1,720,965 research outputs found
On the Impossibility of Learning the Missing Mass
No full textThis paper shows that one cannot learn the probability of rare events without imposing further structural assumptions. The event of interest is that of obtaining an outcome outside the coverage of an i.i.d. sample from a discrete distribution. The probability of this event is referred to as the “missing mass”. The impossibility result can then be stated as: the missing mass is not distribution-free learnable in relative error. The proof is semi-constructive and relies on a coupling argument using a dithered geometric distribution. Via a reduction, this impossibility also extends to both discrete and continuous tail estimation. These results formalize the folklore that in order to predict rare events without restrictive modeling, one necessarily needs distributions with "heavy tails". Keywords: missing mass; rare events; Good-Turing; light tails; heavy tails; no free lunc
Near-Optimal Smoothing of Structured Conditional Probability Matrices
No full textAbstract Utilizing the structure of a probabilistic model can significantly increase its learning speed. Motivated by several recent applications, in particular bigram models in language processing, we consider learning low-rank conditional probability matrices under expected KL-risk. This choice makes smoothing, that is the careful handling of low-probability elements, paramount. We derive an iterative algorithm that extends classical non-negative matrix factorization to naturally incorporate additive smoothing and prove that it converges to the stationary points of a penalized empirical risk. We then derive sample-complexity bounds for the global minimzer of the penalized risk and show that it is within a small factor of the optimal sample complexity. This framework generalizes to more sophisticated smoothing techniques, including absolute-discounting
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
COMPLEX-COEFFICIENT POLYNOMIAL ROOTS BY A STABILITY CRITERION
No full textAbstract. Computation of polynomial roots is a problem that arises in various domains of science and engineering, and has thus received much attention in years, with marked recent progress. This paper introduces a new numerical algorithm for computing the roots of a complex-coefficient polynomial of degree n. The method is based on bracketing, in the spirit of Lehmer-Schur [1], but uses a robust stability criterion from system theory due to Agashe [2], which generalizes the Routh-Hurwitz criterion. The algorithm is simple to implement, and its accuracy is tested using both well- and ill-conditioned polynomials. The results show excellent convergence, as compared to the companion-matrix eigenvalues method used often in numerical packages, such as MATLAB [3]. The algorithm is also flexible: precision can be tuned, and custom search regions can be specified. Key Words. Polynomial, root, algorithm, bracketing and stability. 1
Tradeoffs for Space, Time, Data and Risk in Unsupervised Learning
No full textFaced with massive data, is it possible to trade off (statistical) risk, and (computational) space and time? This challenge lies at the heart of large-scale machine learning. Using k-means clustering as a prototypical unsupervised learn-ing problem, we show how we can strategi-cally summarize the data (control space) in or-der to trade off risk and time when data is generated by a probabilistic model. Our sum-marization is based on coreset constructions from computational geometry. We also de-velop an algorithm, TRAM, to navigate the space/time/data/risk tradeoff in practice. In par-ticular, we show that for a fixed risk (or data size), as the data size increases (resp. risk in-creases) the running time of TRAM decreases. Our extensive experiments on real data sets demonstrate the existence and practical utility of such tradeoffs, not only for k-means but also for Gaussian Mixture Models.
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