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Convergence Rates of Variational Inference in Sparse Deep Learning
Variational inference is becoming more and more popular for approximatin...
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Rate Optimal Variational Bayesian Inference for Sparse DNN
Sparse deep neural network (DNN) has drawn much attention in recent stud...
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Measurement error models: from nonparametric methods to deep neural networks
The success of deep learning has inspired recent interests in applying n...
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Variational Bayes: A report on approaches and applications
Deep neural networks have achieved impressive results on a wide variety ...
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Efficient Variational Inference for Sparse Deep Learning with Theoretical Guarantee
Sparse deep learning aims to address the challenge of huge storage consu...
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Linear-Nonlinear-Poisson Neuron Networks Perform Bayesian Inference On Boltzmann Machines
One conjecture in both deep learning and classical connectionist viewpoi...
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Loss convergence in a causal Bayesian neural network of retail firm performance
We extend the empirical results from the structural equation model (SEM)...
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Generalization Error Bounds for Deep Variational Inference
Variational inference is becoming more and more popular for approximating intractable posterior distributions in Bayesian statistics and machine learning. Meanwhile, a few recent works have provided theoretical justification and new insights on deep neural networks for estimating smooth functions in usual settings such as nonparametric regression. In this paper, we show that variational inference for sparse deep learning retains the same generalization properties than exact Bayesian inference. In particular, we highlight the connection between estimation and approximation theories via the classical bias-variance trade-off and show that it leads to near-minimax rates of convergence for Hölder smooth functions. Additionally, we show that the model selection framework over the neural network architecture via ELBO maximization does not overfit and adaptively achieves the optimal rate of convergence.
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