Semi-supervised learning (SSL) uses unlabeled data for training and has been shown to greatly improve performances when compared to a supervised approach on the labeled data available. This claim depends both on the amount of labeled data available and on the algorithm used. In this paper, we compute analytically the gap between the best fully-supervised approach on labeled data and the best semi-supervised approach using both labeled and unlabeled data. We quantify the best possible increase in performance obtained thanks to the unlabeled data, i.e. we compute the accuracy increase due to the information contained in the unlabeled data. Our work deals with a simple high-dimensional Gaussian mixture model for the data in a Bayesian setting. Our rigorous analysis builds on recent theoretical breakthroughs in high-dimensional inference and a large body of mathematical tools from statistical physics initially developed for spin glasses.
Using exact but non-rigorous methods from statistical physics, @cite_17 @cite_27 determines the critical values for @math and @math at which it becomes information-theoretically possible to reconstruct the membership into clusters better than chance. Rigorous results on this model are given in @cite_10 where bounds on the critical values are obtained. The precises thresholds were then determined in @cite_2 . Our analysis builds on the techniques derived in this last reference with two main modifications: additional work is required to compute the classification accuracy (as opposed to the mean squared error) and to incorporate the side information.
@cite_2 @cite_27 @cite_10 @cite_17
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We consider the problem of Gaussian mixture clustering in the high-dimensional limit where the data consists of m points in n dimensions, n,m → ∞ and α = m n stays finite. Using exact but non-rigorous methods from statistical physics, we determine the critical value of α and the distance between the clusters at which it becomes information-theoretically possible to reconstruct the membership into clusters better than chance. We also determine the accuracy achievable by the Bayes-optimal estimation algorithm. In particular, we find that when the number of clusters is sufficiently large, r > 4+2√α, there is a gap between the threshold for information-theoretically optimal performance and the threshold at which known algorithms succeed. We investigate the minimization of Newton's functional for the problem of the body of minimal resistance with maximal height @math cite butt in the class of convex developable functions defined in a disc. This class is a natural candidate to find a (non-radial) minimizer in accordance with the results of cite lrp2. We prove that the minimizer in this class has a minimal set in the form of a regular polygon with @math sides centered in the disc, and numerical experiments indicate that the natural number @math is a non-decreasing function of @math . The corresponding functions all achieve a lower value of the functional than the optimal radially symmetric function with the same height @math . A citing sentence is one that appears in a scientific article and cites previous work. Citing sentences have been studied and used in many applications. For example, they have been used in scientific paper summarization, automatic survey generation, paraphrase identification, and citation function classification. Citing sentences that cite multiple papers are common in scientific writing. This observation should be taken into consideration when using citing sentences in applications. For instance, when a citing sentence is used in a summary of a scientific paper, only the fragments of the sentence that are relevant to the summarized paper should be included in the summary. In this paper, we present and compare three different approaches for identifying the fragments of a citing sentence that are related to a given target reference. Our methods are: word classification, sequence labeling, and segment classification. Our experiments show that segment classification achieves the best results. We study a random graph model named the "block model" in statistics and the "planted partition model" in theoretical computer science. In its simplest form, this is a random graph with two equal-sized clusters, with a between-class edge probability of @math and a within-class edge probability of @math . A striking conjecture of Decelle, Krzkala, Moore and Zdeborov 'a based on deep, non-rigorous ideas from statistical physics, gave a precise prediction for the algorithmic threshold of clustering in the sparse planted partition model. In particular, if @math and @math , @math and @math then conjectured that it is possible to efficiently cluster in a way correlated with the true partition if @math and impossible if @math for some sufficiently large @math . In a previous work, we proved that indeed it is information theoretically impossible to to cluster if @math . A different independent proof of the same result was recently obtained by Laurent Massoulie. As software becomes ever more ubiquitous and complex in medical devices, it becomes increasingly important to assure that it performs safely and effectively. The critical nature of medical devices necessitates that the software used therein be reliable and free of errors. It becomes imperative, therefore, to have a conformance review process in place to ascertain the correctness of the software and to ensure that it meets all requirements and standards. Formal methods have long been suggested as a means to design and develop medical device software. However, most manufacturers shy from using these techniques, citing them as too complex and time consuming. As a result, (potentially life-threatening) errors are often not discovered until a device is already on the market. In this paper we present a reference model based approach to software conformance checking. Reference models enable the application of formal methods to software conformance checking, and provide a framework for rigorous testing. To illustrate the approach, we develop the reference model for a generic patient controlled analgesic infusion pump, and explain how it can be used to aid software conformance checking in a regulatory environment. A new form of document coupling called co-citation is defined as the frequency with which two documents are cited together. The co-citation frequency of two scientific papers can be determined by comparing lists of citing documents in the Science Citation Index and counting identical entries. Networks of co-cited papers can be generated for specific scientific specialties, and an example is drawn from the literature of particle physics. Co-citation patterns are found to differ significantly from bibliographic coupling patterns, but to agree generally with patterns of direct citation. Clusters of co-cited papers provide a new way to study the specialty structure of science. They may provide a new approach to indexing and to the creation of SDI profiles. Purpose – The purpose of this paper is to suggest an alternative to the widely used Times Cited criterion for analysing citation networks. The approach involves taking account of the natures of the papers that cite a given paper, so as to differentiate between papers that attract the same number of citations.Design methodology approach – ArticleRank is an algorithm that has been derived from Google's PageRank algorithm to measure the influence of journal articles. ArticleRank is applied to two datasets – a citation network based on an early paper on webometrics, and a self‐citation network based on the 19 most cited papers in the Journal of Documentation – using citation data taken from the Web of Knowledge database.Findings – ArticleRank values provide a different ranking of a set of papers from that provided by the corresponding Times Cited values, and overcomes the inability of the latter to differentiate between papers with the same numbers of citations. The difference in rankings between Times Cited ... Abstract Documents in computer-readable form can be used to provide information about other documents, i.e. those they cite. To do this efficiently requires procedures for computer recognition of citing statements. This is not easy, especially for multi-sentence citing statements. Computer recognition procedures have been developed which are accurate to the following extent: 73 of the words in statements selected by computer procedures as being citing statements are words which are correctly attributable to the corresponding documents. The retrieval effectiveness of computer-recognized citing statements was tested in the following way. First, for eight retrieval requests in inorganiic chemistry, average recall by search of Chemical Abstracts Service indexing and Chemical Abstracts abstract text words was found to be 50 . Words from citing statements referring to the papers to be retrieved were then added to the index terms and abstract words as additional access points, and searching was repeated. Average recall increased to 70 . Only words from citing statements published within a year of the cited papers were used. The retrieval effect of citing statement words alone (published within a year) without index or abstract terms was the following: average recall was 40 . When just the words of the titles of the cited papers were added to those citing statement words, average recall increased to 50 . The planted partition model (also known as the stochastic blockmodel) is a classical cluster-exhibiting random graph model that has been extensively studied in statistics, physics, and computer science. In its simplest form, the planted partition model is a model for random graphs on @math nodes with two equal-sized clusters, with an between-class edge probability of @math and a within-class edge probability of @math . Although most of the literature on this model has focused on the case of increasing degrees (ie. @math as @math ), the sparse case @math is interesting both from a mathematical and an applied point of view. A striking conjecture of Decelle, Krzkala, Moore and Zdeborov 'a based on deep, non-rigorous ideas from statistical physics gave a precise prediction for the algorithmic threshold of clustering in the sparse planted partition model. In particular, if @math and @math , then conjectured that it is possible to cluster in a way correlated with the true partition if @math , and impossible if @math for some sufficiently large @math . We prove half of their prediction, showing that it is indeed impossible to cluster if @math . Following , our work establishes a rigorous connection between the clustering problem, spin-glass models on the Bethe lattice and the so called reconstruction problem. This connection points to fascinating applications and open problems. In a document network such as a citation network of scientific documents, web-logs, etc., the content produced by authors exhibits their interest in certain topics. In addition some authors influence other authors' interests. In this work, we propose to model the influence of cited authors along with the interests of citing authors. Moreover, we hypothesize that apart from the citations present in documents, the context surrounding the citation mention provides extra topical information about the cited authors. However, associating terms in the context to the cited authors remains an open problem. We propose novel document generation schemes that incorporate the context while simultaneously modeling the interests of citing authors and influence of the cited authors. Our experiments show significant improvements over baseline models for various evaluation criteria such as link prediction between document and cited author, and quantitatively explaining unseen text. Over the past decade, physicists have developed deep but non-rigorous techniques for studying phase transitions in discrete structures. Recently, their ideas have been harnessed to obtain improved rigorous results on the phase transitions in binary problems such as random @math -SAT or @math -NAESAT (e.g., Coja-Oghlan and Panagiotou: STOC 2013). However, these rigorous arguments, typically centered around the second moment method, do not extend easily to problems where there are more than two possible values per variable. The single most intensely studied example of such a problem is random graph @math -coloring. Here we develop a novel approach to the second moment method in this problem. This new method, inspired by physics conjectures on the geometry of the set of @math -colorings, allows us to establish a substantially improved lower bound on the @math -colorability threshold. The new lower bound is within an additive @math of a simple first-moment upper bound and within @math of the physics conjecture. By comparison, the best previous lower bound left a gap of about @math , unbounded in terms of the number of colors [Achlioptas, Naor: STOC 2004]. Scholars are increasingly citing electronic “web references” which are not preserved in libraries or full text archives. WebCite is a new standard for citing web references. To “webcite” a document involves archiving the cited Web page through www.webcitation.org and citing the WebCite permalink instead of (or in addition to) the unstable live Web page. This journal has amended its “instructions for authors” accordingly, asking authors to archive cited Web pages before submitting a manuscript. Almost 200 other journals are already using the system. We discuss the rationale for WebCite, its technology, and how scholars, editors, and publishers can benefit from the service. Citing scholars initiate an archiving process of all cited Web references, ideally before they submit a manuscript. Authors of online documents and websites which are expected to be cited by others can ensure that their work is permanently available by creating an archived copy using WebCite and providing the citation information including the WebCite link on their Web document(s). Editors should ask their authors to cache all cited Web addresses (Uniform Resource Locators, or URLs) “prospectively” before submitting their manuscripts to their journal. Editors and publishers should also instruct their copyeditors to cache cited Web material if the author has not done so already. Finally, WebCite can process publisher submitted “citing articles” (submitted for example as eXtensible Markup Language [XML] documents) to automatically archive all cited Web pages shortly before or on publication. Finally, WebCite can act as a focussed crawler, caching retrospectively references of already published articles. Copyright issues are addressed by honouring respective Internet standards (robot exclusion files, no-cache and no-archive tags). Long-term preservation is ensured by agreements with libraries and digital preservation organizations. The resulting WebCite Index may also have applications for research assessment exercises, being able to measure the impact of Web services and published Web documents through access and Web citation metrics. @PARASPLIT [J Med Internet Res 2005;7(5):e60] Historically, papers have been physically bound to the journal in which they were published; but in the digital age papers are available individually, no longer tied to their respective journals. Hence, papers now can be read and cited based on their own merits, independently of the journal's physical availability, reputation, or impact factor (IF). We compare the strength of the relationship between journals' IFs and the actual citations received by their respective papers from 1902 to 2009. Throughout most of the 20th century, papers' citation rates were increasingly linked to their respective journals' IFs. However, since 1990, the advent of the digital age, the relation between IFs and paper citations has been weakening. This began first in physics, a field that was quick to make the transition into the electronic domain. Furthermore, since 1990 the overall proportion of highly cited papers coming from highly cited journals has been decreasing and, of these highly cited papers, the proportion not coming from highly cited journals has been increasing. Should this pattern continue, it might bring an end to the use of the IF as a way to evaluate the quality of journals, papers, and researchers. © 2012 Wiley Periodicals, Inc. We consider linear regression in the high-dimensional regime where the number of observations @math is smaller than the number of parameters @math . A very successful approach in this setting uses @math -penalized least squares (a.k.a. the Lasso) to search for a subset of @math parameters that best explain the data, while setting the other parameters to zero. Considerable amount of work has been devoted to characterizing the estimation and model selection problems within this approach. In this paper we consider instead the fundamental, but far less understood, question of . More precisely, we address the problem of computing p-values for single regression coefficients. On one hand, we develop a general upper bound on the minimax power of tests with a given significance level. On the other, we prove that this upper bound is (nearly) achievable through a practical procedure in the case of random design matrices with independent entries. Our approach is based on a debiasing of the Lasso estimator. The analysis builds on a rigorous characterization of the asymptotic distribution of the Lasso estimator and its debiased version. Our result holds for optimal sample size, i.e., when @math is at least on the order of @math . We generalize our approach to random design matrices with i.i.d. Gaussian rows @math . In this case we prove that a similar distributional characterization (termed standard distributional limit') holds for @math much larger than @math . Finally, we show that for optimal sample size, @math being at least of order @math , the standard distributional limit for general Gaussian designs can be derived from the replica heuristics in statistical physics. A model is presented of the manifestation of the birth and development of a scientific specialty in a collection of journal papers. The proposed model, Cumulative Advantage by Paper with Exemplars (CAPE) is an adaptation of Price's cumulative advantage model (D. Price, [1976]. Two modifications are made: (a) references are cited in groups by paper, and (b) the model accounts for the generation of highly cited exemplar references immediately after the birth of the specialty. This simple growth process mimics many characteristic features of real collections of papers, including the structure of the paper-to-reference matrix, the reference-per-paper distribution, the paper-per-reference distribution, the bibliographic coupling distribution, the cocitation distribution, the bibliographic coupling clustering coefficient distribution, and the temporal distribution of exemplar references. The model yields a great deal of insight into the process that produces the connectedness and clustering of a collection of articles and references. Two examples are presented and successfully modeled: a collection of 131 articles on MEMS RF (microelectromechnical systems radio frequency) switches, and a collection of 901 articles on the subject of complex networks. © 2005 Wiley Periodicals, Inc. Compressed sensing is a signal processing technique in which data is acquired directly in a compressed form. There are two modeling approaches that can be considered: the worst-case (Hamming) approach and a statistical mechanism, in which the signals are modeled as random processes rather than as individual sequences. In this paper, the second approach is studied. In particular, we consider a model of the form @math , where each comportment of @math is given by @math , where @math are i.i.d. Gaussian random variables, and @math are binary random variables independent of @math , and not necessarily independent and identically distributed (i.i.d.), @math is a random matrix with i.i.d. entries, and @math is white Gaussian noise. Using a direct relationship between optimum estimation and certain partition functions, and by invoking methods from statistical mechanics and from random matrix theory (RMT), we derive an asymptotic formula for the minimum mean-square error (MMSE) of estimating the input vector @math given @math and @math , as @math , keeping the measurement rate, @math , fixed. In contrast to previous derivations, which are based on the replica method, the analysis carried out in this paper is rigorous. Lack of trust is one of the most frequently cited reasons for consumers not purchasing from Internet vendors. During the last four years a number of empirical studies have investigated the role of trust in the specific context of e-commerce, focusing on different aspects of this multi-dimensional construct. However, empirical research in this area is beset by conflicting conceptualizations of the trust construct, inadequate understanding of the relationships between trust, its antecedents and consequents, and the frequent use of trust scales that are neither theoretically derived nor rigorously validated. The major objective of this paper is to provide an integrative review of the empirical literature on trust in e-commerce in order to allow cumulative analysis of results. The interpretation and comparison of different empirical studies on on-line trust first requires conceptual clarification. A set of trust constructs is proposed that reflects, both institutional phenomena (system trust) and personal and interpersonal forms of trust (dispositional trust, trusting beliefs, trusting intentions and trust-related behaviours), thus facilitating a multi-level and multi-dimensional analysis of research problems related to trust in e-commerce. Estimation of functions of @math variables is considered using ridge combinations of the form @math where the activation function @math is a function with bounded value and derivative. These include single-hidden layer neural networks, polynomials, and sinusoidal models. From a sample of size @math of possibly noisy values at random sites @math , the minimax mean square error is examined for functions in the closure of the @math hull of ridge functions with activation @math . It is shown to be of order @math to a fractional power (when @math is of smaller order than @math ), and to be of order @math to a fractional power (when @math is of larger order than @math ). Dependence on constraints @math and @math on the @math norms of inner parameter @math and outer parameter @math , respectively, is also examined. Also, lower and upper bounds on the fractional power are given. The heart of the analysis is development of information-theoretic packing numbers for these classes of functions. When we write or prepare to write a research paper, we always have appropriate references in mind. However, there are most likely references we have missed and should have been read and cited. As such a good citation recommendation system would not only improve our paper but, overall, the efficiency and quality of literature search. Usually, a citation's context contains explicit words explaining the citation. Using this, we propose a method that "translates" research papers into references. By considering the citations and their contexts from existing papers as parallel data written in two different "languages", we adopt the translation model to create a relationship between these two "vocabularies". Experiments on both CiteSeer and CiteULike dataset show that our approach outperforms other baseline methods and increase the precision, recall and f-measure by at least 5 to 10 , respectively. In addition, our approach runs much faster in the both training and recommending stage, which proves the effectiveness and the scalability of our work. With the advent of Substation Computer Systems dedicated to protection, control and data logging functions in a Substation, it becomes possible to develop new applications which can utilize the processing power available within the substation. The microcomputer based Symmetrical Component Distance Relay (SCDR) described in the references cited at the end of this paper possesses certain characteristics which facilitate real-time monitoring of positive sequence voltage phasor at the local power system bus. With a regression analysis the frequency and rate-of-change of frequency at the bus can also be determined from the positive sequence voltage phase angle. This paper describes the theoretical basis of these computations and describes results of experiments performed in the AEP power system simulation laboratory. Plans for future field tests on the AEP system are also outlined.