73 lines
2.1 KiB
Typst
73 lines
2.1 KiB
Typst
#import "@preview/touying:0.6.1": *
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#import themes.university: *
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#show: university-theme.with(
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aspect-ratio: "16-9",
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config-info(
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title: [bioai - assignment 1],
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author: [fredrik robertsen],
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date: "09.02.2026",
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institution: [ntnu idi],
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logo: box(image("ntnu.png", height: 1em))
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),
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)
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#title-slide(authors: [fredrik robertsen])
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== problem 1 - binary knapsack
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- there are many items, each with a value and weight
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- the knapsack you are wearing can only carry so much weight
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- you want the most bang for your buck
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- what's the best _combination_ of items to keep?
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- combinatory problem, np hard
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- approximate using a genetic algorithm
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- this is like optimizing your inventory in games like skyrim
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- do you want 400 spoons in your pocket, each worth a dime, or do you want that gold bar that weighs a ton?
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- formally, you want to maximize $z = sum_(j=1)^n p_j x_j$ such that $sum_(j=1)^n w_j x_j <= c$ where $x_j in {0, 1}$
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- for item $j$: $p_j$ is the profit; $w_j$ the weight; $x_j$ whether to keep it
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== problem 2 - feature selection
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- similar to the binary knapsack problem
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- this time you have many data points
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- each data point consists of _features_
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- each data point has an associated _output_
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- you wish to eliminate the features that are least influential in producing a given output
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- this is like choosing what items to keep in your knapsack
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- this is like weather forecasting
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- hundreds of features in data
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- which are most relevant?
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- which are noise?
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== general implementation
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- generate a population of randomized chromosomes
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- calculate their fitness values
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- perform a _tournament selection_ to choose parent chromosomes
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- more fit individuals are more likely to be selected
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- introduces less diversity
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- combine two parents to form two children via _single point crossover_
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- mutate children randomly
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- merge children into population, evicting the least fit individuals
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- this is the _elitism survivor selection_
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- repeat
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== specific implementation
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- fitness function
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- used the sum mentioned earlier
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- used linear regression and rmse for feature selection
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== optimizations
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todo
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== results
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todo
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== conclusion
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todo
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