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Machine Learning: The Bare Math Behind Libraries - Supervised Learning

Machine Learning: The Bare Math Behind Libraries - Supervised Learning

During this presentation, we will answer how much you’ll need to invest in a superhero costume to be as popular as Superman. We will generate a unique logo which will stand against the ever popular Batman and create new superhero teams. We shall achieve it using linear regression and neural networks.

Machine learning is one of the hottest buzzwords in technology today as well as one of the most innovative fields in computer science – yet people use libraries as black boxes without basic knowledge of the field. In this session, we will strip them to bare math, so next time you use a machine learning library, you’ll have a deeper understanding of what lies underneath.

During this session, we will first provide a short history of machine learning and an overview of two basic teaching techniques: supervised and unsupervised learning.

We will start by defining what machine learning is and equip you with an intuition of how it works. We will then explain the gradient descent algorithm with the use of simple linear regression to give you an even deeper understanding of this learning method. Then we will project it to supervised neural networks training.

rauluka7

April 23, 2020
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  1. Machine Learning „Field of study that gives computers the ability

    to learn without being explicitly programmed.” Arthur Samuel
  2. Machine Learning „I consider every method that needs training as

    intelligent or machine learning method.” Our Lecturer
  3. Supervised learning • Build your model that performs particular task:

    – Prepare data set consisting of examples & expected outputs
  4. Supervised learning • Build your model that performs particular task:

    – Prepare data set consisting of examples & expected outputs – Present examples to your model
  5. Supervised learning • Build your model that performs particular task:

    – Prepare data set consisting of examples & expected outputs – Present examples to your model – Check how it responds (model’s output values)
  6. Supervised learning • Build your model that performs particular task:

    – Prepare data set consisting of examples & expected outputs – Present examples to your model – Check how it responds (model’s output values) – Adjust model’s params by comparing output values with expected output values
  7. Neural Networks • Inspired by biological brain mechanisms • Many

    applications: – Computer vision – Speech recognition – Compression
  8. Artificial Neuron • Inputs (x 1, … , x n

    ) are features of single example • Multiply each input by weight, sum it and put the sum as an argument of activation function w 1 w 2 w n w 0 Σ x 1 x 2 x n ... s y
  9. Activation function • Sigmoid – Maps sum of neurons signals

    to value from 0 to 1 – Continous, nonlinear – If input is positive it gives values > 0.5 f (x)= 1 1+e(−βx)
  10. Linear Regression • Method for modelling relationship between variables •

    Simplest form: how x relates to y • Examples: – House size vs house price – Voltage vs electric current
  11. Costume price vs number of issues • For given amount

    of money predict in how many comic book issues you’ll appear. Costume price(x) Number of issues (y) 240 6370 480 8697 ... ... 26 2200
  12. Linear regression • Let's have a function: f (x ,Θ)=Θ1

    x+Θ0 f (x,Θ)−number of comicbookissues x−costume price Θ−parameters
  13. Objective function Q(Θ)= 1 2 N ∑ j=0 N (f

    ( xj ,Θ)−y j )2 Q(Θ)−objectivefunction N−numberof datasamples j−indexof particulardatasample
  14. Objective function Q(Θ)= 1 2 N ∑ j=0 N (f

    ( xj ,Θ)−y j )2 Q(Θ)−objectivefunction N−numberof datasamples j−indexof particulardatasample
  15. Objective function Q(Θ)= 1 2 N ∑ j=0 N (f

    ( xj ,Θ)−y j )2 Q(Θ)−objectivefunction N−numberof datasamples j−indexof particulardatasample
  16. Objective function Q(Θ)= 1 2 N ∑ j=0 N (f

    ( xj ,Θ)−y j )2 Q(Θ)−objectivefunction N−numberof datasamples j−indexof particulardatasample
  17. Gradient descent • Find the minimum of the objective function

    • Iteratively update function parameters: Θ0 (t +1)=Θ0 (t)−α 1 N ∑ j=0 N (f ( xj ,Θ)− y j ) Θ1 (t +1)=Θ1 (t )−α 1 N ∑ j=0 N (f (xj ,Θ)− yj ) x t−number of iteration α−learning step
  18. Gradient descent • Find the minimum of the objective function

    • Iteratively update function parameters: Θ0 (t +1)=Θ0 (t)−α 1 N ∑ j=0 N (f ( xj ,Θ)− y j ) Θ1 (t +1)=Θ1 (t )−α 1 N ∑ j=0 N (f (xj ,Θ)− yj ) x t−number of iteration α−learning step
  19. Gradient descent • Find the minimum of the objective function

    • Iteratively update function parameters: Θ0 (t +1)=Θ0 (t)−α 1 N ∑ j=0 N (f ( xj ,Θ)− y j ) Θ1 (t +1)=Θ1 (t )−α 1 N ∑ j=0 N (f (xj ,Θ)− yj ) x t−number of iteration α−learning step
  20. NN – compute error +1 +1 x 1 x 2

    y ( y−expected output)2
  21. NN – backpropagation step • Use gradient descent and computed

    error • Update every weight of every neuron from hidden and output layer
  22. NN – backpropagation step +1 +1 x 1 x 2

    y ( y−expected output)2
  23. Real life problem • You said it can solve non

    linear problems, let's generate superhero logo using it.
  24. Call to Action! • Implement linear regression and simple neural

    network in your favourite programming language • Don’t care about its performance • Check how it works – generate your data sets, get simple ones from the Internet • You’ll gain intuition and understand basic mathematical aparathus
  25. Bibliography • Presentation + code: https://bitbucket.org/medwith/public/downloads/mluvr-coffeJugPart1.zip • https://www.coursera.org/learn/machine-learning • https://www.coursera.org/specializations/deep-learning

    • Math for Machine Learning - Amazon Training and Certification • Linear and Logistic Regression - Amazon Training and Certification • Grus J., Data Science from Scratch: First Principles with Python • Patterson J., Gibson A., Deep Learning: A Practitioner's Approach • Trask A., Grokking Deep Learning • Stroud K. A., Booth D. J, Engineering Mathematics • https://github.com/massie/octave-nn- neural network Octave implementation • https://www.desmos.com/calculator/dnzfajfpym - Nanananana … Batman equation ;) • https://xkcd.com/605/ - extrapolating ;) • http://dilbert.com/strip/2013-02-02 - Dilbert & Machine Learning