# Machine Learning Trick of the Day (2): Gaussian Integral Trick

Today's trick, the Gaussian integral trick, is one that allows us to re-express a (potentially troublesome) function in an alternative form, in particular, as an integral of a Gaussian against another function — integrals against a Gaussian turn out not to be too troublesome … Continue reading Machine Learning Trick of the Day (2): Gaussian Integral Trick

# Machine Learning Trick of the Day (1): Replica Trick

'Tricks' of all sorts are used throughout machine learning, in both research and in production settings. These tricks allow us to address many different types of data analysis problems, being roughly of either an analytical, statistical, algorithmic, or numerical flavour. Today's trick is in the analytical class and comes to us from statistical physics: the popular Replica trick. The replica trick [cite key="engel2001statistical"][cite key="sharp2011effective"][cite key="opper1995statistical"] is used for analytical computation of log-normalising constants (or log-partition functions). More formally, the replica trick provides one of the tools needed for a replica analysis of a probabilistic model — a theoretical analysis of the the properties and expected behaviour of a model. Replica … Continue reading Machine Learning Trick of the Day (1): Replica Trick

# A Statistical View of Deep Learning: Retrospective

Over the past 6 months, I've taken to writing a series of posts (one each month) on a statistical view of deep learning with two principal motivations in mind. The first was as a personal exercise to make concrete and to test the limits of the way that I think about, and use deep learning in my every day work. The second, was to highlight important statistical connections and implications of deep learning that I do not see being made in the popular courses, reviews and books on deep learning, but which are extremely important to keep in mind. Post Links and Summary Links to each post with a short … Continue reading A Statistical View of Deep Learning: Retrospective

# A Statistical View of Deep Learning (VI): What is Deep?

Throughout this series, we have discussed deep networks by examining prototypical instances of these models, e.g., deep feed-forward networks, deep auto-encoders, deep generative models, but have not yet interrogated the key word we have been using. We have not posed the question what … Continue reading A Statistical View of Deep Learning (VI): What is Deep?

# 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 (III): Memory and Kernels

Memory, the ways in which we remember and recall past experiences and data to reason about future events, is a term used frequently in current literature. All models in machine learning consist of a memory that is central to their usage. We … Continue reading A Statistical View of Deep Learning (III): Memory and Kernels

# 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.

# 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.