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Computing p-values of LiNGAM outputs via Multiscale Bootstrap

arXiv.org Machine Learning

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.


A Double Parametric Bootstrap Test for Topic Models

arXiv.org Machine Learning

Non-negative matrix factorization (NMF) is a technique for finding latent representations of data. The method has been applied to corpora to construct topic models. However, NMF has likelihood assumptions which are often violated by real document corpora. We present a double parametric bootstrap test for evaluating the fit of an NMF-based topic model based on the duality of the KL divergence and Poisson maximum likelihood estimation. The test correctly identifies whether a topic model based on an NMF approach yields reliable results in simulated and real data.


Statistical Testing on ASR Performance via Blockwise Bootstrap

arXiv.org Machine Learning

A common question being raised in automatic speech recognition (ASR) evaluations is how reliable is an observed word error rate (WER) improvement comparing two ASR systems, where statistical hypothesis testing and confidence intervals can be utilized to tell whether this improvement is real or only due to random chance. The bootstrap resampling method has been popular for such significance analysis which is intuitive and easy to use. However, this method fails in dealing with dependent data, which is prevalent in speech world - for example, ASR performance on utterances from the same speaker could be correlated. In this paper we present blockwise bootstrap approach - by dividing evaluation utterances into nonoverlapping blocks, this method resamples these blocks instead of original data. We show that the resulting variance estimator of absolute WER difference of two ASR systems is consistent under mild conditions. We also demonstrate the validity of blockwise bootstrap method on both synthetic and real-world speech data.


Bootstrap Site Blueprints - Programmer Books

#artificialintelligence

Since its debut in August 2011, Twitter Bootstrap, now simply Bootstrap, has become by far the most popular framework for empowering and enhancing frontend web design. With Version 3, Bootstrap reaches an exciting new milestone, introducing a mobile-first responsive grid, new and powerful LESS mixins, and a lean code base optimized for modern browsers. "Bootstrap Site Blueprints" is a hands-on guide to the inner workings of Bootstrap's latest and greatest development milestone. In an easy-to-follow, step-by-step format, you'll quickly get to know the ins and outs of Bootstrap while building a portfolio site, a WordPress theme, a business site, an e-commerce interface, and administration interface, and an upscale marketing site. While creating these layouts, you will quickly become comfortable with customizing Bootstrap to meet the needs of your specific projects.


Assessing and Improving Neural Network Predictions by the Bootstrap Algorithm

Neural Information Processing Systems

The bootstrap method offers an computation intensive alternative to estimate the predictive distribution for a neural network even if the analytic derivation is intractable. Theavailable asymptotic results show that it is valid for a large number of linear, nonlinear and even nonparametric regression problems. It has the potential tomodel the distribution of estimators to a higher precision than the usual normal asymptotics. It even may be valid if the normal asymptotics fail. However, the theoretical properties of bootstrap procedures for neural networks - especially nonlinear models - have to be investigated more comprehensively.