Information-Theoretic Analysis of Serial Dependence and Cointegration

This paper is devoted to presenting wider characterizations of memory and cointegration in time series, in terms of information-theoretic statistics such as the entropy and the mutual information between pairs of variables. We suggest a nonparametric and nonlinear methodology for data analysis and for testing the hypotheses of long memory and the existence of a cointegrating relationship in a nonlinear context. This new framework represents a natural extension of the linear-memory concepts based on correlations. Finally, we show that our testing devices seem promising for exploratory analysis with nonlinearly cointegrated time series.Publicad

Convolutional Analysis Operator Learning: Dependence on Training Data

Convolutional analysis operator learning (CAOL) enables the unsupervised training of (hierarchical) convolutional sparsifying operators or autoencoders from large datasets. One can use many training images for CAOL, but a precise understanding of the impact of doing so has remained an open question. This paper presents a series of results that lend insight into the impact of dataset size on the filter update in CAOL. The first result is a general deterministic bound on errors in the estimated filters, and is followed by a bound on the expected errors as the number of training samples increases. The second result provides a high probability analogue. The bounds depend on properties of the training data, and we investigate their empirical values with real data. Taken together, these results provide evidence for the potential benefit of using more training data in CAOL.Comment: 5 pages, 2 figure

Analysis of dependence among size, rate and duration in internet flows

In this paper we examine rigorously the evidence for dependence among data size, transfer rate and duration in Internet flows. We emphasize two statistical approaches for studying dependence, including Pearson's correlation coefficient and the extremal dependence analysis method. We apply these methods to large data sets of packet traces from three networks. Our major results show that Pearson's correlation coefficients between size and duration are much smaller than one might expect. We also find that correlation coefficients between size and rate are generally small and can be strongly affected by applying thresholds to size or duration. Based on Transmission Control Protocol connection startup mechanisms, we argue that thresholds on size should be more useful than thresholds on duration in the analysis of correlations. Using extremal dependence analysis, we draw a similar conclusion, finding remarkable independence for extremal values of size and rate.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS268 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org