Chinese Edition: A Statistical View of Deep Learning (III)/ 从统计学角度来看深度学习

Colleagues from the Capital of Statistics, an online statistics community in China, have been kind enough to translate my third post in this series, A Statistical View of Deep Learning (III): Memory and Kernels,  in the hope that they might be of interest to machine learning and statistics researchers in China (and to Chinese readers). Find it here: 从统计学角度来看深度学习(3):记忆和核方法 Continue reading Chinese Edition: A Statistical View of Deep Learning (III)/ 从统计学角度来看深度学习

Chinese Edition: A Statistical View of Deep Learning (II)/ 从统计学角度来看深度学习

Colleagues from the Capital of Statistics, an online statistics community in China, have been kind enough to translate my second post in this series, A statistical View of Deep Learning (II): Auto-encoders and Free Energy,  in the hope that they might be of interest to machine learning and statistics researchers in China (and to Chinese readers). Find it here: 从统计学角度来看深度学习(2):自动编码器和自由能 Continue reading Chinese Edition: A Statistical View of Deep Learning (II)/ 从统计学角度来看深度学习

Chinese Edition: A statistical View of Deep Learning (I)/ 从统计学角度来看深度学习

Colleagues from the Capital of Statistics, an online statistics community in China, have been kind enough to translate my first post in this series, A statistical View of Deep Learning (I): Recursive GLMs,  in the hope that they might be of interest to machine learning and statistics researchers in China (and to Chinese readers). Find it here: 从统计学角度来看深度学习(1):递归广义线性模型   Continue reading Chinese Edition: A statistical View of Deep Learning (I)/ 从统计学角度来看深度学习

A Statistical View of Deep Learning (IV): Recurrent Nets and Dynamical Systems

Recurrent neural networks (RNNs) are now established as one of the key tools in the machine learning toolbox for handling large-scale sequence data. The ability to specify highly powerful models, advances in stochastic gradient descent, the availability of large volumes of … Continue reading A Statistical View of Deep Learning (IV): Recurrent Nets and Dynamical Systems

A Statistical View of Deep Learning (II): Auto-encoders and Free Energy

With the success of discriminative modelling using deep feedforward neural networks (or using an alternative statistical lens, recursive generalised linear models) in numerous industrial applications, there is an increased drive to produce similar outcomes with unsupervised learning. In this post, I'd like to explore the connections between denoising auto-encoders as a leading approach for unsupervised learning in deep learning, and density estimation in statistics. The statistical view I'll explore casts learning in denoising auto-encoders as that of inference in latent factor (density) models. Such a connection has a number of useful benefits and implications for our machine learning practice.

Continue reading "A Statistical View of Deep Learning (II): Auto-encoders and Free Energy"

A Statistical View of Deep Learning (I): Recursive GLMs

Deep learning and the use of deep neural networks [cite key="bishop1995neural"] are now established as a key tool for practical machine learning. Neural networks have an equivalence with many existing statistical and machine learning approaches and I would like to explore one of these views in this post. In particular, I'll look at the view of deep neural networks as recursive generalised linear models (RGLMs). Generalised linear models form one of the cornerstones of probabilistic modelling and are used in almost every field of experimental science, so this connection is an extremely useful one to have in mind. I'll focus here on what are called feedforward neural networks and leave a discussion of the statistical connections to recurrent networks to another post.

Continue reading "A Statistical View of Deep Learning (I): Recursive GLMs"

Variational Inference: Tricks of the Trade

The NIPS 2014 Workshop on Advances in Variational Inference was abuzz with new methods and ideas for scalable approximate inference. The concluding event of the workshop was a lively debate with David Blei, Neil Lawrence, Zoubin Ghahramani, Shinichi Nakajima and Matthias Seeger on the history, trends and open questions in variational inference. One of the questions posed to our panel and audience was: 'what are your variational inference tricks-of-the-trade?'

My current best-practice at present includes: stochastic approximation, Monte Carlo estimation, amortised inference and powerful software tools. But this is a though-provoking question that has has motivated me think in some more detail through my current variational inference tricks-of-the-trade, which are:
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Bayesian sparsity using spike-and-slab priors

I recently received some queries on our paper: S. Mohamed, K. Heller and Z. Ghahramani. Bayesian and L1 Approaches for Sparse Unsupervised Learning. International Conference on Machine Learning (ICML), June 2012 [cite key="mohamed2012sparse"]. The questions were very good and I thought it would be useful to post these for future reference. The paper looked at Bayesian and optimisation approaches for learning sparse models. For Bayesian models, we advocated the use of spike-and-slab sparse models and specified an adapted latent Gaussian model with an additional set of discrete latent variables to specify when a latent dimension is sparse or not. This … Continue reading Bayesian sparsity using spike-and-slab priors