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Machine Learning

创建日期：2024-04-26 11:00:05

所属分类：计算机computer science

标签： Machine

Machine Learning

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Machine Learning

Problem Set 1
In this assignment you will implement a decision tree classifier that will be used to classify
four synthetic datasets and one real dataset. You will submit a writeup in Word or PDF
that summarizes your results and all code as a zip file. Submit the writeup (with attached
source code) to the Canvas submission locker before 11:59pm on the due date.
Classify Synthetic Data (30 points)
Write a method to estimate a decision tree of maximum depth 3 and apply it to the synthetic
training datasets. Go ahead and train and test on the same dataset (this is bad form in
general, but that is ok for this assignment).
Details:
You may not use a high-level function for decision tree fitting. However, if you’d like
to use a library for managing the tree (such as AnyTree in Python) then that is okay.
Everything else should be coded by you however. If you have questions on whether a
certain library is okay to use just ask and I will let you know!
Along each dimension, consider a finite set of possible splits. One possible way to do
this is to separate data into a finite number of equidistant bins based on the maximal
and minimal value along a given dimension. Another possible way to do this is to
separate data into a finite number of bins such that each bin contains roughly the
same number of examples. These are just two possible ways to do things. If you have
a favorite way of discretizing data, I encourage you to use it!
As mentioned at the start of class, all code should be written in Python 3.9+.
Use entropy and information gain to determine the optimal splits.
Explain any implementation choices you had to make in the final report.
Include the training set error for each synthetic dataset in the final report.
Visualize your classifiers (20 points)
Write a function that creates a visualization of the data set and the output of your best
decision tree. Recall that supervised learning methods are approximating a function, so
we can sample their value anywhere in feature space. Your function will display a graphic
that shows the training data as a scatter plot with the decision tree approximation as a
background.
1
Here is an example:
Your approach must meet the following criteria:
show the training data and clearly distinguish between the class labels: you can color
code the labels or use different markers
show the function approximation: to do this, write a function that grid samples your
prediction function in the area of feature space around the training data and use this
to construct an image. You can use this image as a backdrop for your sample points.
Your writeup must include visualizations for each of your best decision trees for the
synthetic data (so a total of 4 visualizations). Make sure you title each figure with the
dataset name.
Classify Pokemon! (30 Points)
Extend your decision tree to work on a real dataset about fictional monsters! I’ve provided
an additional dataset about Pokemon and whether they are legendary or not. Your job
is to construct a decision tree that can take in various statistics about a Pokemon and
predict whether it is legendary. As before, create a method that estimates a decision tree of
maximum depth 3. Chances are, you will be able to reuse most of the code written for the
first part of this assignment, and I encourage you to do so. You are also allowed to test on
this training data as well. Remember, this is typically a bad thing to do, but it is okay for
this assignment.
Details:
2
You may not use a high-level function for decision tree fitting.
This dataset contains a mixture of data types. You can handle continuous data in this
data similarly to how you handled it for the synthetic datasets; however, be aware that
some dimensions contain nominal data.
As mentioned at the start of class, all code should be written in Python 3.9+.
Use entropy and information gain to determine the optimal splits.
Explain any implementation choices you had to make in the final report.
Include the training set error for this dataset in the final report.
Presentation (20 points)
Your report must be complete and clear. A few key points to remember:
Complete: the report does not need to be long, but should include everything that was
requested.
Clear: your grammar should be correct, your graphics should be clearly labeled and
easy to read.
Concise: I sometimes print out reports to ease grading, don’t make figures larger than
they need to be. Graphics and text should be large enough to get the point across,
but not much larger.
Credit (partial): if you are not able to get something working, or unable to generate a
particular figure, explain why in your report. If you don’t explain, I can’t give partial
credit.
Bonus (10 points, required for graduate students)
Much of the performance of your decision tree is influenced by how you chose to discretize the
continuous values used in the synthetic training set. For this part of the assignment, improve
your decision tree implementation by using cross validation to intelligently choose how many
bins to use for discretization. You should compare at least 3 different discretization schemes.
Are the best schemes different for different datasets? If so, why do you think this happens?
You may use either leave-one-out or a fold-based method. You must include a description
of your algorithm in your writeup that would be sufficient for someone to reimplement your
method.

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