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‎notebooks/02-jax-idioms/04-optimized-learning.ipynb‎

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{
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"cell_type": "code",
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"execution_count": null,
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"id": "frequent-field",
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"id": "0",
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"metadata": {
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"tags": []
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "opened-virgin",
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"id": "1",
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"metadata": {
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"tags": []
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},
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{
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"cell_type": "markdown",
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"id": "lasting-express",
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"id": "2",
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"metadata": {},
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"source": [
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"# Optimized Learning\n",
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},
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{
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"cell_type": "markdown",
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"id": "forward-process",
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"id": "3",
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"metadata": {},
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"source": [
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"## Autograd to JAX\n",
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},
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{
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"cell_type": "markdown",
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"id": "4",
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"metadata": {},
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"source": [
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"## Example: Transforming a function into its derivative\n",
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "demanding-opportunity",
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"tags": []
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},
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Here's another example using a polynomial function:\n",
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{
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"cell_type": "code",
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"execution_count": null,
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"tags": []
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},
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Using grad to solve minimization problems\n",
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{
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"cell_type": "code",
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"execution_count": null,
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"tags": []
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"cell_type": "markdown",
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"id": "beautiful-theory",
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"metadata": {},
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"We know from calculus that the sign of the second derivative tells us whether we have a minima or maxima at a point.\n",
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "former-syracuse",
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"metadata": {},
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"outputs": [],
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"source": [
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},
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Grad is composable an arbitrary number of times. You can keep calling grad as many times as you like."
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]
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},
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"cell_type": "markdown",
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"id": "brazilian-atlas",
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"metadata": {},
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"## Maximum likelihood estimation\n",
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"cell_type": "code",
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"execution_count": null,
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},
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"cell_type": "markdown",
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"id": "atlantic-excellence",
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"metadata": {},
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"Our estimation task will necessitate calculating the total joint log likelihood of our data under a Gaussian model.\n",
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{
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"cell_type": "code",
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"execution_count": null,
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"cell_type": "markdown",
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"If you're wondering why we use `log_sigma` rather than `sigma`, it is a choice made for practical reasons.\n",
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"cell_type": "markdown",
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"Now, we can create the gradient function of our negative log likelihood.\n",
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{
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"cell_type": "code",
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"cell_type": "markdown",
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"Now, we can do the gradient descent step!"
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{
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"cell_type": "markdown",
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"And voila! We have gradient descended our way to the maximum likelihood parameters :)."
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]
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"cell_type": "markdown",
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"## Exercise: Where is the gold? It's at the minima!\n",
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"It should be evident from here that there are two minima in the function.\n",
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"Now, implement the optimization loop!"
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"## Exercise: programming a robot that only moves along one axis\n",
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"For your reference we have the function plotted below."
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‎src/dl_workshop/answers.py‎

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"""
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Answers to the main tutorial notebooks.
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"""
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import jax.numpy as np
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import numpy.random as npr
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from jax import grad
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def f(w):
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def df(w):

‎src/dl_workshop/jax_idioms.py‎

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def goldfield(x, y):
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"""All credit to https://www.analyzemath.com/calculus/multivariable/maxima_minima.html for this function."""
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def grad_ex_1():

‎src/setup.py‎

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"""Setup script."""
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from setuptools import find_packages, setup
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setup(name="dl_workshop", version="0.1", packages=find_packages())

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