Machine Learning . Basic definitions: concept : often described implicitely(„ good politician “) using examples, i.e. training data hypothesis: an attempt to describe the concept in an explicite way concept / hypothesis are presented in the corresponding language
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concept: often described implicitely(„good politician“) using examples, i.e. training data
hypothesis: an attempt to describe the concept in an explicite way
concept / hypothesis are presented in the corresponding language
hypothesis is verified using testing data
background knowledge provides info about the context (properties of environment)
learning algorithm searches the space of hypothesis to find consistent and complete h., the space is restricted by introducing bias
Example 1 „computer game“: Is there a way how to distinguish quickly a friendly robot from the others?
H1 in the form of a decision tree
if neck( r) = bow then „friendly”
= nothing then
if head_shape ( r) = triangle then „friendly“
= tie then
if body_shape( r) = square then „unfriendly“ else
if head_shape( r) = circle then „friendly“
How many correct hypothesis can be designed for a fixed training set E?
Hypothesis are partially ordered
Version space: searches for the subset of hypotheses that have zero training error.
most gen. concept
most spec. concept
Given: Training examples uniformly described by a single set of the same attributes and classified into a small set of classes (most often into 2 classes: positive X negative examples)
Find: a decision tree allowing to characterize the new species
Simple example: robots described by 5 discrete atributes and classified into 2 classes (friendly, unfriendly)
given: S ... the set of classified examples
goal: design a decision tree DT ensuring the same classification as S
1. The root is denoted by S
2. Find the "best" attribute at to be used for splitting the current set S
3. Split the set S into the subsets S1, S2, ..., Snwrt. value of at (all examples in the subset Si have the same value at = vi ). This set denotes a node of the DT
4. For each Sido:
If all examples in Sibelong to the same class or
then create a leaf with the same label,
else go to 1 with S = Si
minimize the entropy (Shanon)
H(Si) = - pi+ log pi+ - pi- log pi-
pi+=the probability that a random example in Si is ,
estimated by frequency
Let the attribute at split S into the subsets S1, S2, ..., Sn. The entropy of this system is defined
H(S,at) = i n = 1 P(S i ) H (Si )
where P(S i ) is probability of the event S i , approx. by relative size |S i | / |S|
Chooseatwith the minimalH(S,at)
Design an automatic controller for F16 for following complex task:
1. Start up and rise upto the heigth 2000 feet
2. Fly 32000 feet north
3. Turn right 330°
4. When 42000 feet from the starting point (direction N-S) turn left and head towards the starting point, the rotation is finished when the course is between 140° and 180°.
5. Adjust the flight direction so that it is paralel to the landing course, tolerance 5° for flight direction and 10° for wing twist wrt. horizont
6. Decrease the heigth and move towards the start of the landing path
Training data: 3 skilled pilots performed the assigned mission, each 30 times
Each flight is described by 1000 vectors characterizing ( total of 90000 training examples): · Position and state of the plane
· Pilot’s control action
Position and state
Each of the 7 phases calls for a specific type of control.
The training data are divided into 7 disjunctive sets which are used to design specific decision trees (independently for each task phase and each control action). Control ensured by 7 * 4 decison trees.