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      blogContent/posts/data-science/csci-331-review-2.md

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Idea: escape local maxima by allowing some bad moves but gradually decrease their size and frequency. Idea: escape local maxima by allowing some bad moves but gradually decrease their size and frequency.
This is similar to gradient descent. This is similar to gradient descent.
Idea comes from making glass where you start very hot and then slowely cool down the temperature.
Idea comes from making glass where you start very hot and then slowly cool down the temperature.
## Beam search ## Beam search
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## Genetic algorithms ## Genetic algorithms
Inspired by Charles Darwin's theory of evolution. Inspired by Charles Darwin's theory of evolution.
The algorithm is an extension of local beam search with cuccessors generated from pairs of individuals rather than a successor function.
The algorithm is an extension of local beam search with successors generated from pairs of individuals rather than a successor function.
![GA overview](media/exam1/gaOverview.png) ![GA overview](media/exam1/gaOverview.png)
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### Probability space ### Probability space
The probability space $\omega$ is all possible outcomes.
The probability space $\Omega$ is all possible outcomes.
A dice roll has 6 possible outcomes. A dice roll has 6 possible outcomes.
### Atomic Event ### Atomic Event
An atomic event w is a single element from the probability space. An atomic event w is a single element from the probability space.
$w \in \omega$
$w \in \Omega$
Ex: rolling a dice of 4 Ex: rolling a dice of 4
The probability of w is between [0,1]. The probability of w is between [0,1].
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### Event ### Event
An event A is any subset of the probability space $\omega$
An event A is any subset of the probability space $\Omega$
The probability of an event is the sum of the probabilities of the atom events in the event. The probability of an event is the sum of the probabilities of the atom events in the event.
Ex: probability of rolling a even number dice is 1/2. Ex: probability of rolling a even number dice is 1/2.

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