# Questions tagged [decision-trees]

Use this tag for questions about graphs or models of decisions and their possible consequences including chance-event outcomes, resource costs, and utility.

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### 12 Balls , prove you have to put 4 balls on each side in order to find odd ball is 3 times

You have twelve (12) balls and a set of balance scales. One (1) of the balls is a different weight to the other eleven (11) balls. You are allowed to use the balance scales three (3) times. You ...
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### Finding the change in value between two simple NPV-weighted decision trees

I'm a student in a finance class, with a professor who's been known to be both sloppy with his arithmetic and very defensive when asked about errors. He currently insists that his answer to the ...
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### How to optimise a boolean expression

I am working on an optimization problem involving Boolean expressions and wanted some help as I have very little knowledge about the topic. The problem statement is as follows: There are a set of ...
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### Variable transformation for training a machine learning model

Suppose you have a train set $\mathbf{T}$ and you want to train some Machine Learning models. Each row of $\mathbf{T}$ consists in a set(vector) of attributes or variables $\mathbf{x} = (x_1, x_2...)$ ...
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### Entropy and its relation to proportion

I have that entropy is $$H(X) = - \sum_i^m p_i \log_2 (p_i)$$ And my understanding is that for a fair coin toss entropy would be maximised as there's the greatest amount of uncertainty for a ...
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### Probability of On-Time arrival - Tree diagram

I need to determine the branches of a tree diagram for the following problem. John's car is in the garage and he has to take a bus to get to school. He needs to make all three connections on time to ...
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### Expected loss for regression tree with absolute loss function in case of choosing labels randomly

Suppose we have a regression tree (binary). The absolute loss function $L(y,\hat{y})=|y-\hat{y}|$. I know that the optimal prediction that minimizes $\frac{1}{n}\sum_{i=1}^{n}|y_{i}-\hat{y}|$ is the ...
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### Calculating probability of sending a bit given an error occurred in a noisy channel

A digital signal “1” or “0” is transmitted through a noisy channel, the received data may be different from the signal sent out. Suppose the transmitter sends out “0” with probability 0.7, and “1” ...
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### How does hyper-plane equation divide vector space into cells convex polyhedrons?

I came across some specific algorithm that divides high-dimensional vector space into non-overlapping cells of convex polyhedron. It does this by using tree based binary partitions (which might not ...
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### Sequencing events of Truth or Lie in possibility Trees

I have issues with the answer for this question problem: Clarence is known to speak the truth two out of three times. He throws a fair, six-sided die and reports that it shows a 6. What is the ...
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### Table tennis win probability

This problem is from my teacher and I think their answer is wrong. The problem is in the context of table tennis. The players in the tournament final are Ani and Bertha. The score in the game is ...
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### VC-dimension of the class of decision trees

I need to show that the VC-dimension of the class of decision trees over the domain ${0,1}^d$ is $2^d$ I tried to show that any binary classi er can be implemented as a decision tree of height at ...
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### How would I solve a classic Bayes Theorem problem using a probability tree? To help visualize what Bayes Theorem is doing.

For example Assume that a test for a disease gives a positive result for 2.5% of people who do not have the disease, but does not test negative if the person has the disease. What is the ...
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### Shannon entropy of a fair dice

The formula for Shannon entropy is as follows, $$\text{Entropy}(S) = - \sum_i p_i \log_2 p_i$$ Thus, a fair six sided dice should have the entropy, - \sum_{i=1}^6 \dfrac{1}{6} \log_2 \dfrac{1}{6}...
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### What type of tree is this?

The checkmarks I've drawn means that the branch ends or a node with the same number allready exists in the tree. I.e it means it reaches some cycle or ends the branching. I don't know if this is even ...
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### number of nodes in a decision tree

I don't know how to prove/disprove this: In a decision tree for sort algorithm there are at least $2^{n!}$ nodes. I know that the number of leaves is $n!$
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### Boosting tree for feature generation v.s. Boosting tree for classification

I am referring to this sample (http://scikit-learn.org/stable/auto_examples/ensemble/plot_feature_transformation.html#sphx-glr-auto-examples-ensemble-plot-feature-transformation-py) for the context. ...
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### Poisson Process (Expected Waiting Time) w Tree Diagram

Hi everyone so I have a quick question. Say for example we have a supermarket in which customers arrive with an intensity of 10 per hour. The supermarket has 3 aisles, A,B and C. The probability of ...
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### Why do we want a decision tree to be shallow? Why do we split to maximize information gain?

When constructing a decision tree, we use a measure such as the Gini Impurity or Information Gain to decide which split is best. IIUC, we want to have as shallow as tree as possible. But why do we ...
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### Monty hall problem probability 2/6?

For the Monty hall problem, with 3 doors, two of which have sheep and 1 has a car. I calculated the probability of getting the car if you swap being 2/6 instead of 2/3. I have drawn this tree diagram ...