Conditional Dependence via U-Statistics Pruning
The problem of measuring conditional dependence between two random phenomena arises when a third one (a confounder) has a potential influence on the amount of information between them. A typical issue in this challenging problem is the inversion of ill-conditioned autocorrelation matrices. This paper presents a novel measure of conditional dependence based on the use of incomplete unbiased statistics of degree two, which allows to re-interpret independence as uncorrelatedness on a finite-dimensional feature space. This formulation enables to prune data according to observations of the confounder itself, thus avoiding matrix inversions altogether. The proposed approach is articulated as an extension of the Hilbert-Schmidt independence criterion, which becomes expressible through kernels that operate on 4-tuples of data.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
On The Energy Statistics of Feature Maps in Pruning of Neural Networks with Skip-Connections
We propose a new structured pruning framework for compressing Deep Neural Networks (DNNs) with skip connections, based on measuring the statistical dependency of hidden layers and predicted outputs. The dependence measur…
Tail Risk Analysis for Financial Time Series
This book chapter illustrates how to apply extreme value statistics to financial time series data. Such data often exhibits strong serial dependence, which complicates assessment of tail risks. We discuss the two main ap…
Time SeriesNonparametric Tests of Conditional Independence for Time Series
We propose consistent nonparametric tests of conditional independence for time series data. Our methods are motivated from the difference between joint conditional cumulative distribution function (CDF) and the product o…
Time SeriesTime Series AnalysisConditional Independence Test Based on Transport Maps
Testing conditional independence between two random vectors given a third is a fundamental and challenging problem in statistics, particularly in multivariate nonparametric settings due to the complexity of conditional s…
A Projection Based Conditional Dependence Measure with Applications to High-dimensional Undirected Graphical Models
Measuring conditional dependence is an important topic in statistics with broad applications including graphical models. Under a factor model setting, a new conditional dependence measure based on projection is proposed.…