Machine Learning Trick of the Day (8): Instrumental Thinking2

· Read in · 1499 words · All posts in series · trick is unlike the others we've conjured. It will not reveal a clever manipulation of a probability or an integral or a derivative, or produce a code one-liner. But like all our other tricks, it will give us a powerful instrument in our ...

Machine Learning Trick of the Day (7): Density Ratio Trick2

· Read in · 1481 words · All posts in series · probability on its own is often an uninteresting thing. But when we can compare probabilities, that is when their full splendour is revealed. By comparing probabilities we are able form judgements; by comparing probabilities we can exploit the elements of our world that ...

Cognitive Machine Learning: Prologue4

· Read in · 980 words · All posts in series  · of inspiration is one thing we do not lack in machine learning. This is what, for me at least, makes  machine learning research such a rewarding and exciting area to work in. We gain inspiration from our traditional neighbours in statistics, signal processing and control engineering, information theory and ...

Machine Learning Trick of the Day (6): Tricks with Sticks2

· Read in  · Our first encounters with probability are often through a collection of simple games. The games of probability are played with coins, dice, cards, balls and urns, and sticks and strings. Using these games, we built an intuition that allows us to reason and act in ways that account for randomness in the world. But ...

Machine Learning Trick of the Day (5): Log Derivative Trick12

Machine learning involves manipulating probabilities. These probabilities are most often represented as normalised-probabilities or as log-probabilities. An ability to shrewdly alternate between these two representations is a vital step towards strengthening the probabilistic dexterity we need to solve modern machine learning problems. Today's trick, the log derivative trick, helps us to do just this, using the property of the derivative of the logarithm. This ...

Machine Learning Trick of the Day (4): Reparameterisation Tricks11

Our ability to rewrite statistical problems in an equivalent but different form, to reparameterise them, is one of the most general-purpose tools we have in mathematical statistics. We used reparameterisation in all the tricks we explored in this series so far: trick 1 re-expressed a log-partition function in terms of copies (replicas) of the marginal probability, trick 2 re-expressed a ...

Machine Learning Trick of the Day (3): Hutchinson's Trick6

Hutchinson's estimator  is a simple way to obtain a stochastic estimate of the trace of a matrix. This is a simple trick that uses randomisation to transform the algebraic problem of computing the trace into the statistical problem of computing an expectation of a quadratic function. The randomisation technique used in this trick is just one from a ...

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 and can provide many statistical and computational benefits. One popular setting where we can exploit such ...

Machine Learning Trick of the Day (1): Replica Trick3

'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 ...

A Statistical View of Deep Learning: Retrospective1

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 ...