arXiv subjects

Shohei Shimizu

Publications and source records attributed to Shohei Shimizu.

40 records · Page 3Linked to original sources

arXiv2011

Finding Exogenous Variables in Data with Many More Variables than Observations

Many statistical methods have been proposed to estimate causal models in classical situations with fewer variables than observations (p >n). In this paper, we propose a method to find exogenous variables in a linear non-Gaussian causal model, which requires much smaller sample sizes than conventional methods and works even when p>>n. The key idea is to identify which variables are exogenous based on non-Gaussianity instead of estimating the entire structure of the model. Exogenous variables work as triggers that activate a causal chain in the model, and their identification leads to more efficient experimental designs and better understanding of the causal mechanism. We present experiments with artificial data and real-world gene expression data to evaluate the method.

stat.ML↗

arXiv2010

GroupLiNGAM: Linear non-Gaussian acyclic models for sets of variables

Finding the structure of a graphical model has been received much attention in many fields. Recently, it is reported that the non-Gaussianity of data enables us to identify the structure of a directed acyclic graph without any prior knowledge on the structure. In this paper, we propose a novel non-Gaussianity based algorithm for more general type of models; chain graphs. The algorithm finds an ordering of the disjoint subsets of variables by iteratively evaluating the independence between the variable subset and the residuals when the remaining variables are regressed on those. However, its computational cost grows exponentially according to the number of variables. Therefore, we further discuss an efficient approximate approach for applying the algorithm to large sized graphs. We illustrate the algorithm with artificial and real-world datasets.

cs.AI↗

arXiv2010

Computing p-values of LiNGAM outputs via Multiscale Bootstrap

Structural equation models and Bayesian networks have been widely used to study causal relationships between continuous variables. Recently, a non-Gaussian method called LiNGAM was proposed to discover such causal models and has been extended in various directions. An important problem with LiNGAM is that the results are affected by the random sampling of the data as with any statistical method. Thus, some analysis of the statistical reliability or confidence level should be conducted. A common method to evaluate a confidence level is a bootstrap method. However, a confidence level computed by ordinary bootstrap method is known to be biased as a probability-value ($p$-value) of hypothesis testing. In this paper, we propose a new procedure to apply an advanced bootstrap method called multiscale bootstrap to compute confidence levels, i.e., p-values, of LiNGAM outputs. The multiscale bootstrap method gives unbiased $p$-values with asymptotic much higher accuracy. Experiments on artificial data demonstrate the utility of our approach.

stat.ML↗

arXiv2006

Estimation of linear, non-gaussian causal models in the presence of confounding latent variables

The estimation of linear causal models (also known as structural equation models) from data is a well-known problem which has received much attention in the past. Most previous work has, however, made an explicit or implicit assumption of gaussianity, limiting the identifiability of the models. We have recently shown (Shimizu et al, 2005; Hoyer et al, 2006) that for non-gaussian distributions the full causal model can be estimated in the no hidden variables case. In this contribution, we discuss the estimation of the model when confounding latent variables are present. Although in this case uniqueness is no longer guaranteed, there is at most a finite set of models which can fit the data. We develop an algorithm for estimating this set, and describe numerical simulations which confirm the theoretical arguments and demonstrate the practical viability of the approach. Full Matlab code is provided for all simulations.

cs.AI↗