First couple scenes of bayes

This commit is contained in:
Grant Sanderson
2019-12-06 17:11:04 -08:00
parent 72006334f5
commit cfc5ecc59c

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@ -0,0 +1,788 @@
from manimlib.imports import *
OUTPUT_DIRECTORY = "bayes"
HYPOTHESIS_COLOR = YELLOW
NOT_HYPOTHESIS_COLOR = GREY
EVIDENCE_COLOR1 = BLUE_C
EVIDENCE_COLOR2 = BLUE_D
NOT_EVIDENCE_COLOR1 = RED
NOT_EVIDENCE_COLOR2 = RED_E
#
def get_bayes_formula(expand_denominator=False):
t2c = {
"{H}": HYPOTHESIS_COLOR,
"{\\neg H}": NOT_HYPOTHESIS_COLOR,
"{E}": EVIDENCE_COLOR1,
}
substrings_to_isolate = ["P", "\\over", "=", "\\cdot", "+"]
tex = "P({H} | {E}) = {P({H}) \\cdot P({E} | {H}) \\over "
if expand_denominator:
tex += "P({H}) \\cdot P({E} | {H}) + P({\\neg H}) \\cdot P({E} | {\\neg H})}"
else:
tex += "P({E})}"
formula = TexMobject(
tex,
tex_to_color_map=t2c,
substrings_to_isolate=substrings_to_isolate,
)
formula.posterior = formula[:6]
formula.prior = formula[8:12]
formula.likelihood = formula[13:19]
if expand_denominator:
pass
formula.denom_prior = formula[20:24]
formula.denom_likelihood = formula[25:31]
formula.denom_anti_prior = formula[32:36]
formula.denom_anti_likelihood = formula[37:42]
else:
formula.p_evidence = formula[20:]
return formula
class BayesDiagram(VGroup):
CONFIG = {
"height": 2,
"square_style": {
"fill_color": DARK_GREY,
"fill_opacity": 1,
"stroke_color": WHITE,
"stroke_width": 2,
},
"rect_style": {
"stroke_color": WHITE,
"stroke_width": 1,
"fill_opacity": 1,
},
"hypothesis_color": HYPOTHESIS_COLOR,
"not_hypothesis_color": NOT_HYPOTHESIS_COLOR,
"evidence_color1": EVIDENCE_COLOR1,
"evidence_color2": EVIDENCE_COLOR2,
"not_evidence_color1": NOT_EVIDENCE_COLOR1,
"not_evidence_color2": NOT_EVIDENCE_COLOR2,
}
def __init__(self, prior, likelihood, antilikelihood, **kwargs):
super().__init__(**kwargs)
square = Square(side_length=self.height)
square.set_style(**self.square_style)
# Create all rectangles
h_rect, nh_rect, he_rect, nhe_rect, hne_rect, nhne_rect = [
square.copy().set_style(**self.rect_style)
for x in range(6)
]
# Add as attributes
self.square = square
self.h_rect = h_rect # Hypothesis
self.nh_rect = nh_rect # Not hypothesis
self.he_rect = he_rect # Hypothesis and evidence
self.hne_rect = hne_rect # Hypothesis and not evidence
self.nhe_rect = nhe_rect # Not hypothesis and evidence
self.nhne_rect = nhne_rect # Not hypothesis and not evidence
# Stretch the rectangles
for rect in h_rect, he_rect, hne_rect:
rect.stretch(prior, 0, about_edge=LEFT)
for rect in nh_rect, nhe_rect, nhne_rect:
rect.stretch(1 - prior, 0, about_edge=RIGHT)
he_rect.stretch(likelihood, 1, about_edge=DOWN)
hne_rect.stretch(1 - likelihood, 1, about_edge=UP)
nhe_rect.stretch(antilikelihood, 1, about_edge=DOWN)
nhne_rect.stretch(1 - antilikelihood, 1, about_edge=UP)
# Color the rectangles
h_rect.set_fill(self.hypothesis_color)
nh_rect.set_fill(self.not_hypothesis_color)
he_rect.set_fill(self.evidence_color1)
hne_rect.set_fill(self.not_evidence_color1)
nhe_rect.set_fill(self.evidence_color2)
nhne_rect.set_fill(self.not_evidence_color2)
# Add them
self.hypothesis_split = VGroup(h_rect, nh_rect)
self.evidence_split = VGroup(he_rect, hne_rect, nhe_rect, nhne_rect)
# Don't add hypothesis split by default
self.add(self.square, self.evidence_split)
def generate_braces(self):
pass # TODO
class ProbabilityBar(VGroup):
CONFIG = {
"color1": BLUE_D,
"color2": GREY_BROWN,
"height": 0.5,
"width": 6,
"rect_style": {
"stroke_width": 1,
"stroke_color": WHITE,
"fill_opacity": 1,
},
"include_braces": True,
"brace_direction": UP,
"include_percentages": True,
}
def __init__(self, p=0.5, **kwargs):
super().__init__(**kwargs)
self.add_backbone()
self.add_p_tracker(p)
self.add_bars()
if self.include_braces:
self.braces = always_redraw(lambda: self.get_braces())
self.add(self.braces)
if self.include_percentages:
self.percentages = always_redraw(lambda: self.get_percentages())
self.add(self.percentages)
def add_backbone(self):
backbone = Line()
backbone.set_opacity(0)
backbone.set_width(self.width)
self.backbone = backbone
self.add(backbone)
def add_p_tracker(self, p):
self.p_tracker = ValueTracker(p)
def add_bars(self):
bars = VGroup(Rectangle(), Rectangle())
bars.set_height(self.height)
colors = [self.color1, self.color2]
for bar, color in zip(bars, colors):
bar.set_style(**self.rect_style)
bar.set_fill(color=color)
bars.add_updater(self.update_bars)
self.bars = bars
self.add(bars)
def update_bars(self, bars):
vects = [LEFT, RIGHT]
p = self.p_tracker.get_value()
values = [p, 1 - p]
total_width = self.backbone.get_width()
for bar, vect, value in zip(bars, vects, values):
bar.set_width(value * total_width, stretch=True)
bar.move_to(self.backbone, vect)
return bars
def get_braces(self):
return VGroup(*[
Brace(
bar,
self.brace_direction,
min_num_quads=1,
buff=SMALL_BUFF,
)
for bar in self.bars
])
def get_percentages(self):
p = self.p_tracker.get_value()
labels = VGroup(*[
Integer(value, unit="\\%")
for value in [
np.floor(p * 100),
100 - np.floor(p * 100),
]
])
for label, bar in zip(labels, self.bars):
label.set_height(0.75 * bar.get_height())
min_width = 0.75 * bar.get_width()
if label.get_width() > min_width:
label.set_width(min_width)
label.move_to(bar)
label.set_stroke(BLACK, 5, background=True)
return labels
def add_icons(self, *icons, buff=SMALL_BUFF):
if hasattr(self, "braces"):
refs = self.braces
else:
refs = self.bars
for icon, ref in zip(icons, refs):
icon.ref = ref
icon.add_updater(lambda i: i.next_to(
i.ref,
self.brace_direction,
buff=buff
))
self.icons = VGroup(*icons)
self.add(self.icons)
class Steve(SVGMobject):
CONFIG = {
"file_name": "steve",
"fill_color": GREY,
"sheen_factor": 0.5,
"sheen_direction": UL,
"stroke_width": 0,
"height": 3,
"include_name": True,
}
def __init__(self, **kwargs):
super().__init__(**kwargs)
if self.include_name:
self.add_name()
def add_name(self):
self.name = TextMobject("Steve")
self.name.match_width(self)
self.name.next_to(self, DOWN, SMALL_BUFF)
self.add(self.name)
class LibrarianIcon(SVGMobject):
CONFIG = {
"file_name": "book",
"stroke_width": 0,
"fill_color": LIGHT_GREY,
"sheen_factor": 0.5,
"sheen_direction": UL,
"height": 0.75,
}
def __init__(self, **kwargs):
super().__init__(**kwargs)
class FarmerIcon(SVGMobject):
CONFIG = {
# "file_name": "pitch_fork_and_roll",
"file_name": "farming",
"stroke_width": 0,
"fill_color": GREEN_E,
"sheen_factor": 0.5,
"sheen_direction": UL,
"height": 1.5,
}
def __init__(self, **kwargs):
super().__init__(**kwargs)
# Scenes
# class Test(Scene):
# def construct(self):
# icon = FarmerIcon()
# icon.scale(2)
# self.add(icon)
# # self.add(get_submobject_index_labels(icon))
# class FullFormulaIndices(Scene):
# def construct(self):
# formula = get_bayes_formula(expand_denominator=True)
# formula.set_width(FRAME_WIDTH - 1)
# self.add(formula)
# self.add(get_submobject_index_labels(formula))
class IntroduceFormula(Scene):
def construct(self):
formula = get_bayes_formula()
formula.set_width(FRAME_WIDTH - 1)
def get_formula_slice(*indices):
return VGroup(*[formula[i] for i in indices])
H_label = formula.get_part_by_tex("{H}")
E_label = formula.get_part_by_tex("{E}")
hyp_label = TextMobject("Hypothesis")
hyp_label.set_color(HYPOTHESIS_COLOR)
hyp_label.next_to(H_label, UP, LARGE_BUFF)
evid_label = TextMobject("Evidence")
evid_label.set_color(EVIDENCE_COLOR1)
evid_label.next_to(E_label, DOWN, LARGE_BUFF)
hyp_arrow = Arrow(hyp_label.get_bottom(), H_label.get_top(), buff=SMALL_BUFF)
evid_arrow = Arrow(evid_label.get_top(), E_label.get_bottom(), buff=SMALL_BUFF)
self.add(formula[:6])
# self.add(get_submobject_index_labels(formula))
# return
self.play(
FadeInFrom(hyp_label, DOWN),
GrowArrow(hyp_arrow),
FadeInFrom(evid_label, UP),
GrowArrow(evid_arrow),
)
self.wait()
# Prior
self.play(
ShowCreation(formula.get_part_by_tex("=")),
TransformFromCopy(
get_formula_slice(0, 1, 2, 5),
get_formula_slice(8, 9, 10, 11),
),
)
self.wait()
# Likelihood
lhs_copy = formula[:6].copy()
likelihood = formula[13:19]
run_time = 1
self.play(
lhs_copy.next_to, likelihood, UP,
DrawBorderThenFill(formula.get_part_by_tex("\\cdot")),
run_time=run_time,
)
self.play(
Swap(lhs_copy[2], lhs_copy[4]),
run_time=run_time,
)
self.play(
lhs_copy.move_to, likelihood,
run_time=run_time,
)
self.wait()
# Evidence
self.play(
ShowCreation(formula.get_part_by_tex("\\over")),
TransformFromCopy(
get_formula_slice(0, 1, 4, 5),
get_formula_slice(20, 21, 22, 23),
),
)
self.wait()
class StateGoal(PiCreatureScene):
CONFIG = {
"default_pi_creature_kwargs": {
"color": BLUE_B,
"height": 2,
},
}
def construct(self):
you = self.pi_creature
line = NumberLine(
x_min=-2,
x_max=12,
include_tip=True
)
line.to_edge(DOWN, buff=1.5)
line.to_edge(LEFT, buff=-0.5)
you.next_to(line.n2p(0), UP)
you_label = TextMobject("you")
you_label.next_to(you, RIGHT, MED_LARGE_BUFF)
you_arrow = Arrow(you_label.get_left(), you.get_right() + 0.5 * LEFT, buff=0.1)
now_label = TextMobject("Now")
later_label = TextMobject("Later")
now_label.next_to(line.n2p(0), DOWN)
later_label.next_to(line.n2p(10), DOWN)
self.add(line, now_label)
self.add(you)
self.play(
FadeInFrom(you_label, LEFT),
GrowArrow(you_arrow),
you.change, "pondering",
)
self.wait()
you_label.add(you_arrow)
self.play(
you.change, "horrified",
you.look, DOWN,
you.next_to, line.n2p(10), UP,
MaintainPositionRelativeTo(you_label, you),
FadeInFromPoint(later_label, now_label.get_center()),
)
self.wait()
bubble = you.get_bubble(
height=4,
width=6,
)
bubble.set_fill(opacity=0)
formula = get_bayes_formula()
bubble.position_mobject_inside(formula)
self.play(
you.change, "confused", bubble,
ShowCreation(bubble),
)
self.play(FadeIn(formula))
self.play(you.change, "hooray", formula)
self.wait(2)
# Levels of understanding
# Turn bubble into level points
level_points = VGroup(*[bubble.copy() for x in range(3)])
for n, point in enumerate(level_points):
point.set_width(0.5)
point.set_height(0.5, stretch=True)
point.add(*[
point[-1].copy().scale(1.2**k)
for k in range(1, n + 1)
])
point[:3].scale(1.2**n, about_point=point[3].get_center())
point.set_stroke(width=2)
point.set_fill(opacity=0)
level_points.arrange(DOWN, buff=LARGE_BUFF)
title = TextMobject("Levels of understanding")
title.scale(1.5)
title.to_corner(UL)
underline = Line()
underline.match_width(title)
underline.move_to(title, DOWN)
title.add(underline)
level_points.next_to(title, DOWN, buff=1.5)
level_points.to_edge(LEFT)
level_points.set_submobject_colors_by_gradient(GREEN, YELLOW, RED)
self.remove(bubble)
self.play(
formula.to_corner, UR,
Uncreate(line),
FadeOutAndShift(now_label, DOWN),
FadeOutAndShift(later_label, DOWN),
FadeOut(you_label),
FadeOut(you_arrow),
FadeOut(you),
*[
ReplacementTransform(bubble.copy(), point)
for point in level_points
],
)
self.play(Write(title, run_time=1))
self.wait()
# Write level 1
level_labels = VGroup(
TextMobject("What is it saying?"),
TextMobject("Why is it true?"),
TextMobject("When is it useful?"),
)
for lp, ll in zip(level_points, level_labels):
ll.scale(1.25)
ll.match_color(lp)
ll.next_to(lp, RIGHT)
formula_parts = VGroup(
formula.prior,
formula.likelihood,
formula.p_evidence,
formula.posterior,
).copy()
formula_parts.generate_target()
formula_parts.target.scale(1.5)
formula_parts.target.arrange(DOWN, buff=LARGE_BUFF, aligned_edge=LEFT)
formula_parts.target.next_to(formula, DOWN, buff=LARGE_BUFF)
formula_parts.target.shift(3 * LEFT)
equal_signs = VGroup(*[
TextMobject("=").next_to(fp, RIGHT)
for fp in formula_parts.target
])
kw = {
"tex_to_color_map": {
"hypothesis": HYPOTHESIS_COLOR,
"evidence": EVIDENCE_COLOR1,
},
"alignment": "",
}
meanings = VGroup(
TextMobject("Probability a hypothesis is true\\\\(before any evidence)", **kw),
TextMobject("Probability of seeing the evidence \\quad \\\\if the hypothesis is true", **kw),
TextMobject("Probability of seeing the evidence", **kw),
TextMobject("Probability a hypothesis is true\\\\given some evidence", **kw),
)
for meaning, equals in zip(meanings, equal_signs):
meaning.scale(0.5)
meaning.next_to(equals, RIGHT)
self.play(
FadeIn(level_labels[0], lag_ratio=0.1),
MoveToTarget(formula_parts),
LaggedStartMap(FadeInFrom, equal_signs, lambda m: (m, RIGHT)),
LaggedStartMap(FadeIn, meanings),
)
self.wait()
# Write level 2
diagram = BayesDiagram(0.35, 0.5, 0.2, height=2.5)
diagram.next_to(formula, DOWN, aligned_edge=LEFT)
braces = VGroup(*[
Brace(diagram.he_rect, vect, buff=SMALL_BUFF)
for vect in [DOWN, LEFT]
])
formula_parts.generate_target()
formula_parts.target[:2].scale(0.5)
formula_parts.target[0].next_to(braces[0], DOWN, SMALL_BUFF)
formula_parts.target[1].next_to(braces[1], LEFT, SMALL_BUFF)
pe_picture = VGroup(
diagram.he_rect.copy(),
TexMobject("+"),
diagram.nhe_rect.copy()
)
pe_picture.arrange(RIGHT, buff=SMALL_BUFF)
pe_picture.next_to(equal_signs[2], RIGHT)
phe_picture = VGroup(
diagram.he_rect.copy(),
Line().match_width(pe_picture),
pe_picture.copy(),
)
phe_picture.arrange(DOWN, buff=MED_SMALL_BUFF)
phe_picture.next_to(equal_signs[3], RIGHT)
pe_picture.scale(0.5, about_edge=LEFT)
phe_picture.scale(0.3, about_edge=LEFT)
self.play(
FadeOut(meanings),
FadeOut(equal_signs[:2]),
MoveToTarget(formula_parts),
FadeIn(diagram),
LaggedStartMap(GrowFromCenter, braces),
FadeIn(level_labels[1], lag_ratio=0.1),
level_labels[0].set_opacity, 0.5,
)
self.play(
TransformFromCopy(diagram.he_rect, pe_picture[0]),
TransformFromCopy(diagram.nhe_rect, pe_picture[2]),
FadeIn(pe_picture[1]),
)
self.play(
TransformFromCopy(pe_picture, phe_picture[2]),
TransformFromCopy(pe_picture[0], phe_picture[0]),
ShowCreation(phe_picture[1])
)
self.wait()
# Write level 3
steve = Steve(height=3)
steve.to_edge(RIGHT, buff=2)
arrow = Arrow(level_points.get_bottom(), level_points.get_top(), buff=0)
arrow.shift(0.25 * LEFT)
self.play(
LaggedStartMap(
FadeOutAndShift,
VGroup(
VGroup(diagram, braces, formula_parts[:2]),
VGroup(formula_parts[2], equal_signs[2], pe_picture),
VGroup(formula_parts[3], equal_signs[3], phe_picture),
),
lambda m: (m, 3 * RIGHT),
),
FadeIn(level_labels[2], lag_ratio=0.1),
level_labels[1].set_opacity, 0.5,
)
self.wait()
self.play(
GrowArrow(arrow),
level_points.shift, 0.5 * RIGHT,
level_labels.shift, 0.5 * RIGHT,
level_labels.set_opacity, 1,
)
self.wait()
self.play(Write(steve, run_time=3))
self.wait()
# Transition to next scene
self.play(
steve.to_corner, UR,
Uncreate(arrow),
LaggedStartMap(
FadeOutAndShift,
VGroup(
title,
formula,
*level_points,
*level_labels,
),
lambda m: (m, DOWN),
),
)
self.wait()
class DescriptionOfSteve(Scene):
def construct(self):
self.write_description()
self.compare_probabilities()
def write_description(self):
steve = Steve(height=3)
steve.to_corner(UR)
description = TextMobject(
"""
Steve is very shy and withdrawn,\\\\
invariably helpful but with very\\\\
little interest in people or in the\\\\
world of reality. A meek and tidy\\\\
soul, he has a need for order and\\\\
structure, and a passion for detail.\\\\
""",
tex_to_color_map={
"shy and withdrawn": BLUE,
"meek and tidy": WHITE,
"soul": WHITE,
},
alignment="",
)
description.to_edge(LEFT)
description.match_y(steve)
self.add(steve)
self.play(
FadeIn(description),
run_time=3,
lag_ratio=0.01,
rate_func=linear,
)
self.wait(3)
mt_parts = VGroup(
description.get_part_by_tex("meek"),
description.get_part_by_tex("soul"),
)
lines = VGroup(*[
Line(mob.get_corner(DL), mob.get_corner(DR), color=YELLOW)
for mob in mt_parts
])
self.play(
ShowCreation(lines),
mt_parts.set_color, YELLOW,
)
self.play(FadeOut(lines))
self.wait()
def compare_probabilities(self):
bar = ProbabilityBar(0.5, width=10)
icons = VGroup(
LibrarianIcon(),
FarmerIcon(),
)
for icon, text, half in zip(icons, ["Librarian", "Farmer"], bar.bars):
icon.set_height(0.7)
label = TextMobject(text)
label.next_to(icon, DOWN, buff=SMALL_BUFF)
label.set_color(
interpolate_color(half.get_color(), WHITE, 0.5)
)
icon.add(label)
bar.add_icons(*icons)
bar.move_to(1.75 * DOWN)
bar.icons.set_opacity(0)
q_marks = TexMobject(*"???")
q_marks.scale(1.5)
q_marks.space_out_submobjects(1.5)
q_marks.next_to(bar, DOWN)
self.play(FadeIn(bar))
self.wait()
self.play(
bar.p_tracker.set_value, 0.9,
bar.icons[0].set_opacity, 1,
)
self.wait()
self.play(
bar.p_tracker.set_value, 0.1,
bar.icons[1].set_opacity, 1,
)
self.play(
LaggedStartMap(
FadeInFrom, q_marks,
lambda m: (m, UP),
run_time=2,
),
ApplyMethod(
bar.p_tracker.set_value, 0.7,
run_time=8,
)
)
for value in 0.3, 0.7:
self.play(
bar.p_tracker.set_value, 0.3,
run_time=7,
)
class IntroduceKahnemanAndTversky(Scene):
def construct(self):
images = Group(
ImageMobject("kahneman"),
ImageMobject("tversky"),
)
danny, amos = images
images.set_height(3.5)
images.arrange(DOWN, buff=0.5)
images.to_edge(LEFT, buff=MED_LARGE_BUFF)
names = VGroup(
TextMobject("Daniel\\\\Kahneman", alignment=""),
TextMobject("Amos\\\\Tversky", alignment=""),
)
for name, image in zip(names, images):
name.scale(1.25)
name.next_to(image, RIGHT)
image.name = name
prize = ImageMobject("nobel_prize", height=1)
prize.move_to(danny, UR)
prize.shift(MED_SMALL_BUFF * UR)
books = Group(
ImageMobject("thinking_fast_and_slow"),
ImageMobject("undoing_project"),
)
books.set_height(5)
books.arrange(RIGHT, buff=0.5)
books.to_edge(RIGHT, buff=MED_LARGE_BUFF)
self.play(
FadeInFrom(danny, DOWN),
FadeInFrom(danny.name, LEFT),
)
self.play(
FadeInFrom(amos, UP),
FadeInFrom(amos.name, LEFT),
)
self.wait()
self.play(FadeInFromLarge(prize))
self.wait()
for book in books:
self.play(FadeInFrom(book, LEFT))
self.wait()