AWS Pilot Project(s)

QTM 

Institute for quantitative theory and methods

Recall, Fall 2017 Proposal:

 

"I want to provide a hosted computing environment on AWS for teaching a large introductory data science class that my department will offer starting fall 2018.  More broadly, a group of faculty are putting together a proposal for the future of data science at Emory and I hope for this hosted environment to be adopted more broadly at Emory for teaching similar courses."

 

Data 8: The Foundations of Data Science

 

The UC Berkeley Foundations of Data Science course combines three perspectives: inferential thinking, computational thinking, and real-world relevance.

 

 

The course is offered in partnership with the Berkeley Division of Data Sciences.

 

data-8.github.io

Infrastructure

All of the software components of the course are maintained as open-source projects. We encourage you to contact us if you want any help using them. We also have prepared a guide on how to set up course infrastructure.

 

The OK autograder and submission system: The assignments depend on a Python-based autograder that includes client-side tests available to students at any time and server-side tests intended for correctness-based grading.

 

Hosted Computing Environment: We provide a hosted environment for our students to edit and execute their Notebooks. It includes two components, a Kubernetes-based deployment of JupyterHub that we have specifically designed for courses, and an assignment server that loads assignments into the students’ environment.

Current

 

  1. Mathematical intuition

  2. Definition

Kolmogorov

Every continuous function of several variables defined on the unit cube can be represented as a superposition of continuous functions of one variable and the operation of addition (1957).

f(x1,x2,…,xn)=∑i=12n+1fi(∑j=1nϕi,j(xj))f(x_1,x_2, \ldots, x_n) = \sum\limits_{i=1}^{2n+1}f_i(\sum\limits_{j=1}^{n}\phi_{i,j}(x_j))
f(x_1,x_2, \ldots, x_n) = \sum\limits_{i=1}^{2n+1}f_i(\sum\limits_{j=1}^{n}\phi_{i,j}(x_j))

Thus, it is as if there are no functions of several variables at all. There are only simple combinations of functions of one variable.

f1f_1
f_1
fif_i
f_i
f2n+1f_{2n+1}
f_{2n+1}
f(x1,x2,…,xn)=∑i=12n+1fi(∑j=1nϕi,j(xj))f(x_1,x_2, \ldots, x_n) = \sum\limits_{i=1}^{2n+1}f_i(\sum\limits_{j=1}^{n}\phi_{i,j}(x_j))
f(x_1,x_2, \ldots, x_n) = \sum\limits_{i=1}^{2n+1}f_i(\sum\limits_{j=1}^{n}\phi_{i,j}(x_j))
x1x_1
x_1
x2x_2
x_2
xnx_n
x_n
ϕ1,n\phi_{1,n}
\phi_{1,n}
ϕ2n+1,n\phi_{2n+1,n}
\phi_{2n+1,n}
ϕ2n+1,1\phi_{2n+1,1}
\phi_{2n+1,1}
ϕ1,1\phi_{1,1}
\phi_{1,1}
ϕ1,2\phi_{1,2}
\phi_{1,2}
ϕ2n+1,2\phi_{2n+1,2}
\phi_{2n+1,2}
ff
f
f(x1,x2,⋯ ,xn)=ϕ(∑i=1nwixi+θ)f(x_1,x_2,\cdots,x_n) = \phi(\sum\limits_{i=1}^n w_i x_i+\theta)
f(x_1,x_2,\cdots,x_n) = \phi(\sum\limits_{i=1}^n w_i x_i+\theta)
w1w_1
w_1
w2w_2
w_2
wnw_n
w_n
x1x_1
x_1
x2x_2
x_2
xnx_n
x_n
Rn→fR1\mathbb{R}^n \stackrel{f}{\rightarrow}\mathbb{R}^1
\mathbb{R}^n \stackrel{f}{\rightarrow}\mathbb{R}^1

  • one ''hidden layer"

  • one "node"

  • "activation" phi

  • "threshold" theta

ϕ\phi
\phi

Definition of a feedforward neural network 

Definition of a feedforward neural network 

f(x1,x2,⋯ ,xn)=∑i=12Wiϕi(∑j=1nwi,jxi+θi)f(x_1,x_2,\cdots,x_n) = \sum\limits_{i=1}^{2}W_i\phi_i(\sum\limits_{j=1}^n w_{i,j} x_i+\theta_i)
f(x_1,x_2,\cdots,x_n) = \sum\limits_{i=1}^{2}W_i\phi_i(\sum\limits_{j=1}^n w_{i,j} x_i+\theta_i)
w1,1w_{1,1}
w_{1,1}
w1,2w_{1,2}
w_{1,2}
w1,nw_{1,n}
w_{1,n}
x1x_1
x_1
x2x_2
x_2
xnx_n
x_n
Rn→fR1\mathbb{R}^n \stackrel{f}{\rightarrow}\mathbb{R}^1
\mathbb{R}^n \stackrel{f}{\rightarrow}\mathbb{R}^1

  • one ''hidden layer"

  • two "nodes"

W1W_1
W_1
W2W_2
W_2
w2,1w_{2,1}
w_{2,1}
w2,2w_{2,2}
w_{2,2}
w2,nw_{2,n}
w_{2,n}

Definition of a feedforward neural network 

(vector notation)

f(x⃗)=W⃗Tϕ(w⃗Tx⃗+θ⃗)+ηf(\vec{x}) = \vec{W}^T\phi(\vec{w}^T\vec{x}+\vec{\theta})+\eta
f(\vec{x}) = \vec{W}^T\phi(\vec{w}^T\vec{x}+\vec{\theta})+\eta
x⃗\vec{x}
\vec{x}
Rn→fR1\mathbb{R}^n \stackrel{f}{\rightarrow}\mathbb{R}^1
\mathbb{R}^n \stackrel{f}{\rightarrow}\mathbb{R}^1
W⃗\vec{W}
\vec{W}
w⃗\vec{w}
\vec{w}

Google's TensorFlow and ML workbench

  • Google Cloud Platform Datalab (https://cloud.google.com/datalab/)

  • TensorFlow and high-level framework (ML Workbench)

import google.datalab.contrib.mlworkbench.commands

Thank you!

Copy of Introduction to neural networks

By Jeremy Jacobson

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Copy of Introduction to neural networks

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