start presentation

report/main.typ

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-#import "@preview/touying:0.6.1": *
-#import themes.simple: *
-
-#show: simple-theme.with(aspect-ratio: "16-9")
-
-= Title
-
-== First Slide
-
-Hello, Touying!
-
-#pause
-
-Hello, Typst!

report/presentation.typ

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