4 Proposed Research Projects • SmartHome – Encouraging patients with mild cognitive disabilities to use digital memory notebook for activities of daily living • Diabetes – Encouraging patients to use program and follow exercise advice to maintain glucose levels • Machine Learning Curriculum Development – Automatically construct a set of tasks such that it’s faster to learn the set than to directly learn the final (target) task • Lifelong Machine Learning – Get a team of parrot drones and turtlebots to coordinate for a search and rescue. Build a library of past tasks to learn the n+1 st task faster All at risk because of the government shutdown
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4 Proposed Research Projects SmartHome – Encouraging patients with mild cognitive disabilities to use digital memory notebook for activities of daily living.
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4 Proposed Research Projects• SmartHome
– Encouraging patients with mild cognitive disabilities to use digital memory notebook for activities of daily living
• Diabetes– Encouraging patients to use program and follow exercise advice to
maintain glucose levels• Machine Learning Curriculum Development
– Automatically construct a set of tasks such that it’s faster to learn the set than to directly learn the final (target) task
• Lifelong Machine Learning– Get a team of parrot drones and turtlebots to coordinate for a search
and rescue. Build a library of past tasks to learn the n+1st task faster
All at risk because of the government shutdown
Thu
• Homework• (some?) labs• Contest : only 1 try– Will open classroom early
• General approach:
• A: action• S: pose• O: observationPosition at time t depends on position previous position and action, and current observation
Models of Belief
Axioms of Probability Theory• denotes probability that proposition A is true.• denotes probability that proposition A is false.
1. 2. 3.
1)Pr(0 A
1)Pr( True 0)Pr( False
)Pr()Pr()Pr()Pr( BABABA
A Closer Look at Axiom 3
B
BA A BTrue
)Pr()Pr()Pr()Pr( BABABA
Using the Axioms to Prove
(Axiom 3 with )
(by logical equivalence)
∨
Discrete Random Variables
• X denotes a random variable.
• X can take on a countable number of values in {x1, x2, …, xn}.
• P(X=xi), or P(xi), is the probability that the random variable X takes on value xi.
• P(xi) is called probability mass function.
• E.g. 2.0)( RoomP
Continuous Random Variables• takes on values in the continuum.
• , or , is a probability density function.
• E.g.b
a
dxxpbax )()),(Pr(
x
p(x)
Probability Density Function
• Since continuous probability functions are defined for an infinite number of points over a continuous interval, the probability at a single point is always 0.
x
p(x)Magnitude of curve could be greater than 1 in some areas. The total area under the curve must add up to 1.
Joint Probability• Notation
• If X and Y are independent then
Conditional Probability
• is the probability of x given y
• If X and Y are independent then
Inference by Enumeration
=0.4
Law of Total Probability
y
yxPxP ),()(
y
yPyxPxP )()|()(
x
xP 1)(
Discrete case
1)( dxxp
Continuous case
dyypyxpxp )()|()(
dyyxpxp ),()(
Bayes Formula
)( yxp
evidence
prior likelihood
)(
)()|()(
yP
xPxyPyxP
)()|()()|(),( xPxyPyPyxPyxP
Posterior (conditional) probability distribution
)( xyp
)(xp Prior probability distribution
If y is a new sensor reading:
Model of the characteristics of the sensor
)(yp
Does not depend on x
Bayes Formula
evidence
prior likelihood
)(
)()|()(
yP
xPxyPyxP
)()|()()|(),( xPxyPyPyxPyxP
x
xPxyP
xPxyPyxP
)()|(
)()|()(
Bayes Rule with Background Knowledge
)|(
)|(),|(),|(
zyP
zxPzxyPzyxP
Conditional Independence
equivalent to
and),|()( xzyPzyP
),|()( yzxPzxP
)|()|(),( zyPzxPzyxP
Simple Example of State Estimation
• Suppose a robot obtains measurement • What is ?
Causal vs. Diagnostic Reasoning
• is diagnostic.• is causal.• Often causal knowledge is easier to obtain.• Bayes rule allows us to use causal knowledge: