow unbounded at the final time T. Consequently, the entropic interpolation (Schroedinger Bridge) is provided by a diffusion process which is not finite-energy, thereby placing this case outside of most of the current theory. In this paper, we show that a feasible interpolation can be derived as a limiting case of earlier results for non-degenerate cases, and that it can be expressed in closed form. Moreover, we show that such interpolation belongs to the same reciprocal class of the uncontrolled evolution. By doing so we also highlight a time-symmetry of the problem, contrasting dual formulations in the forward and reverse time-directions, where in each the control grows unbounded as time approaches the end-point (in the forward and reverse time-direction, respectively)
Variations on the Author
Full text link“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
Full text linkWe 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
Dispelling the Myths Behind First-author Citation Counts
Full text linkWe 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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