andrew_gelman_stats andrew_gelman_stats-2014 andrew_gelman_stats-2014-2324 knowledge-graph by maker-knowledge-mining
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Introduction: Ben Murell writes: Our reply to Kinney and Atwal has come out (http://www.pnas.org/content/early/2014/04/29/1403623111.full.pdf) along with their response (http://www.pnas.org/content/early/2014/04/29/1404661111.full.pdf). I feel like they somewhat missed the point. If you’re still interested in this line of discussion, feel free to post, and maybe the Murrells and Kinney can bash it out in your comments! Background: Too many MC’s not enough MIC’s, or What principles should govern attempts to summarize bivariate associations in large multivariate datasets? Heller, Heller, and Gorfine on univariate and multivariate information measures Kinney and Atwal on the maximal information coefficient Mr. Pearson, meet Mr. Mandelbrot: Detecting Novel Associations in Large Data Sets Gorfine, Heller, Heller, Simon, and Tibshirani don’t like MIC The fun thing is that all these people are sending me their papers, and I’m enough of an outsider in this field that each of the
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1 Ben Murell writes: Our reply to Kinney and Atwal has come out (http://www. [sent-1, score-0.041]
2 If you’re still interested in this line of discussion, feel free to post, and maybe the Murrells and Kinney can bash it out in your comments! [sent-11, score-0.361]
3 Background: Too many MC’s not enough MIC’s, or What principles should govern attempts to summarize bivariate associations in large multivariate datasets? [sent-12, score-1.018]
4 Heller, Heller, and Gorfine on univariate and multivariate information measures Kinney and Atwal on the maximal information coefficient Mr. [sent-13, score-0.684]
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same-blog 1 1.0 2324 andrew gelman stats-2014-05-07-Once more on nonparametric measures of mutual information
Introduction: Ben Murell writes: Our reply to Kinney and Atwal has come out (http://www.pnas.org/content/early/2014/04/29/1403623111.full.pdf) along with their response (http://www.pnas.org/content/early/2014/04/29/1404661111.full.pdf). I feel like they somewhat missed the point. If you’re still interested in this line of discussion, feel free to post, and maybe the Murrells and Kinney can bash it out in your comments! Background: Too many MC’s not enough MIC’s, or What principles should govern attempts to summarize bivariate associations in large multivariate datasets? Heller, Heller, and Gorfine on univariate and multivariate information measures Kinney and Atwal on the maximal information coefficient Mr. Pearson, meet Mr. Mandelbrot: Detecting Novel Associations in Large Data Sets Gorfine, Heller, Heller, Simon, and Tibshirani don’t like MIC The fun thing is that all these people are sending me their papers, and I’m enough of an outsider in this field that each of the
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Introduction: Malka Gorfine writes: We noticed that the important topic of association measures and tests came up again in your blog, and we have few comments in this regard. It is useful to distinguish between the univariate and multivariate methods. A consistent multivariate method can recognise dependence between two vectors of random variables, while a univariate method can only loop over pairs of components and check for dependency between them. There are very few consistent multivariate methods. To the best of our knowledge there are three practical methods: 1) HSIC by Gretton et al. (http://www.gatsby.ucl.ac.uk/~gretton/papers/GreBouSmoSch05.pdf) 2) dcov by Szekely et al. (http://projecteuclid.org/euclid.aoas/1267453933) 3) A method we introduced in Heller et al (Biometrika, 2013, 503—510, http://biomet.oxfordjournals.org/content/early/2012/12/04/biomet.ass070.full.pdf+html, and an R package, HHG, is available as well http://cran.r-project.org/web/packages/HHG/index.html). A
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Introduction: Justin Kinney writes: I wanted to let you know that the critique Mickey Atwal and I wrote regarding equitability and the maximal information coefficient has just been published . We discussed this paper last year, under the heading, Too many MC’s not enough MIC’s, or What principles should govern attempts to summarize bivariate associations in large multivariate datasets? Kinney and Atwal’s paper is interesting, with my only criticism being that in some places they seem to aim for what might not be possible. For example, they write that “mutual information is already widely believed to quantify dependencies without bias for relationships of one type or another,” which seems a bit vague to me. And later they write, “How to compute such an estimate that does not bias the resulting mutual information value remains an open problem,” which seems to me to miss the point in that unbiased statistical estimates are not generally possible and indeed are often not desirable. Their
Introduction: Justin Kinney writes: Since your blog has discussed the “maximal information coefficient” (MIC) of Reshef et al., I figured you might want to see the critique that Gurinder Atwal and I have posted. In short, Reshef et al.’s central claim that MIC is “equitable” is incorrect. We [Kinney and Atwal] offer mathematical proof that the definition of “equitability” Reshef et al. propose is unsatisfiable—no nontrivial dependence measure, including MIC, has this property. Replicating the simulations in their paper with modestly larger data sets validates this finding. The heuristic notion of equitability, however, can be formalized instead as a self-consistency condition closely related to the Data Processing Inequality. Mutual information satisfies this new definition of equitability but MIC does not. We therefore propose that simply estimating mutual information will, in many cases, provide the sort of dependence measure Reshef et al. seek. For background, here are my two p
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Introduction: Mon : Crowdstorming a dataset Tues : Ken Rice presents a unifying approach to statistical inference and hypothesis testing Wed : The health policy innovation center: how best to move from pilot studies to large-scale practice? Thurs : Heller, Heller, and Gorfine on univariate and multivariate information measures Fri : Discovering general multidimensional associations Sat : “The graph clearly shows that mammography adds virtually nothing to survival and if anything, decreases survival (and increases cost and provides unnecessary treatment)” Sun : Honored oldsters write about statistics
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same-blog 1 0.96118128 2324 andrew gelman stats-2014-05-07-Once more on nonparametric measures of mutual information
Introduction: Ben Murell writes: Our reply to Kinney and Atwal has come out (http://www.pnas.org/content/early/2014/04/29/1403623111.full.pdf) along with their response (http://www.pnas.org/content/early/2014/04/29/1404661111.full.pdf). I feel like they somewhat missed the point. If you’re still interested in this line of discussion, feel free to post, and maybe the Murrells and Kinney can bash it out in your comments! Background: Too many MC’s not enough MIC’s, or What principles should govern attempts to summarize bivariate associations in large multivariate datasets? Heller, Heller, and Gorfine on univariate and multivariate information measures Kinney and Atwal on the maximal information coefficient Mr. Pearson, meet Mr. Mandelbrot: Detecting Novel Associations in Large Data Sets Gorfine, Heller, Heller, Simon, and Tibshirani don’t like MIC The fun thing is that all these people are sending me their papers, and I’m enough of an outsider in this field that each of the
Introduction: Malka Gorfine writes: We noticed that the important topic of association measures and tests came up again in your blog, and we have few comments in this regard. It is useful to distinguish between the univariate and multivariate methods. A consistent multivariate method can recognise dependence between two vectors of random variables, while a univariate method can only loop over pairs of components and check for dependency between them. There are very few consistent multivariate methods. To the best of our knowledge there are three practical methods: 1) HSIC by Gretton et al. (http://www.gatsby.ucl.ac.uk/~gretton/papers/GreBouSmoSch05.pdf) 2) dcov by Szekely et al. (http://projecteuclid.org/euclid.aoas/1267453933) 3) A method we introduced in Heller et al (Biometrika, 2013, 503—510, http://biomet.oxfordjournals.org/content/early/2012/12/04/biomet.ass070.full.pdf+html, and an R package, HHG, is available as well http://cran.r-project.org/web/packages/HHG/index.html). A
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Introduction: Justin Kinney writes: I wanted to let you know that the critique Mickey Atwal and I wrote regarding equitability and the maximal information coefficient has just been published . We discussed this paper last year, under the heading, Too many MC’s not enough MIC’s, or What principles should govern attempts to summarize bivariate associations in large multivariate datasets? Kinney and Atwal’s paper is interesting, with my only criticism being that in some places they seem to aim for what might not be possible. For example, they write that “mutual information is already widely believed to quantify dependencies without bias for relationships of one type or another,” which seems a bit vague to me. And later they write, “How to compute such an estimate that does not bias the resulting mutual information value remains an open problem,” which seems to me to miss the point in that unbiased statistical estimates are not generally possible and indeed are often not desirable. Their
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Introduction: Malka Gorfine, Ruth Heller, and Yair Heller write a comment on the paper of Reshef et al. that we discussed a few months ago. Just to remind you what’s going on here, here’s my quick summary from December: Reshef et al. propose a new nonlinear R-squared-like measure. Unlike R-squared, this new method depends on a tuning parameter that controls the level of discretization, in a “How long is the coast of Britain” sort of way. The dependence on scale is inevitable for such a general method. Just consider: if you sample 1000 points from the unit bivariate normal distribution, (x,y) ~ N(0,I), you’ll be able to fit them perfectly by a 999-degree polynomial fit to the data. So the scale of the fit matters. The clever idea of the paper is that, instead of going for an absolute measure (which, as we’ve seen, will be scale-dependent), they focus on the problem of summarizing the grid of pairwise dependences in a large set of variables. As they put it: “Imagine a data set with hundreds
Introduction: Justin Kinney writes: Since your blog has discussed the “maximal information coefficient” (MIC) of Reshef et al., I figured you might want to see the critique that Gurinder Atwal and I have posted. In short, Reshef et al.’s central claim that MIC is “equitable” is incorrect. We [Kinney and Atwal] offer mathematical proof that the definition of “equitability” Reshef et al. propose is unsatisfiable—no nontrivial dependence measure, including MIC, has this property. Replicating the simulations in their paper with modestly larger data sets validates this finding. The heuristic notion of equitability, however, can be formalized instead as a self-consistency condition closely related to the Data Processing Inequality. Mutual information satisfies this new definition of equitability but MIC does not. We therefore propose that simply estimating mutual information will, in many cases, provide the sort of dependence measure Reshef et al. seek. For background, here are my two p
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Introduction: Ben Murell writes: Our reply to Kinney and Atwal has come out (http://www.pnas.org/content/early/2014/04/29/1403623111.full.pdf) along with their response (http://www.pnas.org/content/early/2014/04/29/1404661111.full.pdf). I feel like they somewhat missed the point. If you’re still interested in this line of discussion, feel free to post, and maybe the Murrells and Kinney can bash it out in your comments! Background: Too many MC’s not enough MIC’s, or What principles should govern attempts to summarize bivariate associations in large multivariate datasets? Heller, Heller, and Gorfine on univariate and multivariate information measures Kinney and Atwal on the maximal information coefficient Mr. Pearson, meet Mr. Mandelbrot: Detecting Novel Associations in Large Data Sets Gorfine, Heller, Heller, Simon, and Tibshirani don’t like MIC The fun thing is that all these people are sending me their papers, and I’m enough of an outsider in this field that each of the
Introduction: Justin Kinney writes: Since your blog has discussed the “maximal information coefficient” (MIC) of Reshef et al., I figured you might want to see the critique that Gurinder Atwal and I have posted. In short, Reshef et al.’s central claim that MIC is “equitable” is incorrect. We [Kinney and Atwal] offer mathematical proof that the definition of “equitability” Reshef et al. propose is unsatisfiable—no nontrivial dependence measure, including MIC, has this property. Replicating the simulations in their paper with modestly larger data sets validates this finding. The heuristic notion of equitability, however, can be formalized instead as a self-consistency condition closely related to the Data Processing Inequality. Mutual information satisfies this new definition of equitability but MIC does not. We therefore propose that simply estimating mutual information will, in many cases, provide the sort of dependence measure Reshef et al. seek. For background, here are my two p
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Introduction: Malka Gorfine, Ruth Heller, and Yair Heller write a comment on the paper of Reshef et al. that we discussed a few months ago. Just to remind you what’s going on here, here’s my quick summary from December: Reshef et al. propose a new nonlinear R-squared-like measure. Unlike R-squared, this new method depends on a tuning parameter that controls the level of discretization, in a “How long is the coast of Britain” sort of way. The dependence on scale is inevitable for such a general method. Just consider: if you sample 1000 points from the unit bivariate normal distribution, (x,y) ~ N(0,I), you’ll be able to fit them perfectly by a 999-degree polynomial fit to the data. So the scale of the fit matters. The clever idea of the paper is that, instead of going for an absolute measure (which, as we’ve seen, will be scale-dependent), they focus on the problem of summarizing the grid of pairwise dependences in a large set of variables. As they put it: “Imagine a data set with hundreds
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