dag chapter

Author: alexanderthclark

figures/poetryplots/dag-argue.pdf

@@ -146,6 +146,9 @@ \section{Activity Calendar}
 \section{Heatmaps}
 \input{tex/poetry/heat.tex}
 
+\section{Directed Graphs}
+\input{tex/poetry/dag.tex}
+
 \section{Speedometer}
 \input{tex/poetry/speedometer.tex}
 

figures/poetryplots/df-plot.pdf

@@ -0,0 +1,12 @@
+fig, ax = plt.figure(), plt.axes()
+ax.set_aspect(1)
+ax.set_xlim(-4,4)
+ax.set_ylim(-3,3)
+ax.axis('off')
+
+persuasive = make_node((0,1.5), 1, 'Persuasiveness')
+logic = make_node((2.5,-1.5), 1, 'Logic')
+decibels = make_node((-2.5,-1.5), 1, 'Decibels')
+
+directed_edge(logic, persuasive)
+directed_edge(decibels, persuasive)

figures/poetryplots/heat-basic.pdf

@@ -0,0 +1,32 @@
+def directed_edge(c1, c2, ax = None):
+    """Draw an arrow from c1 to c2."""
+
+    if ax is None:
+        ax = plt.gca()
+
+    center1 = c1.center
+    center2 = c2.center
+
+    length = np.linalg.norm(np.array(center1) - np.array(center2))
+
+    r1 = c1.get_radius()
+    r2 = c2.get_radius()
+
+    x1, x2 = center1[0], center2[0]
+    y1, y2 = center1[1], center2[1]
+
+    # Find start and end of arrow based on circle radii
+    # based on linear weights from convex combos
+    tail_weight = r1 / length
+    tail_x = (1-tail_weight)*x1 + tail_weight*x2
+    tail_y = (1-tail_weight)*y1 + tail_weight*y2
+
+    head_weight = r2/ length
+    head_x = (1-head_weight)*x2 + head_weight*x1
+    head_y = (1-head_weight)*y2 + head_weight*y1
+
+    ax.annotate('', xy = (head_x, head_y),
+                xytext = (tail_x, tail_y),
+                arrowprops = dict(headwidth = 14,
+                                  linewidth = .1,
+                                  width = 2))

figures/poetryplots/heat-cbar.pdf

@@ -0,0 +1,16 @@
+def make_node(center, radius = 'auto', label = '', ax = None):
+    """Plot labeled circle object to represent a node.
+    Rrun after any changes to axes limits, aspect changes, etc if using radius = 'auto'."""
+    if ax is None:
+        ax = plt.gca()
+    t = ax.text(center[0], center[1], label, ha = 'center', va = 'center')
+    if radius == 'auto':
+        plt.gcf().canvas.draw()
+        box = t.get_window_extent().transformed(ax.transData.inverted())
+        width = box.x1 - box.x0
+        radius = (width/2)*1.2
+    c = plt.Circle(center, radius,
+                   facecolor = (.9,.99,.9),
+                   edgecolor = 'black')
+    ax.add_artist(c)
+    return c

figures/poetryplots/heat-log.pdf

@@ -0,0 +1,16 @@
+%\subsection{Directed Graphs}
+Directed graphs arise in many settings. For plotting a large graph, like follower-following relationships in a social network, you might be best served making use of packages like networkx and nxviz. In other cases, you might do better working by hand. The \link{https://graphviz.readthedocs.io/en/stable/index.html}{graphviz} library is one possible solution. Here, we'll work directly with matplotlib. One directed graph use case might be in illustrating the directed acyclic graph (or DAG) representing a causal theory. In the directed acyclic graph framework (mostly associated with Judea Pearl's work in causal inference), a directed edge from $X$ to $Y$ means $X$ causes $Y$, at least in part. This lends itself well to plotting. Below we'll make a plot, using \code{plt.Circle()} to draw nodes and and creating edges with \code{ax.annotate()}.
+
+Here, we create the nodes as circle objects and then draw the edges using \code{ax.annotate()}. Below, the circular nodes are created with the function \code{make_node()}. Then, the directed edge is drawn with \code{directed_edge()}. This doesn't allow for an edge from one node back to itself. 
+
+\pyfile{dag-node.py}
+
+\pyfile{dag-edge.py}
+
+The DAG plotted below describes the theory that the persuasiveness of an argument is caused by its logical soundness and the decibel level at which it is communicated. 
+
+\pyfile{dag-argue.py}
+
+\begin{center}
+    \includegraphics[width = 0.7\textwidth]{figures/poetryplots/dag-argue.pdf}
+\end{center}