Calvo Machine Learning Lecture (#167)

* update lecture on gradient method

* fix the title levels

* add tag in calvo

* update aligned

* update aligned

* update first regression

* install statsmodel and update code

* update regressions

* minor update to improve code efficiency

* Tom's July 6 edits of calvo machine learning lecture

* update calvo for faster descent

* Rename equation labels

* update calvo_gradient with new section on more structured approach

* delete irrelevant part

* Tom's July 13 edits of calvo ML lecture

* update notes

* update lecture with new notes

* fix two small typos

* upload the old version

* update old version with correct note

* add old version into TOC

* fix everything in the gradient computation!

* update compute_μ for better clarity

* Update formulas and compute closed form gradient

* update two sentences and collect formulas

* Tom's edits of calvo_gradient lecture

* Tom's second edits of calvo_gradient, July 16

* Tom's July 17 edits of calvo_ML lecture

* Tom's July 18 edits of calvoML lecture

* keep a copy of experiments

* update lecture with notes

* update lecture with new notes

* Tom's July 21 edits of calvo_ml lecture

* FIX: align* to aligned

* ENH: enable sphinx-proof and use prf:definition

* small change on the printing of the decision rules

---------

Co-authored-by: Humphrey Yang <u6474961@anu.edu.au>
Co-authored-by: thomassargent30 <ts43@nyu.edu>

Author: 3 people

environment.yml

@@ -15,5 +15,6 @@ dependencies:
     - ghp-import==1.1.0
     - sphinxcontrib-youtube==1.1.0
     - sphinx-togglebutton==0.3.1
+    - sphinx-proof
     # Temporary
     - numba==0.59.1

lectures/_config.yml

@@ -31,7 +31,7 @@ latex:
       targetname: quantecon-python-advanced.tex
 
 sphinx:
-  extra_extensions: [sphinx_multitoc_numbering, sphinxext.rediraffe, sphinx_tojupyter, sphinx_exercise, sphinx_togglebutton]
+  extra_extensions: [sphinx_multitoc_numbering, sphinxext.rediraffe, sphinx_tojupyter, sphinx_exercise, sphinx_togglebutton, sphinx_proof]
   config:
     bibtex_reference_style: author_year
     linkcheck_ignore: ['https://doi.org/10.3982/ECTA8070',

lectures/_toc.yml

@@ -65,6 +65,7 @@ parts:
   chapters:
   - file: un_insure
   - file: dyn_stack
+  - file: calvo_machine_learn
   - file: calvo
   - file: opt_tax_recur
   - file: amss

lectures/calvo.md

@@ -844,6 +844,7 @@ Under the  Markov perfect timing protocol
  * a government takes $\bar \mu$ as given when it chooses $\mu_t$
  * we equate $\mu_t = \mu$ only *after* we have computed a time $t$ government's first-order condition for $\mu_t$.
 
+(compute_lq)=
 ## Outcomes under three timing protocols
 
 We  want to compare outcome sequences  $\{ \theta_t,\mu_t \}$ under three timing protocols associated with