Bayes is BAE

Before programming, before formal probability there was Bayes. He introduced the notion that multiple uncertain estimates which are related could be combined to form a more certain estimate. It turns out that this extremely simple idea has a profound impact on how we write programs and how we can think about life. The applications range from machine learning and robotics to determining cancer treatments. In this talk we'll take an in depth look at Bayses rule and how it can be applied to solve problems in programming and beyond.

Transcript

1. WELCOME
2. Bayes is BAE
4. Introducing our Protagonist
11. Divine Benevolence, or an Attempt to Prove That the Principal End of the Divine Providence and Government is the Happiness of His Creatures
12. &
13. An Introduction to the Doctrine of Fluxions, and a Defence of the Mathematicians Against the Objections of the Author of The Analyst
14. Harry Potter & the Sorcerer’s Stone
15. Why do we care?
18. 1720s
24. No
28. Machine learning
29. Artificial Intelligence
30. They Call me @Schneems
31. Maintain Sprockets
32. Georgia Tech Online Masters
33. Georgia Tech Online Masters
36. Automatic Certificate
 Management
37. SSL
38. Heroku CI
39. Review Apps
40. Self Promotion
48. But wait Schneems, what can we do? “
49. Call your state representatives
50. But wait Schneems, what can we do more? “
51. degerrymander texas .org
52. Un-Patriotic Un-Texan
53. Back to Bayes
54. Artificial Intelligence
62. Low Information state
64. Predict
65. Measure
66. Measure + Predict
67. Convolution
68. Kalman Filter
72. Do you like money?
77. P(A ∣ B) = P(B ∣ A) P(A) P(B)
78. Probability P(A ∣ B) = P(B ∣ A) P(A) P(B)
79. Probability of $3.7 mil given Heads P(A ∣ B) = P(B ∣ A) P(A) P(B)
80. Probability of $3.7 mil given Heads P(A ∣ B) = P(B ∣ A) P(A) P(B)
81. probability of heads P(A ∣ B) = P(B ∣ A) P(A) P(B) P(B) =
82. probability of heads P(B) = H H H T
83. P(B) = H H H T probability of heads P(B) = 0.5 * 0.5 + 0.5 * 1 0.75 P(B) =
84. 0.75 P(A ∣ B) = P(B ∣ A) P(A) P(B) P(B) = 0.75
85. P(A) = P(A ∣ B) = P(B ∣ A) P(A) P(B) 0.75 probability of $3.7 million
86. probability of $3.7 million $$$ Nope P(A) =
87. $$$ Nope 0.5 probability of $3.7 million P(A) = P(A) =
88. P(A ∣ B) = P(B ∣ A) P(A) P(B) 0.50 0.75 0.50 P(A) =
89. P(A ∣ B) = P(B ∣ A) P(A) P(B) P(B ∣ A) = 0.75 0.50 probability of heads given $3.7
90. probability of heads given $3.7 H T P(B ∣ A) =
91. P(B ∣ A) = 0.5 P(A ∣ B) = P(B ∣ A) P(A) P(B) 0.75 0.5 * 0.5
92. $3.7 mil given Heads P(A ∣ B) = P(B ∣ A) P(A) P(B) 0.75 0.5 * 0.5 P(A ∣ B) = 1 3 = 0.3333
93. P(A ∣ B) = P(B ∣ A) P(A) P(B)
94. P(A ∣ B) = P(B ∣ A) P(A) P(B)
95. YouTube Channel: Art of the Problem
96. P(A ∣ B) = P(B ∣ A) P(A) P(B)
97. I lied about Bayes Rule
98. P(A ∣ B) = P(B ∣ A) P(A) P(B)
99. P(Ai ∣ B) = P(B ∣ Ai ) P(Ai ) ∑ j P(B ∣ Aj ) P(Aj )
100. P(A ∣ B) = P(B ∣ A) P(A) P(B) P(Ai ∣ B) = P(B ∣ Ai ) P(Ai ) ∑ j P(B ∣ Aj ) P(Aj )
101. Total Probability
102. $3.7 mil $0
103. $3.7 mil $0 Heads
104. $3.7 mil $0 Tails Heads
105. $3.7 mil $0 Heads Tails
106. $3.7 mil $0 Heads Tails
107. $3.7 mil $0 Heads Tails
108. P(Hea d s) = P(Hea d s ∣ $$$)P($$$) + P(Hea d s ∣ $0)P($0) $3.7 mil $0 Heads Tails
109. $3.7 mil $0 P(Hea d s) = P(Hea d s ∣ $$$)P($$$) + P(Hea d s ∣ $0)P($0) Heads Tails
110. P(B) = ∑ j P(B ∣ Aj ) P(Aj ) Total Probability
111. P(B) = H H H T probability of heads P(B) = 0.5 * 0.5 + 0.5 * 1 0.75 P(B) =
112. P(B) = ∑ j P(B ∣ Aj ) P(Aj ) P(Hea d s) = P(Hea d s ∣ $$$)P($$$) + P(Hea d s ∣ $0)P($0) Total Probability
113. Let’s make it tougher
114. P(Ai ∣ B) = P(B ∣ Ai ) P(Ai ) ∑ j P(B ∣ Aj ) P(Aj )
115. P(Coini ∣ HH ) = P(HH ∣ Coini ) P(Coini ) ∑ j P(HH ∣ Coinj ) P(Coinj )
116. P(Coini ∣ HH ) = P(HH ∣ Coini ) P(Coini ) ∑ j P(HH ∣ Coinj ) P(Coinj ) P(HH ∣ Coini ) = 0.5 * 0.5
117. P(Coini ∣ HH ) = P(HH ∣ Coini ) P(Coini ) ∑ j P(HH ∣ Coinj ) P(Coinj ) 0.5 P(Coini ) =
118. P(Coini ∣ HH ) = P(HH ∣ Coini ) P(Coini ) ∑ j P(HH ∣ Coinj ) P(Coinj ) ∑ j P(B ∣ Aj ) P(Aj ) = P(HH ∣ $$$)P($$$) + P(HH ∣ $0)P($0) ∑ j P(B ∣ Aj ) P(Aj ) = 0.25(0.5) + 1.0(0.5)
119. P(Coini ∣ HH ) = P(HH ∣ Coini ) P(Coini ) ∑ j P(HH ∣ Coinj ) P(Coinj ) ∑ j P(B ∣ Aj ) P(Aj ) = P(HH ∣ $$$)P($$$) + P(HH ∣ $0)P($0) ∑ j P(B ∣ Aj ) P(Aj ) = 0.25(0.5) + 1.0(0.5)
120. P(Coin$$$ ∣ HH ) = 0.25(0.5) 0.625 = 1 5 = 0.2 P(Coini ∣ HH ) = P(HH ∣ Coini ) P(Coini ) ∑ j P(HH ∣ Coinj ) P(Coinj )
121. P(Coin$$$ ∣ HH ) = 0.25(0.5) 0.625 = 1 5 = 0.2 P(Coini ∣ HH ) = P(HH ∣ Coini ) P(Coini ) ∑ j P(HH ∣ Coinj ) P(Coinj )
122. P(Coini ∣ HH ) = 0.25(0.5) 0.625 = 1 5 = 0.2 P(Coini ∣ HH ) = P(HH ∣ Coini ) P(Coini ) ∑ j P(HH ∣ Coinj ) P(Coinj )
123. Who is ready for a break?
124. Lets take a break from math
125. With more math
126. P(A ∣ B) = P(B ∣ A) P(A) P(B)
127. P(A ∣ B) = P(B ∣ A) P(A) P(B) P(Ai ∣ B) = P(B ∣ Ai ) P(B) P(Ai )
128. P(Ai ∣ B) = P(B ∣ Ai ) P(B) P(Ai ) Prior
129. P(Ai ∣ B) = P(B ∣ Ai ) P(B) P(Ai ) Posterior
130. The kalman filter is a recursive bayes estimation
131. Prediction/ Prior
132. Measure/ Posterior
134. Simon D. Levy
135. alt it u decurrent time = 0.75 alt it u deprevious time
136. alt it u decurrent time = 0.75 alt it u deprevious time
137. a = rate_of_decent = 0.75 x = initial_position = 1000 r = measure_error = x * 0.20
138. x_guess = measure_array[0] p = estimate_error = 1 x_guess_array = []
139. for k in range(10): measure = measure_array[k]
140. for k in range(10): measure = measure_array[k] # Predict x_guess = a * x_guess
141. for k in range(10): measure = measure_array[k] # Predict x_guess = a * x_guess p = a * p * a
142. for k in range(10): measure = measure_array[k] # Predict x_guess = a * x_guess p = a * p * a # Update gain = p / (p + r) x_guess = x_guess + gain * (measure - x_guess)
143. for k in range(10): measure = measure_array[k] # Predict x_guess = a * x_guess p = a * p * a # Update gain = p / (p + r) x_guess = x_guess + gain * (measure - x_guess) Low Predict Error, low gain
144. for k in range(10): measure = measure_array[k] # Predict x_guess = a * x_guess p = a * p * a # Update gain = p / (p + r) x_guess = x_guess + 0 * (measure - x_guess) Low Predict Error, low gain
145. for k in range(10): measure = measure_array[k] # Predict x_guess = a * x_guess p = a * p * a # Update gain = p / (p + r) x_guess = x_guess + 0 * (measure - x_guess) Low Predict Error, low gain
146. for k in range(10): measure = measure_array[k] # Predict x_guess = a * x_guess p = a * p * a # Update gain = p / (p + r) x_guess = x_guess + 1 * (measure - x_guess) High Predict Error, High gain
147. for k in range(10): measure = measure_array[k] # Predict x_guess = a * x_guess p = a * p * a # Update gain = p / (p + r) x_guess = x_guess + 1 * (measure - x_guess) High Predict Error, High gain
148. Prediction less certain
149. Prediction more certain
150. for k in range(10): measure = measure_array[k] # Predict x_guess = a * x_guess p = a * p * a # Update gain = p / (p + r) x_guess = x_guess + gain * (measure - x_guess) p = (1 - g) * p
158. That’s it for Kalman Filters
159. Bayes Rule
160. Two most important parts
169. Algorithms to Live By
170. The Signal and the Noise
171. Audio: Mozart Requiem in D minor https://www.youtube.com/watch?v=sPlhKP0nZII
172. http:// bit.ly/ kalman-tutorial
173. http:// bit.ly/ kalman-notebook
174. Udacity & Georgia Tech
175. BAE
176. BAE
177. BAE
178. BAE
179. Questions?
180. Questions?
181. Test Audio
182. Test Audio 2
183. Simon D. Levy
194. What is g?
196. Prediction
197. Measurement
198. Convolution
199. Prediction less certain
200. Prediction more certain
201. Prediction error is not constant
202. What is g?
205. What is g?
207. Introducing r
212. Prediction + Measurement
213. i.e. Prediction + Update
214. Prediction Update
215. Prediction Update ✅
216. Prediction
217. Prediction
218. Prediction Update ✅ ✅
219. $3.7 mil $0
220. $3.7 mil $0