# VG441 Homework 1 solution

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Original Work ?

## Description

Problem 1
Prove that the derivative of θ
T XT Xθ with respect to θ is 2XT Xθ.

Problem 2
Age Home Owner Car Owner Having Kids Salary
40 Yes Yes Yes 10000
20 No No No 500
50 Yes No Yes 8000
30 Yes No No 5000

• Run GBM on paper for two iterations (i.e., stopping at F2 and PR2). No more than 4 leaves. Use
learning rate γ = 0.1. Features can be re-used in DT.
• Run XGBoost on paper for two iterations (i.e., stopping at F2 and PR2). No more than 4 leaves.
Use regularizer λ = 1 and pruning γ = 0 and learning rate µ = 0.1.

Problem 3 (Open-Ended)
Dataset
California housing price data in the 1990-2000. 1–9 are the features and 10 is the target.
1. longitude: A measure of how far west a house is; a higher value is farther west
2. latitude: A measure of how far north a house is; a higher value is farther north
3. housingMedianAge: Median age of a house within a block; a lower number is a newer building
4. totalRooms: Total number of rooms within a block

5. totalBedrooms: Total number of bedrooms within a block
6. population: Total number of people residing within a block
7. households: Total number of households, a group of people residing within a home unit, for a block
8. medianIncome: Median income for households within a block of houses (measured in tens of thousands of US Dollars)

9. oceanProximity: Location of the house w.r.t ocean/sea
10. medianHouseValue: Median house value for households within a block (measured in US Dollars)