Machine Learning

Getting Started

DeepLearning.TV YouTube playlist -- good starter!

Tuts

UFLDL Stanford (Deep Learning) Tutorial

Principles of training multi-layer neural network using backpropagation <-- Great visual guide!

Courses

Neural Networks for Machine Learning — Geoffrey Hinton, UToronto

- Coursera course
- Vids (on YouTube)
- same, better organized
- Intro vid for course
- Hinton's homepage
- Bayesian Nets Tutorial -- helpful for later parts of Hinton

Deep learning at Oxford 2015 (Nando de Freitas)

Notes for Andrew Ng's Coursera course.

Hugo Larochelle: Neural networks class - Université de Sherbrooke

Karpathy -- CS231n

Boltzmann Machines

Boltzmann Distribution connects the probability of a system being in a certain state with the energy of that state: $P(s)\propto e^{{-kE_{s}}}$ where $E_{s}$ is the energy for that state.

So we can write: $P(s)={\frac {1}{Z}}e^{{-kE_{s}}}$ where $Z$ is the PARTITION FUNCTION (energy summed over all possible states). Reversing we can write $E_{s}=-{\frac {1}{k}}ln(ZP(s))$

IIUC there is a wide class of systems that settle down into a Boltzmann distribution.

Each (binary) vector of unit-outputs creates a corresponding Energy state. Let's assume these energy states form a Boltzmann distribution.

Then we can calculate the probability of a given unit's state being ON just by knowing the system's energy gap between that unit being ON and OFF: $p_{{\text{i=on}}}={\frac {1}{1+\exp(-{\frac {\Delta E_{i}}{T}})}}$ where $\Delta E_{i}=E_{{\text{i=off}}}-E_{{\text{i=on}}}$ (working here)

Yup that's a good ole Sigmoid!

So if you seed your network with a random input vector (10001010110...), keep choosing random nodes & updating them using the above probability logic, eventually it should settle into a (locally)maximally probable state.

So, let's say you want it to recognise 3 particular shapes: 111 000 000, 000 111 000 and 000 000 111. If it's weights are set up just right, and you throw in 001 111 000, it should converge to 000 111 000 -- as the closest local energy basin.

That demonstrate its retrieval ability. But how about its storage ability?

i.e. If you feed in those three training images, we need some way of twiddling the weights to create 3 appropriate basins.

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Think: Hopfield Net, but each neuron stochastically has state 0 or 1. Prob(state <- 1) = sigma(-z) where z = preactivation.

Boltzmann distribution: Wikipedia Susskind lecture

Hopfield to Boltzmann http://haohanw.blogspot.co.uk/2015/01/boltzmann-machine.html

Hinton's Lecture, then:

https://en.wikipedia.org/wiki/Boltzmann_machine

http://www.scholarpedia.org/article/Boltzmann_machine

Hinton (2010) -- A Practical Guide to Training Restricted Boltzmann Machines

https://www.researchgate.net/publication/242509302_Learning_and_relearning_in_Boltzmann_machines

Papers

Applying Deep Learning To Enhance Momentum Trading Strategies In Stocks

- Hinton, Salakhutdinov (2006) -- Reducing the Dimensionality of Data with Neural Networks

Books

Nielsen -- Neural Networks and Deep Learning <-- online book

http://www.deeplearningbook.org/

https://page.mi.fu-berlin.de/rojas/neural/ <-- Online book

S/W

http://playground.tensorflow.org

TensorFlow in IPython YouTube (5 vids)

SwiftNet <-- My own back propagating NN (in Swift)

Misc

Oxford AI/Trader

Links: https://github.com/memo/ai-resources

http://colah.github.io/posts/2014-03-NN-Manifolds-Topology/ <-- Great article!

http://karpathy.github.io/2015/05/21/rnn-effectiveness/

https://www.youtube.com/watch?v=gfPUWwBkXZY <-- Hopfield vid

http://www.gitxiv.com/ <-- Amazing projects here!