#!/usr/bin/env python
# coding: utf-8

# # Welcome to CS545: Machine Learning
# 
# ## Instructors
# 
# - [Chuck Anderson](http://www.cs.colostate.edu/~anderson) and [Dejan Markovikj](https://www.linkedin.com/in/markovikj/)

# ## Lectures
# - Tuesday and Thursday: 11:00 - 12:15, Computer Science Building, Room 130.  See "Overview" web page.
#     - All students can watch recorded lecture videos through Echo360 in Canvas
# - Presentation and discussions of lecture notes and assignments and all other topics of interest to you!

# ## Grading
# 
# - 6 or 7 Assignments: combinations of python implementations and applications of machine learning algorithms with text, math and visualizations that explain the algorithms and results.
# - Final assignment will be a project you design yourself.  It will count about as much as two regular assignments.
# - Check in solutions through Canvas as jupyter notebooks
# - Possibly some quizzes.
# - No exams!

# ## Questions?
# - What is [python](https://www.python.org/)?  
# - What is a [jupyter notebook](https://jupyter.org/)? This [tutorial](https://www.youtube.com/watch?v=3jZYC9rGrNg) is helpful.
# - And what do you mean by [machine learning](https://mitsloan.mit.edu/ideas-made-to-matter/machine-learning-explained)?

# # Machine Learning
# 
# ## Supervised Learning
# - Given samples of inputs and correct outputs, find a computational model that takes an input and produces approximately correct outputs, even for other inputs.
# - For example, predict stock prices, or classify a patient's symptoms into likely diagnoses.

# ## Unsupervised Learning
# - Given samples of input data, find similarities, dissimilarities, anomolies, trends, and low-dimensional representations of the data.
# - For example, identify network attacks, or a faulty sensor.

# ## Reinforcement Learning
# - Find sequences of decisions, or actions, that optimize some measure of success over time.
# - Requires trying many actions to see which ones produce good results.
# - For example, learn to take shortest paths, or learn to play chess.

# ## Examples of algorithms that we will cover:
# - Regression (supervised learning)
# - Classification (supervised learning)
# - Clustering (unsupervised learning)
# - Q-Learning (reinforcement learning)
# 
# All using deep learning (artificial neural networks), implemented ourselves mostly using `numpy` and sometimes using public frameworks, such as `pytorch` and `jax`.

# # Python
# 
# If you have no or just a little experience with python, it may be difficult for you to gain the necessary experience fast enough.
# 
# 1. True or False: Python code must be compiled before being run.
# 2. True or False: Variables in python can be assigned values of any type.
# 3. True or False: Python is to be avoided for big machine learning tasks because execution is so slow.
# 4. True or False: Python is free and available on all platforms.
# 5. True of False: Knowing python will not help you get a job.
# 
# Easy to install on your own laptop.  The [Anaconda distribution](https://www.anaconda.com/products/individual) is recommended.  

# [Popularity of Python](http://pypl.github.io/PYPL.html) judged by accesses of tutorials on github.
# 
# [Popularity of Python, and other languages, for Deep Learning](https://iglu.net/machine-learning-programming/)

# ## Python Packages We Will Use
# 
#     numpy
#     matplotlib
#     pandas
#     pytorch
#     jax 
#     
# and others

# In[ ]:


import numpy as np
import matplotlib.pyplot as plt

plt.plot(np.sin(0.1 * np.arange(100)));


# ## jupyter notebook
# 
# Finally, we have
# - literate programming
# - executable documents
# - reproducible results
# - super tutorials
# - excellent lab notebook for computer scientists
# - executable lecture notes!
# 
# Github, and some IDEs ([VSCode](https://code.visualstudio.com/docs/datascience/jupyter-notebooks)), can render them in browsers.

# ## Let's see what you know.
# 
# How would you do these?
# 
# 1. Assign to variable $W$ a 5 x 2 matrix (`numpy` array)  of random values between -0.1 and 0.1
# 2. Assign to variable  a $X$ 10 x 5 matrix of random values between 0 and 10.
# 3. Multiply two matrices, $X$ and $W$.
# 4. Take the transpose of $XW$, which is $(XW)^T$.
# 5. Multiply all elements of matrix $X$ by 2 and subtract 1 from all elements.
# 6. Iteratively make small adjustments to an initial matrix $W$ to make it converge on values in matrix $Z$.

# In[ ]:


# 1. Assign to variable W a 5 x 2 matrix (numpy array) of random values between -0.1 and 0.1


# In[ ]:


# 2. Assign to variable X a 10 x 5 matrix of random values between 0 and 10.


# In[ ]:


# 3. Multiply two matrices, X and W.


# In[ ]:


# 4. Take the transpose of XW.


# In[ ]:


# 5. Multiply all elements of matrix X by 2 and subtract 1 from all elements.


# In[ ]:


# Iteratively make small adjustments to an initial matrix `W` to
# make it converge on values in matrix `Z`.


# In[ ]:


# Iteratively make small adjustments to an initial matrix `W` to
# make it converge on values in matrix `Z`.

Z = np.array([1,2,3])
W = np.random.uniform(-10, 10, 3)
for step in range(300):
    W += 0.1 * (Z - W)
    if step % 30 == 0:
        print(f'{step=} {W=} {Z=}')


# # A Curious Story of High-Dimensional Spaces
# 
# Here is a wild statement.  In a high-dimensional space, most of the points lie on the surface of the hypercube shell!
# 
# Huh?  As discussed at [this stackexchange post](https://datascience.stackexchange.com/questions/27388/what-does-it-mean-when-we-say-most-of-the-points-in-a-hypercube-are-at-the-bound), consider the volume of the hypercube in $d$-dimensional space with each side of the hypercube being of length 1.
# 
# $$ 1 \cdot 1 \cdot 1 \cdot \ldots \cdot 1 = 1^d$$
# 
# Nothing surprising here.

# Now, let's look at the volume of the "interior" of this hypercube.  Let's define the interior as the space from 0.01 to 0.99 along each dimension. This would be
# 
# $$ 0.98 \cdot 0.98 \cdot 0.98 \ldots \cdot 0.98 = 0.98^d$$
# 
# So what?  Well, let's look at the results of these calculations.  First let's consider two dimensions.

# In[ ]:


0.98**2


# In[ ]:


d = 2
print(f'Total volume {1**d}.  Interior volume {0.98**d}')


# How about 10 dimensions, or 50?

# In[ ]:


d = 10
print(f'Total volume {1**d}.  Interior volume {0.98**d}')


# In[ ]:


d = 50
print(f'Total volume {1**d}.  Interior volume {0.98**d}')


# Okay, this is getting tedious.  Let's automate this and calculate interior volume for a range of dimensions up to 100, and plot it. 

# In[ ]:


def interior_volume(d):
    return (1 - 0.01 * 2) ** d

dims = np.arange(1, 100, 1)
plt.plot(dims, interior_volume(dims))
plt.xlabel('dimensions')
plt.ylabel('interior volume')
plt.grid('on')


# Keep going, up to 1000 dimensions.

# In[ ]:


dims = np.arange(1, 1000, 1)
plt.plot(dims, interior_volume(dims))
plt.xlabel('dimensions')
plt.ylabel('interior volume')
plt.grid('on')

plt.text(500, 0.6, 'WHOA!', fontsize=40);


# Go back to definition of `interior_volume` and try a thinner shell.

# # *It's the questions that drive us, Mr. Anderson.*   
# 
#                     - Agent Smith from The Matrix

# 1. What are the general categories of machine learning?
# 
# 1. What will I learn in this class?
# 1. Why are we using python and jupyter notebooks, and what are jupyter notebooks?
# 1. Will we be using GPUs?
# 1. What deep learning software frameworks are there, and which ones will we be using?

# 6. Why do you think you can teach this stuff?
# 1. How can I get a job in machine learning?
# 1. My math background is weak. Will I do okay in this course?
# 1. My python coding and debugging is weak. Will I do okay in this course?
# 1. Why are there no exams?