Yasuhiro Sogawa

2011 Special Issue: Estimating exogenous variables in data with more variables than observations

Many statistical methods have been proposed to estimate causal models in classical situations with fewer variables than observations. However, modern datasets including gene expression data increase the needs of high-dimensional causal modeling in challenging situations with orders of magnitude more variables than observations. 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 under orders of magnitude more variables than observations. Exogenous variables work as triggers that activate causal chains 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.

An experimental comparison of linear non-Gaussian causal discovery methods and their variants

Many multivariate Gaussianity-based techniques for identifying causal networks of observed variables have been proposed. These methods have several problems such that they cannot uniquely identify the causal networks without any prior knowledge. To alleviate this problem, a non-Gaussianity-based identification method LiNGAM was proposed. Though the LiNGAM potentially identifies a unique causal network without using any prior knowledge, it needs to properly examine independence assumptions of the causal network and search the correct causal network by using finite observed data points only. On another front, a kernel based independence measure that evaluates the independence more strictly was recently proposed. In addition, some advanced generic search algorithms including beam search have been extensively studied in the past. In this paper, we propose some variants of the LiNGAM method which introduce the kernel based method and the beam search enabling more accurate causal network identification. Furthermore, we experimentally characterize the LiNGAM and its variants in terms of accuracy and robustness of their identification.

Active learning for noisy oracle via density power divergence

The accuracy of active learning is critically influenced by the existence of noisy labels given by a noisy oracle. In this paper, we propose a novel pool-based active learning framework through robust measures based on density power divergence. By minimizing density power divergence, such as β-divergence and γ-divergence, one can estimate the model accurately even under the existence of noisy labels within data. Accordingly, we develop query selecting measures for pool-based active learning using these divergences. In addition, we propose an evaluation scheme for these measures based on asymptotic statistical analyses, which enables us to perform active learning by evaluating an estimation error directly. Experiments with benchmark datasets and real-world image datasets show that our active learning scheme performs better than several baseline methods.

Discovery of exogenous variables in data with more variables than observations

Many statistical methods have been proposed to estimate causal models in classical situations with fewer variables than observations. However, modern datasets including gene expression data increase the needs of high-dimensional causal modeling in challenging situations with orders of magnitude more variables than observations. 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 orders of magnitude more variables than observations. Exogenous variables work as triggers that activate causal chains 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.

Estimation of Parametric Roll in Random Seaways

This chapter attempts to provide a guideline for quantifying the magnitude of parametric roll of a ship in irregular seaways. First, in the light of physical model experiments with a scaled ship model in irregular water waves, it is shown that parametric roll of this ship model is a practically nonergodic process. Second, a guideline is developed by randomly sampling time series from the measured records. It is tentatively recommended that we should conduct physical and/or numerical experiments of more than 12-realizations and more than 360 excitation cycles for accurately estimating the magnitude of parametric rolling. The results of parametric roll estimation sufficiently above the threshold should be used for practical stability assessment. Finally, a container ship example is used to compare the numerical results with physical data.

Robust active learning for linear regression via density power divergence

The performance of active learning (AL) is crucially influenced by the existence of outliers in input samples. In this paper, we propose a robust pool-based AL measure based on the density power divergence. It is known that the density power divergence can be accurately estimated even under the existence of outliers within data. We further derive an AL scheme based on an asymptotic statistical analysis on the M-estimator. The performance of the proposed framework is investigated empirically using artificial and real-world data.