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What are Multivariate Techniques

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26/01/2021 1

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What are Multivariate Techniques

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Background

Signal

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Machine Learning - Multivariate Techniques

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Regression

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Regression -> model functional behaviour

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Multi-Variate Classification

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Classification: Different Approaches

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Signal Probability Instead of Hard Decisions

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Machine learning: Basic terminology

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Where are the neural networks?

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Neural Networks

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Perceptron

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The Biological Inspiration: the Neuron

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Feedforward Neural Network with One Hiden Layer

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Network Training

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Backpropagation

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Neural Network Output and Decision Boundaries

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Example of Overtraining

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Monitoring Overtraining

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Deep Neural Networks

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How do NNs work?

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How do NNs learn?

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How do NNs learn?

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How do NNs learn?

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Typical Applications

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Input Preprocesing

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Training

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Training: (Stochastic) Gradient Descent

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Training: more optimisers

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Underfitting and overtraining

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Overtraining solutions

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Deep-learning Neural Network

TensorFlowTM

MNIST example

Scientific application:

Higgs CP measurement at LHC

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Since 2010 new era in Machine Learning:

rapidly increasing areas of applications

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Neural network

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Since 2010 new era: rapidly increasing areas of applications

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Neural network

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Deep-Learning tutorial @ udacity

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https://www.udacity.com/course/

deep-learning--ud730

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Supervised Classifications

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Supervised Classifications

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Classifications for Detection

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Classifications for Ranking

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Logistic classifier: Linear model

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Softmax

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„One hot” encoding

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„One hot” encoding

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Optimisation: Cross-Entropy

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Multinomial logistic classification

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Optimisation of average loss

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Gradient decent

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Normalised input and output

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Normalised input and output

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Initialisation

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Training, validation, testing

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Gradient Descent

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Stochastic Gradient Descent

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SDG: optimising with momentum

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SDG: learning rate

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SDG: „black magic”

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Input – linear - output

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Linear models are linear

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Linear models are stable

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• This is still linear

• Lets introduce non-linearity

Linear models are here to stay

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RELU: Rectified Linear Unit

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Networks of RELU

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The Chain Rule

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Back - propagation

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Optimisation tricks

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Optimisation trick: dropout

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Deep networks

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Deep networks

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tensorflow.org/paper/whitepaper2015.pdf

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Hand-written diggits: MNIST

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Simple linear model

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Slides from M. Gorner tutorial

http://www.youtube.com/watch?v=vq2nnJ4g6NO

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TensorFlow full python code

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Slides from M. Gorner@youtube

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Simple linear model

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Slides from M. Gorner@youtube

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Multi-layer connected network

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Slides from M. Gorner@youtube

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Multi-layer connected network

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Slides from M. Gorner@youtube

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• \

All tricks count

Slides from M. Gorner@youtube 79

But noisy accuracy Use RELU

Exponentialy reduce learning rates Add drop-out

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Can do better with conv network

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References

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http://www.deeplearning.book.org

http://download.tensorflow.org/paper/whitepaper2015.pdf

https://www.tensorflow.org/

http://www.youtube.com/watch?v=vq2nnJ4g6NO

https://www.udacity.com/course/deep-learning--ud730

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