# Semi-supervised learning with deep generative models

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Abstract:

The ever-increasing size of modern data sets combined with the difficulty of obtaining label information has made semi-supervised learning one of the problems of significant practical importance in modern data analysis. We revisit the approach to semi-supervised learning with generative models and develop new models that allow for effecti...More

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Introduction

- Semi-supervised learning considers the problem of classification when only a small subset of the observations have corresponding class labels.
- The simplest algorithm for semi-supervised learning is based on a self-training scheme (Rosenberg et al, 2005) where the the model is bootstrapped with additional labelled data obtained from its own highly confident predictions; this process being repeated until some termination condition is reached
- These methods are heuristic and prone to error since they can reinforce poor predictions.

Highlights

- Semi-supervised learning considers the problem of classification when only a small subset of the observations have corresponding class labels
- Such problems are of immense practical interest in a wide range of applications, including image search (Fergus et al, 2009), genomics (Shi and Zhang, 2011), natural language parsing (Liang, 2005), and speech analysis (Liu and Kirchhoff, 2013), where unlabelled data is abundant, but obtaining class labels is expensive or impossible to obtain for the entire data set
- By far the best results were obtained using the stack of models M1 and M2. This combined model provides accurate test-set predictions across all conditions, and outperforms the previously best methods. We tested this deep generative model for supervised learning with all available labels, and obtain a test-set performance of 0.96%, which is among the best published results for this permutation-invariant MNIST classification task
- Since all the components of our model are parametrised by neural networks we can readily exploit convolutional or more general locally-connected architectures – and forms a promising avenue for future exploration
- We have developed new models for semi-supervised learning that allow us to improve the quality of prediction by exploiting information in the data density using generative models
- We have developed an efficient variational optimisation algorithm for approximate Bayesian inference in these models and demonstrated that they are amongst the most competitive models currently available for semisupervised learning

Results

- With which the most important results and figures can be reproduced, is available at http://github.com/dpkingma/nips14-ssl.
- This combined model provides accurate test-set predictions across all conditions, and outperforms the previously best methods
- The authors tested this deep generative model for supervised learning with all available labels, and obtain a test-set performance of 0.96%, which is among the best published results for this permutation-invariant MNIST classification task.
- The authors see that nearby regions of latent space correspond to similar writing styles, independent of the class; the left region represents upright writing styles, while the right-side represents slanted styles

Conclusion

**Discussion and Conclusion**

The approximate inference methods introduced here can be extended to the model’s parameters, harnessing the full power of variational learning.- The authors have developed an efficient variational optimisation algorithm for approximate Bayesian inference in these models and demonstrated that they are amongst the most competitive models currently available for semisupervised learning.
- The authors hope that these results stimulate the development of even more powerful semi-supervised classification methods based on generative models, of which there remains much scope

Summary

## Introduction:

Semi-supervised learning considers the problem of classification when only a small subset of the observations have corresponding class labels.- The simplest algorithm for semi-supervised learning is based on a self-training scheme (Rosenberg et al, 2005) where the the model is bootstrapped with additional labelled data obtained from its own highly confident predictions; this process being repeated until some termination condition is reached
- These methods are heuristic and prone to error since they can reinforce poor predictions.
## Results:

With which the most important results and figures can be reproduced, is available at http://github.com/dpkingma/nips14-ssl.- This combined model provides accurate test-set predictions across all conditions, and outperforms the previously best methods
- The authors tested this deep generative model for supervised learning with all available labels, and obtain a test-set performance of 0.96%, which is among the best published results for this permutation-invariant MNIST classification task.
- The authors see that nearby regions of latent space correspond to similar writing styles, independent of the class; the left region represents upright writing styles, while the right-side represents slanted styles
## Conclusion:

**Discussion and Conclusion**

The approximate inference methods introduced here can be extended to the model’s parameters, harnessing the full power of variational learning.- The authors have developed an efficient variational optimisation algorithm for approximate Bayesian inference in these models and demonstrated that they are amongst the most competitive models currently available for semisupervised learning.
- The authors hope that these results stimulate the development of even more powerful semi-supervised classification methods based on generative models, of which there remains much scope

- Table1: Benchmark results of semi-supervised classification on MNIST with few labels
- Table2: Semi-supervised classification on the SVHN dataset with 1000 labels
- Table3: Semi-supervised classification on the NORB dataset with 1000 labels

Reference

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