1,721,204 research outputs found
Issues concerning the approximation underlying the spectral representation theorem
Full text linkIn many important textbooks the formal statement of the Spectral RepresentationTheorem is followed by a process version, usually informal, stating thatany stationary stochastic process g is the limit in quadratic mean of asequence of processes, each consisting of a finite sum of harmonicoscillations with stochastic weights. The natural issues, whether the approximationerror is stationary, or whether at least it converges to zero uniformly int , have not been explicitly addressed in the literature. The paper shows that in allrelevant cases, for T unbounded the process convergence is not uniform in t. Equivalently, when T is unbounded the numberof harmonic oscillations necessary to approximate a stationary stochastic process with a preassigned accuracydepends on t . The conclusion is that the process version of the Spectral RepresentationTheorem should explicitely mention that in general the approximation of a stationary stochastic processby a finite sum of harmonic oscillations, given the accuracy, is valid for t belongingto a bounded subset of the real axis (of the set of integers in the discrete-parametercase)
Statistical relational learning for game theory
No full textIn this paper we motivate the use of models and algorithms from the area of Statistical Relational Learning (SRL) as a framework for the description and the analysis of games. SRL combines the powerful formalism of first-order logic with the capability of probabilistic graphical models in handling uncertainty in data and representing dependencies between random variables: for this reason, SRL models can be effectively used to represent several categories of games, including games with partial information, graphical games and stochastic games. Inference algorithms can be used to approach the opponent modeling problem, as well as to find Nash equilibria or Pareto optimal solutions. Structure learning algorithms can be applied, in order to automatically extract probabilistic logic clauses describing the strategies of an opponent with a high-level, human-interpretable formalism. Experiments conducted using Markov logic networks, one of the most used SRL frameworks, show the potential of the approach
Argumentation mining: State of the art and emerging trends
Full text linkArgumentation mining aims at automatically extracting structured arguments from unstructured textual documents. It has recently become a hot topic also due to its potential in processing information originating from the Web, and in particular from social media, in innovative ways. Recent advances in machine learning methods promise to enable breakthrough applications to social and economic sciences, policy making, and information technology: something that only a few years ago was unthinkable. In this survey article, we introduce argumentation models and methods, review existing systems and applications, and discuss challenges and perspectives of this exciting new research area
MARGOT: A web server for argumentation mining
Full text linkArgumentation mining is a recent challenge concerning the automatic extraction of arguments from unstructured textual corpora. Argumentation mining technologies are rapidly evolving and show a clear potential for application in diverse areas such as recommender systems, policy-making and the legal domain. There is a long-recognised need for tools that enable users to browse, visualise, search, and manipulate arguments and argument structures. There is, however, a lack of widely accessible tools. In this article we describe the technology behind MARGOT, the first online argumentation mining system designed to reach out to the wider community of potential users of these new technologies. We evaluate its performance and discuss its possible application in the analysis of content from various domains
The generalized dynamic factor model: Representation theory
No full textThis paper, along with the companion paper Forni, Hallin, Lippi, and Reichlin (2000, Review of Economics and Statistics 82, 540-554), introduces a new model-the generalized dynamic factor model-for the empirical analysis of financial and macroeconomic data sets characterized by a large number of observations both cross section and over time. This model provides a generalization of the static approximate factor model of Chamberlain (1983, Econometrica 51, 1181-1304) and Chamberlain and Rothschild (1983, Econometrica 51, 1305-1324) by allowing serial correlation within and across individual processes and of the dynamic factor model of Sargent and Sims (1977, in C.A. Sims (ed.), New Methods in Business Cycle Research, pp. 45-109) and Geweke (1977, in D.J. Aigner & A.S. Goldberger (eds.), Latent Variables in Socio-Economic Models, pp. 365-383) by allowing for nonorthogonal idiosyncratic terms. Whereas the companion paper concentrates on identification and estimation, here we give a full characterization of the generalized dynamic factor model in terms of observable spectral density matrices, thus laying a firm basis for empirical implementation of the model. Moreover, the common factors are obtained as limits of linear combinations of dynamic principal components. Thus the paper reconciles two seemingly unrelated statistical constructions
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