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Preliminary end to eop/independence
This commit is contained in:
Grant Sanderson
parent
ceb7f467ad
commit
25bd813486
2 changed files with 407 additions and 22 deletions
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@ -29,6 +29,7 @@ from mobject.svg_mobject import *
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from mobject.tex_mobject import *
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from scene.scene import ProgressDisplay
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import scipy
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#revert_to_original_skipping_status
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@ -59,17 +60,18 @@ def get_quiz(*questions):
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return quiz
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def get_slot_group(bool_list, buff = MED_LARGE_BUFF, include_qs = True):
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n = len(bool_list)
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lines = VGroup(*[
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Line(ORIGIN, MED_LARGE_BUFF*RIGHT)
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for x in range(3)
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for x in range(n)
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])
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lines.arrange_submobjects(RIGHT, buff = buff)
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if include_qs:
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labels = VGroup(*[
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TextMobject("Q%d"%d) for d in range(1, 4)
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TextMobject("Q%d"%d) for d in range(1, n+1)
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])
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else:
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labels = VGroup(*[VectorizedPoint() for d in range(3)])
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labels = VGroup(*[VectorizedPoint() for d in range(n)])
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for label, line in zip(labels, lines):
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label.scale(0.7)
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label.next_to(line, DOWN, SMALL_BUFF)
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@ -100,7 +102,7 @@ def get_slot_group(bool_list, buff = MED_LARGE_BUFF, include_qs = True):
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return slot_group
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def get_probability_of_slot_group(bool_list, conditioned_list = None):
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filler_tex = "Filler"
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filler_tex = "Fi"*len(bool_list)
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if conditioned_list is None:
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result = TexMobject("P(", filler_tex, ")")
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else:
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@ -2748,8 +2750,6 @@ class CorrectForDependence(NameBinomial):
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self.revert_to_original_skipping_status()
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def construct(self):
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self.force_skipping()
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self.mention_dependence()
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self.show_tendency_to_align()
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self.adjust_chart()
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@ -2757,12 +2757,16 @@ class CorrectForDependence(NameBinomial):
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def mention_dependence(self):
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brace = Brace(self.checkmarks, LEFT)
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words = brace.get_text("What if there's \\\\ correlation?")
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formula = self.formula
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cross = Cross(formula)
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self.play(
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GrowFromCenter(brace),
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Write(words)
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)
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self.dither(2)
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self.dither()
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self.play(ShowCreation(cross))
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self.dither()
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def show_tendency_to_align(self):
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checkmarks = self.checkmarks
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@ -2776,15 +2780,52 @@ class CorrectForDependence(NameBinomial):
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top_rect.highlight(GREEN)
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indices_to_follow = [1, 4, 5, 7]
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self.revert_to_original_skipping_status()
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self.play(ShowCreation(top_rect))
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self.play(*self.get_arrow_flip_anims([0]))
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self.dither()
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self.play(*self.get_arrow_flip_anims(indices_to_follow))
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self.dither()
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self.play(FocusOn(self.chart.bars))
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def adjust_chart(self):
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pass
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chart = self.chart
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bars = chart.bars
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old_bars = bars.copy()
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old_bars.generate_target()
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bars.generate_target()
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for group, vect in (old_bars, LEFT), (bars, RIGHT):
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for bar in group.target:
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side = bar.get_edge_center(vect)
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bar.stretch(0.5, 0)
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bar.move_to(side, vect)
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for bar in old_bars.target:
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bar.highlight(average_color(RED_E, BLACK))
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dist = get_binomial_distribution(10, 0.65)
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values = np.array(map(dist, range(11)))
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alt_values = values + 0.1
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alt_values[0] -= 0.06
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alt_values[1] -= 0.03
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alt_values /= sum(alt_values)
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arrows = VGroup()
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arrow_template = Arrow(
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0.5*UP, ORIGIN, buff = 0,
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tip_length = 0.15,
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color = WHITE
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)
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for value, alt_value, bar in zip(values, alt_values, bars):
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arrow = arrow_template.copy()
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if value < alt_value:
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arrow.rotate(np.pi)
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arrow.next_to(bar, UP)
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arrows.add(arrow)
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self.play(
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MoveToTarget(old_bars),
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MoveToTarget(bars),
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)
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self.dither()
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self.play(*map(ShowCreation, arrows))
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self.play(chart.change_bar_values, alt_values)
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######
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@ -2825,18 +2866,362 @@ class CorrectForDependence(NameBinomial):
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for mover in movers
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]
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class ButWhatsTheAnswer(TeacherStudentsScene):
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def construct(self):
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self.student_says(
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"But what's the \\\\ actual answer?",
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target_mode = "confused"
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)
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self.change_student_modes(*["confused"]*3)
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self.dither()
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self.play(self.teacher.change, "pondering")
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self.dither(3)
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class AssumeOrderDoesntMatter(Scene):
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def construct(self):
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self.add_title()
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self.show_equality()
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self.mention_correlation()
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def add_title(self):
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title = TextMobject(
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"Softer simplifying assumption: " +\
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"Order doesn't matter"
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)
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title.to_edge(UP)
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self.add(title)
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self.title = title
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def show_equality(self):
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n = 3
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prob_groups = VGroup(*[
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VGroup(*map(
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get_probability_of_slot_group,
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filter(
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lambda t : sum(t) == k,
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it.product(*[[True, False]]*n)
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)
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))
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for k in range(n+1)
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])
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for prob_group in prob_groups:
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for prob in prob_group[:-1]:
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equals = TexMobject("=")
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equals.next_to(prob, RIGHT)
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prob.add(equals)
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prob_group.arrange_submobjects(RIGHT)
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max_width = 2*SPACE_WIDTH - 1
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if prob_group.get_width() > max_width:
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prob_group.scale_to_fit_width(max_width)
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prob_groups.arrange_submobjects(DOWN, buff = 0.7)
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prob_groups.next_to(self.title, DOWN, MED_LARGE_BUFF)
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self.play(FadeIn(
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prob_groups[1],
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run_time = 2,
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submobject_mode = "lagged_start"
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))
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self.dither(2)
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self.play(FadeIn(
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VGroup(prob_groups[0], *prob_groups[2:]),
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run_time = 3,
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submobject_mode = "lagged_start"
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))
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self.dither()
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self.prob_groups = prob_groups
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def mention_correlation(self):
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everything = VGroup(*self.get_top_level_mobjects())
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question = TextMobject("But what is ``correlation''?")
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question.highlight(BLUE)
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question.to_edge(UP)
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bottom = question.get_bottom()
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self.play(
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Write(question),
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everything.next_to, bottom, DOWN, LARGE_BUFF
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)
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self.dither()
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class FormulaCanBeRediscovered(PointOutSimplicityOfFormula):
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def construct(self):
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prob = self.get_probability_expression(full = False)
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corner = self.teacher.get_corner(UP+LEFT)
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prob.next_to(corner, UP, MED_LARGE_BUFF)
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brace = Brace(prob, UP)
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rediscover = brace.get_text("Rediscover")
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self.play(
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Write(prob),
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self.teacher.change, "hesitant", prob
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)
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self.dither()
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self.play(
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GrowFromCenter(brace),
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Write(rediscover, run_time = 1)
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)
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self.change_student_modes(*["happy"]*3)
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self.dither(2)
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class CompareTwoSituations(PiCreatureScene):
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def construct(self):
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randy = self.randy
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top_left, top_right = screens = [
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ScreenRectangle(height = 3).to_corner(vect)
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for vect in UP+LEFT, UP+RIGHT
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]
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arrow = DoubleArrow(*screens, buff = SMALL_BUFF)
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arrow.highlight(BLUE)
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for screen, s in zip(screens, ["left", "right"]):
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self.play(
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randy.change, "raise_%s_hand"%s, screen,
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ShowCreation(screen)
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)
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self.dither(3)
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self.play(
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randy.change, "pondering", arrow,
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ShowCreation(arrow)
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)
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self.dither(2)
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####
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def create_pi_creature(self):
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self.randy = Randolph().to_edge(DOWN)
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return self.randy
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class SkepticalOfDistributions(TeacherStudentsScene):
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CONFIG = {
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"chart_height" : 3,
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}
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def construct(self):
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self.show_binomial()
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self.show_alternate_distributions()
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self.emphasize_underweighted_tails()
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def show_binomial(self):
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binomial = self.get_binomial()
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binomial.next_to(self.teacher.get_corner(UP+LEFT), UP)
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title = TextMobject("Probable scores")
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title.scale(0.85)
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title.next_to(binomial.bars, UP, 1.5*LARGE_BUFF)
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self.play(
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Write(title, run_time = 1),
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FadeIn(binomial, run_time = 1, submobject_mode = "lagged_start"),
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self.teacher.change, "raise_right_hand"
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)
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for values in binomial.values_list:
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self.play(binomial.change_bar_values, values)
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self.dither()
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self.student_says(
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"Is that valid?", target_mode = "sassy",
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student_index = 0,
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run_time = 1
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)
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self.play(self.teacher.change, "guilty")
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self.dither()
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binomial.add(title)
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self.binomial = binomial
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def show_alternate_distributions(self):
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poisson = self.get_poisson()
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VGroup(poisson, poisson.title).next_to(
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self.students, UP, LARGE_BUFF
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).shift(RIGHT)
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gaussian = self.get_gaussian()
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VGroup(gaussian, gaussian.title).next_to(
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poisson, RIGHT, LARGE_BUFF
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)
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self.play(
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FadeIn(poisson, submobject_mode = "lagged_start"),
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RemovePiCreatureBubble(self.students[0]),
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self.teacher.change, "raise_right_hand",
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self.binomial.scale, 0.5,
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self.binomial.to_corner, UP+LEFT,
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)
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self.play(Write(poisson.title, run_time = 1))
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self.play(FadeIn(gaussian, submobject_mode = "lagged_start"))
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self.play(Write(gaussian.title, run_time = 1))
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self.dither(2)
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self.change_student_modes(
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*["sassy"]*3,
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added_anims = [self.teacher.change, "plain"]
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)
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self.dither(2)
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self.poisson = poisson
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self.gaussian = gaussian
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def emphasize_underweighted_tails(self):
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poisson_arrows = VGroup()
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arrow_template = Arrow(
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ORIGIN, UP, color = GREEN,
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tip_length = 0.15
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)
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for bar in self.poisson.bars[-4:]:
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arrow = arrow_template.copy()
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arrow.next_to(bar, UP, SMALL_BUFF)
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poisson_arrows.add(arrow)
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gaussian_arrows = VGroup()
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for prop in 0.2, 0.8:
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point = self.gaussian[0][0].point_from_proportion(prop)
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arrow = arrow_template.copy()
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arrow.next_to(point, UP, SMALL_BUFF)
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gaussian_arrows.add(arrow)
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for arrows in poisson_arrows, gaussian_arrows:
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self.play(
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ShowCreation(
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arrows,
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submobject_mode = "lagged_start",
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run_time = 2
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),
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*[
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ApplyMethod(pi.change, "thinking", arrows)
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for pi in self.pi_creatures
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]
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)
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self.dither()
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self.dither(2)
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####
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def get_binomial(self):
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k_range = range(11)
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dists = [
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get_binomial_distribution(10, p)
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for p in 0.2, 0.8, 0.5
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]
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values_list = [
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map(dist, k_range)
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for dist in dists
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]
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chart = BarChart(
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values = values_list[-1],
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bar_names = k_range
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)
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chart.scale_to_fit_height(self.chart_height)
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chart.values_list = values_list
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return chart
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def get_poisson(self):
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k_range = range(11)
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L = 2
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values = [
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np.exp(-L) * (L**k) / (scipy.special.gamma(k+1))
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for k in k_range
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]
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chart = BarChart(
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values = values,
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bar_names = k_range,
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bar_colors = [RED, YELLOW]
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)
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chart.scale_to_fit_height(self.chart_height)
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title = TextMobject(
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"Poisson distribution \\\\",
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"$e^{-\\lambda}\\frac{\\lambda^k}{k!}$"
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)
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title.scale(0.75)
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title.move_to(chart, UP)
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title.shift(MED_SMALL_BUFF*RIGHT)
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title[0].shift(SMALL_BUFF*UP)
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chart.title = title
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return chart
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def get_gaussian(self):
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axes = VGroup(self.binomial.x_axis, self.binomial.y_axis).copy()
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graph = FunctionGraph(
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lambda x : 5*np.exp(-x**2),
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mark_paths_closed = True,
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fill_color = BLUE_E,
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fill_opacity = 1,
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stroke_color = BLUE,
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)
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graph.scale_to_fit_width(axes.get_width())
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graph.move_to(axes[0], DOWN)
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title = TextMobject(
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"Gaussian distribution \\\\ ",
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"$\\frac{1}{\\sqrt{2\\pi \\sigma^2}} e^{-\\frac{(x-\\mu)^2}{2\\sigma^2}}$"
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)
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title.scale(0.75)
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title.move_to(axes, UP)
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title.shift(MED_SMALL_BUFF*RIGHT)
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title[0].shift(SMALL_BUFF*UP)
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result = VGroup(axes, graph)
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result.title = title
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return result
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class IndependencePatreonThanks(PatreonThanks):
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CONFIG = {
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"specific_patrons" : [
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"Ali Yahya",
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"Desmos",
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"Burt Humburg",
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"CrypticSwarm",
|
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"Juan Benet",
|
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"Mayank M. Mehrotra",
|
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"Lukas Biewald",
|
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"Samantha D. Suplee",
|
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"James Park",
|
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"Erik Sundell",
|
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"Yana Chernobilsky",
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"Kaustuv DeBiswas",
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"Kathryn Schmiedicke",
|
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"Karan Bhargava",
|
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"Yu Jun",
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"Dave Nicponski",
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"Damion Kistler",
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"Markus Persson",
|
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"Yoni Nazarathy",
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"Corey Ogburn",
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"Ed Kellett",
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"Joseph John Cox",
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"Dan Buchoff",
|
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"Luc Ritchie",
|
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"Tianyu Ge",
|
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"Ted Suzman",
|
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"Amir Fayazi",
|
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"Linh Tran",
|
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"Andrew Busey",
|
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"Michael McGuffin",
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"John Haley",
|
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"Mourits de Beer",
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"Ankalagon",
|
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"Eric Lavault",
|
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"Tomohiro Furusawa",
|
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"Boris Veselinovich",
|
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"Julian Pulgarin",
|
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"Jeff Linse",
|
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"Cooper Jones",
|
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"Ryan Dahl",
|
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"Mark Govea",
|
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"Robert Teed",
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"Jason Hise",
|
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"Meshal Alshammari",
|
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"Bernd Sing",
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"Nils Schneider",
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"James Thornton",
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"Mustafa Mahdi",
|
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"Mathew Bramson",
|
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"Jerry Ling",
|
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"Vecht",
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"Shimin Kuang",
|
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"Rish Kundalia",
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"Achille Brighton",
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"Ripta Pasay",
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],
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}
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|
|
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Loading…
Add table
Reference in a new issue