1,720,966 research outputs found
Finding the Graph of Epidemic Cascades
No full textWe consider the problem of finding the graph on which an epidemic cascade spreads, given only the times when each node gets infected. While this is a problem of importance in several contexts – offline and online social networks, e-commerce, epidemiology, vulnerabilities in infrastructure networks – there has been very little work, analytical or empirical, on finding the graph. Clearly, it is impossible to do so from just one cascade; our interest is in learning the graph from a small number of cascades. For the classic and popular “independent cascade ” SIR epidemics, we analytically establish the num-ber of cascades required by both the global maximum-likelihood (ML) estimator, and a natural greedy algorithm. Both results are based on a key observation: the global graph learning problem decouples into n local problems – one for each node. For a node of degree d, we show that its neighborhood can be reliably found once it has been infected O(d2 log n) times (for ML on general graphs) or O(d log n) times (for greedy on trees). We also provide a corresponding information-theoretic lower bound of Ω(d log n); thus our bounds are essentially tight. Furthermore, if we are given side-information in the form of a super-graph of the actual graph (as is often the case), then the number of cascade samples required – in all cases – becomes independent of the network size n. Finally, we show that for a very general SIR epidemic cascade model, the Markov graph of infection times is obtained via the moralization of the network graph
No Quantum Speedup over Gradient Descent for Non-Smooth Convex Optimization
Get PDFWe study the first-order convex optimization problem, where we have black-box access to a (not necessarily smooth) function f:ℝⁿ → ℝ and its (sub)gradient. Our goal is to find an ε-approximate minimum of f starting from a point that is distance at most R from the true minimum. If f is G-Lipschitz, then the classic gradient descent algorithm solves this problem with O((GR/ε)²) queries. Importantly, the number of queries is independent of the dimension n and gradient descent is optimal in this regard: No deterministic or randomized algorithm can achieve better complexity that is still independent of the dimension n.
In this paper we reprove the randomized lower bound of Ω((GR/ε)²) using a simpler argument than previous lower bounds. We then show that although the function family used in the lower bound is hard for randomized algorithms, it can be solved using O(GR/ε) quantum queries. We then show an improved lower bound against quantum algorithms using a different set of instances and establish our main result that in general even quantum algorithms need Ω((GR/ε)²) queries to solve the problem. Hence there is no quantum speedup over gradient descent for black-box first-order convex optimization without further assumptions on the function family
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
Spectrum Approximation Beyond Fast Matrix Multiplication: Algorithms and Hardness
Get PDFUnderstanding the singular value spectrum of an n x n matrix A is a fundamental task in countless numerical computation and data analysis applications. In matrix multiplication time, it is possible to perform a full SVD of A and directly compute the singular values \sigma_1,...,\sigma_n. However, little is known about algorithms that break this runtime barrier.
Using tools from stochastic trace estimation, polynomial approximation, and fast linear system solvers, we show how to efficiently isolate different ranges of A's spectrum and approximate the number of singular values in these ranges. We thus effectively compute an approximate histogram of the spectrum, which can stand in for the true singular values in many applications.
We use our histogram primitive to give the first algorithms for approximating a wide class of symmetric matrix norms and spectral sums faster than the best known runtime for matrix multiplication. For example, we show how to obtain a (1 + \epsilon) approximation to the Schatten 1-norm (i.e. the nuclear or trace norm) in just ~ O((nnz(A)n^{1/3} + n^2)\epsilon^{-3}) time for A with uniform row sparsity or \tilde O(n^{2.18} \epsilon^{-3}) time for dense matrices. The runtime scales smoothly for general Schatten-p norms, notably becoming \tilde O (p nnz(A) \epsilon^{-3}) for any real p >= 2.
At the same time, we show that the complexity of spectrum approximation is inherently tied to fast matrix multiplication in the small \epsilon regime. We use fine-grained complexity to give conditional lower bounds for spectrum approximation, showing that achieving milder \epsilon dependencies in our algorithms would imply triangle detection algorithms for general graphs running in faster than state of the art matrix multiplication time. This further implies, through a reduction of (Williams & William, 2010), that highly accurate spectrum approximation algorithms running in subcubic time can be used to give subcubic time matrix multiplication. As an application of our bounds, we show that precisely computing all effective resistances in a graph in less than matrix multiplication time is likely difficult, barring a major algorithmic breakthrough
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
Provable Efficient Online Matrix Completion via Non-convex Stochastic Gradient Descent
Get PDFAbstract Matrix completion, where we wish to recover a low rank matrix by observing a few entries from it, is a widely studied problem in both theory and practice with wide applications. Most of the provable algorithms so far on this problem have been restricted to the offline setting where they provide an estimate of the unknown matrix using all observations simultaneously. However, in many applications, the online version, where we observe one entry at a time and dynamically update our estimate, is more appealing. While existing algorithms are efficient for the offline setting, they could be highly inefficient for the online setting. In this paper, we propose the first provable, efficient online algorithm for matrix completion. Our algorithm starts from an initial estimate of the matrix and then performs non-convex stochastic gradient descent (SGD). After every observation, it performs a fast update involving only one row of two tall matrices, giving near linear total runtime. Our algorithm can be naturally used in the offline setting as well, where it gives competitive sample complexity and runtime to state of the art algorithms. Our proofs introduce a general framework to show that SGD updates tend to stay away from saddle surfaces and could be of broader interests to other non-convex problems
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