<b>NonpModelCheck</b>: An <i>R</i> Package for Nonparametric Lack-of-Fit Testing and Variable Selection

Zambom, Adriano Zanin; Akritas, Michaël G.

doi:10.18637/jss.v077.i10

Cited by 4 publications

(2 citation statements)

References 34 publications

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“…Investigators have found that a linear model taking log(Y ) as response and 4 out of the 8 covariates as predictors describe the data well (see [81,Section 9.4] and also [81,Section 10.6]). In particular, this linear model can be [5], VSURF [54], npvarselec [148], and MMPC [83] (all using their default settings). The selected variables, obtained by the different methods, are shown in Table 6.…”

Section: Surgical Datamentioning

confidence: 99%

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Kernel Partial Correlation Coefficient -- a Measure of Conditional Dependence

Huang¹,

Deb²,

Sen³

2020

Preprint

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In this paper we propose and study a class of simple, nonparametric, yet interpretable measures of conditional dependence between two random variables Y and Z given a third variable X, all taking values in general topological spaces. The population version of any of these nonparametric measures -defined using the theory of reproducing kernel Hilbert spaces (RKHSs) -captures the strength of conditional dependence and it is 0 if and only if Y and Z are conditionally independent given X, and 1 if and only if Y is a measurable function of Z and X. Thus, our measure -which we call kernel partial correlation (KPC) coefficient -can be thought of as a nonparametric generalization of the classical partial correlation coefficient that possesses the above properties when (X, Y, Z) is jointly normal. We describe two consistent methods of estimating KPC. Our first method of estimation is graph-based and utilizes the general framework of geometric graphs, including K-nearest neighbor graphs and minimum spanning trees. A sub-class of these estimators can be computed in near linear time and converges at a rate that automatically adapts to the intrinsic dimensionality of the underlying distribution(s). Our second strategy involves direct estimation of conditional mean embeddings using cross-covariance operators in the RKHS framework. Using these empirical measures we develop forward stepwise (high-dimensional) nonlinear variable selection algorithms. We show that our algorithm, using the graph-based estimator, yields a provably consistent model-free variable selection procedure, even in the high-dimensional regime when the number of covariates grows exponentially with the sample size, under suitable sparsity assumptions. Extensive simulation and real-data examples illustrate the superior performance of our methods compared to existing procedures. The recent conditional dependence measure proposed by Azadkia and Chatterjee [5] can also be viewed as a special case of our general framework.

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Section: Surgical Datamentioning

confidence: 99%

“…It can be seen the variables selected by KFOCI (with 1-NN, 2-NN, 3-NN graphs) are very similar to those selected by the carefully analyzed linear regression approach 20 . Further, KFOCI selects the same set of variables as many well-implemented variable selection algorithms such as VSURF [54], npvarselec [148], and MMPC [83].…”

Section: Surgical Datamentioning

confidence: 99%