The success of deep learning has inspired a lot of recent interests in exploiting neural network structures for statistical inference and learning. In this paper, we review some popular deep neural network structures ...
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The success of deep learning has inspired a lot of recent interests in exploiting neural network structures for statistical inference and learning. In this paper, we review some popular deep neural network structures and techniques under the framework of nonparametric regression with measurement errors. In particular, we demonstrate how to use a fully connected feed-forward neural network to approximate the regression function f (x), explain how to use a normalizing flow to approximate the prior distribution of X, and detail how to construct an inference network to generate approximate posterior samples of X. After reviewing recent advances in variational inference for deep neural networks, such as the importance weighted autoencoder, doubly reparametrized gradient estimator, and nonlinear independent components estimation, we describe an inference procedure built upon these advances. An extensive numerical study is presented to compare the neural network approach with classical nonparametric methods, which suggests that the neural network approach is more flexible in accommodating different classes of regression functions and performs superior or comparable to the best available method in many settings.
Marginal maximum likelihood (MML) estimation is the preferred approach to fitting item response theory models in psychometrics due to the MML estimator's consistency, normality, and efficiency as the sample size t...
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Marginal maximum likelihood (MML) estimation is the preferred approach to fitting item response theory models in psychometrics due to the MML estimator's consistency, normality, and efficiency as the sample size tends to infinity. However, state-of-the-art MML estimation procedures such as the Metropolis-Hastings Robbins-Monro (MH-RM) algorithm as well as approximate MML estimation procedures such as variational inference (VI) are computationally time-consuming when the sample size and the number of latent factors are very large. In this work, we investigate a deep learning-based VI algorithm for exploratory item factor analysis (IFA) that is computationally fast even in large data sets with many latent factors. The proposed approach applies a deep artificial neural network model called an importance-weightedautoencoder (IWAE) for exploratory IFA. The IWAE approximates the MML estimator using an importance sampling technique wherein increasing the number of importance-weighted (IW) samples drawn during fitting improves the approximation, typically at the cost of decreased computational efficiency. We provide a real data application that recovers results aligning with psychological theory across random starts. Via simulation studies, we show that the IWAE yields more accurate estimates as either the sample size or the number of IW samples increases (although factor correlation and intercepts estimates exhibit some bias) and obtains similar results to MH-RM in less time. Our simulations also suggest that the proposed approach performs similarly to and is potentially faster than constrained joint maximum likelihood estimation, a fast procedure that is consistent when the sample size and the number of items simultaneously tend to infinity.
Adversarial variational Bayes (AVB) can infer the parameters of a generative model from the data using approximate maximum likelihood. The likelihood of deep generative models model is intractable. However, it can be ...
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ISBN:
(纸本)9783030617059;9783030617042
Adversarial variational Bayes (AVB) can infer the parameters of a generative model from the data using approximate maximum likelihood. The likelihood of deep generative models model is intractable. However, it can be approximated by a lower bound obtained in terms of an approximate posterior distribution of the latent variables of the data q. The closer q is to the actual posterior, the tighter the lower bound is. Therefore, by maximizing the lower bound one should expect to also maximize the likelihood. Traditionally, the approximate distribution q is Gaussian. AVB relaxes this limitation and allows for flexible distributions that may lack a closed-form probability density function. Implicit distributions obtained by letting a source of Gaussian noise go through a deep neural network are examples of these distributions. Here, we combine AVB with the importance weighted autoencoder, a technique that has been shown to provide a tighter lower bound on the marginal likelihood. This is expected to lead to a more accurate parameter estimation of the generative model via approximate maximum likelihood. We have evaluated the proposed method on three datasets, MNIST, Fashion MNIST, and Omniglot. The experiments show that the proposed method improves the test log-likelihood of a generative model trained using AVB.
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