arXiv subjects

Joe Suzuki

Publications and source records attributed to Joe Suzuki.

25 records · Page 2Linked to original sources

arXiv2014

Identifiability of an Integer Modular Acyclic Additive Noise Model and its Causal Structure Discovery

The notion of causality is used in many situations dealing with uncertainty. We consider the problem whether causality can be identified given data set generated by discrete random variables rather than continuous ones. In particular, for non-binary data, thus far it was only known that causality can be identified except rare cases. In this paper, we present necessary and sufficient condition for an integer modular acyclic additive noise (IMAN) of two variables. In addition, we relate bivariate and multivariate causal identifiability in a more explicit manner, and develop a practical algorithm to find the order of variables and their parent sets. We demonstrate its performance in applications to artificial data and real world body motion data with comparisons to conventional methods.

stat.ML↗

arXiv2014

Causal Discovery in a Binary Exclusive-or Skew Acyclic Model: BExSAM

Discovering causal relations among observed variables in a given data set is a major objective in studies of statistics and artificial intelligence. Recently, some techniques to discover a unique causal model have been explored based on non-Gaussianity of the observed data distribution. However, most of these are limited to continuous data. In this paper, we present a novel causal model for binary data and propose an efficient new approach to deriving the unique causal model governing a given binary data set under skew distributions of external binary noises. Experimental evaluation shows excellent performance for both artificial and real world data sets.

stat.ML↗

arXiv2013

A Construction of Bayesian Networks from Databases Based on an MDL Principle

This paper addresses learning stochastic rules especially on an inter-attribute relation based on a Minimum Description Length (MDL) principle with a finite number of examples, assuming an application to the design of intelligent relational database systems. The stochastic rule in this paper consists of a model giving the structure like the dependencies of a Bayesian Belief Network (BBN) and some stochastic parameters each indicating a conditional probability of an attribute value given the state determined by the other attributes' values in the same record. Especially, we propose the extended version of the algorithm of Chow and Liu in that our learning algorithm selects the model in the range where the dependencies among the attributes are represented by some general plural number of trees.

cs.AI↗

arXiv2012

Discovering causal structures in binary exclusive-or skew acyclic models

Discovering causal relations among observed variables in a given data set is a main topic in studies of statistics and artificial intelligence. Recently, some techniques to discover an identifiable causal structure have been explored based on non-Gaussianity of the observed data distribution. However, most of these are limited to continuous data. In this paper, we present a novel causal model for binary data and propose a new approach to derive an identifiable causal structure governing the data based on skew Bernoulli distributions of external noise. Experimental evaluation shows excellent performance for both artificial and real world data sets.

cs.LG↗

arXiv2010

The Hannan-Quinn Proposition for Linear Regression

We consider the variable selection problem in linear regression. Suppose that we have a set of random variables $X_1,...,X_m,Y,ε$ such that $Y=\sum_{k\in π}α_kX_k+ε$ with $π\subseteq \{1,...,m\}$ and $α_k\in {\mathbb R}$ unknown, and $ε$ is independent of any linear combination of $X_1,...,X_m$. Given actually emitted $n$ examples $\{(x_{i,1}...,x_{i,m},y_i)\}_{i=1}^n$ emitted from $(X_1,...,X_m, Y)$, we wish to estimate the true $π$ using information criteria in the form of $H+(k/2)d_n$, where $H$ is the likelihood with respect to $π$ multiplied by -1, and $\{d_n\}$ is a positive real sequence. If $d_n$ is too small, we cannot obtain consistency because of overestimation. For autoregression, Hannan-Quinn proved that, in their setting of $H$ and $k$, the rate $d_n=2\log\log n$ is the minimum satisfying strong consistency. This paper solves the statement affirmative for linear regression as well which has a completely different setting.

math.ST↗

arXiv2010

Nonparametric Estimation and On-Line Prediction for General Stationary Ergodic Sources

We proposed a learning algorithm for nonparametric estimation and on-line prediction for general stationary ergodic sources. We prepare histograms each of which estimates the probability as a finite distribution, and mixture them with weights to construct an estimator. The whole analysis is based on measure theory. The estimator works whether the source is discrete or continuous. If it is stationary ergodic, then the measure theoretically given Kullback-Leibler information divided by the sequence length $n$ converges to zero as $n$ goes to infinity. In particular, for continuous sources, the method does not require existence of a probability density function.

cs.IT↗

arXiv2010

A Generalization of the Chow-Liu Algorithm and its Application to Statistical Learning

We extend the Chow-Liu algorithm for general random variables while the previous versions only considered finite cases. In particular, this paper applies the generalization to Suzuki's learning algorithm that generates from data forests rather than trees based on the minimum description length by balancing the fitness of the data to the forest and the simplicity of the forest. As a result, we successfully obtain an algorithm when both of the Gaussian and finite random variables are present.

cs.IT↗