project 2 ready, typos may be corrected later

doc/src/Projects/2018/Project2/Project2.do.txt

@@ -2,11 +2,6 @@ TITLE: Project 2 on Machine Learning, deadline November 5
 AUTHOR: "Data Analysis and Machine Learning FYS-STK3155/FYS4155":"http://www.uio.no/studier/emner/matnat/fys/FYS3155/index-eng.html" {copyright, 1999-present|CC BY-NC} at Department of Physics, University of Oslo, Norway
 DATE: today
 
-o add note to nielsen's text
-o add about ising model
-o link to where we have the data
-o explain how to fit the model
-o link to mehta's article
 
 ===== Classification and Regression, from linear and logistic regression to neural networks  =====
 
@@ -88,14 +83,12 @@ system as
 
 !bt
 \begin{equation*}
-  E=-J\sum_{<kl>}^{N}s_ks_l-{\cal B}\sum_k^Ns_k,
+  E=-J\sum_{<kl>}^{N}s_ks_l,
 \end{equation*}
 !et
 with  $s_k=\pm 1$, $N$ is the total number of spins,
 $J$ is a coupling constant expressing the strength of the interaction
-between neighboring spins and
-${\cal B}$ is an external magnetic field interacting with the magnetic
-moment set up by the spins.   We will discard the magnetic field part. 
+between neighboring spins.
 
 The symbol $<kl>$ indicates that we sum over nearest
 neighbors only.
@@ -119,6 +112,7 @@ Consider the 1D Ising model with nearest-neighbor interactions
   E[\hat{s}]=-J\sum_{j=1}^{N}s_{j}s_{j+1},
 \end{equation*}
 !et
+
 on a chain of length $N$ with so-called periodic boundary conditions and $S_j=\pm 1$ Ising spin variables.
 In one dimension, this model has no phase transition at finite temperature.
 
@@ -136,7 +130,6 @@ import numpy as np
 import scipy.sparse as sp
 np.random.seed(12)
 
-
 import warnings
 #Comment this to turn on warnings
 warnings.filterwarnings('ignore')
@@ -172,17 +165,18 @@ In the absence of any prior knowledge, one sensible choice is the all-to-all Isi
 E_\mathrm{model}[\boldsymbol{s}^i] = - \sum_{j=1}^N \sum_{k=1}^N J_{j,k}s_{j}^is_{k}^i.
 \]
 !et
+
 Here $i$ represents a particular spin configuration (one of the possible $n$ configurations we generated with the code above).
 
 This model is uniquely defined by the non-local coupling strengths $J_{jk}$ which we want to learn.
-The model is linear in ${\mathbf J}$ which makes it possible to use linear regression.
+The model is linear in $\mathbf{J}$ which makes it possible to use linear regression.
 
 To apply linear regression, we recast this model in the form
 !bt
 \[
 E_\mathrm{model}^i \equiv \mathbf{X}^i \cdot \mathbf{J},
 \]
-!ec
+!et
 
 where the vectors $\mathbf{X}^i$ represent all two-body interactions
 $\{s_{j}^is_{k}^i \}_{j,k=1}^N$, and the index $i$ runs over the