# 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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### Explicit formula for $F(a,i)=p_iF(a-1,i-1)+(1-p_i)F(a,i-1)$

So, I have this node tree that I have constructed in this way: I start at 0 at the top and add 1 if I go left and do nothing if I go right. I go left with a probability $p_i$ for level $i$ in the tree ...
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1 vote
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### Relationship Between Gini Index and Decision Trees

I am trying to learn about the mathematics behind how Decision Tree algorithms work (https://en.wikipedia.org/wiki/Decision_tree_learning). For example (and for simplicity sake), consider a dataset ...
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### What is the average number of questions needed for decision tree

Assume you're using the optimal strategy, where you ask the fewest number of questions to guess the animal from this decision tree. What is the average number of questions you need to ask? Is there ...
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### Why is the value of information gain negative?

Here is a sample dataset. I have to calculate the Information gain in Variable. Am I missing anything as information gain should not be negative? Variable Class ...
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### Can two combined events have a probability greater than the events themselves?

I'm presented with the following conditional probability problem: There are 2 bags with different numbers of lemon and grape candies: Bag #1: 5 lemon candies, 5 grape candies (10 candies total) Bag #...
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### Generalization of Tree Diagrams

In simple probility theory one learns about tree diagrams and their rules. First you draw them with the outcomes. Then you write the probility of each event according to Laplace's formula and then to ...
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### How to find the threshold to split the data based on a feature in decision trees

I was studying decision trees from a book about machine learning and it says that the rule applied to partition the data in a node of the tree is the one that maximizes the information gain, which is ...
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1 vote
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### Product of sizes of subtrees of a perfect binary tree

A perfect binary tree is a binary tree for which every parent node has exactly two children and each leaf occurs at the same depth (alternatively, same height) in the tree. A perfect binary tree of ...
25 views

### Find partitions based on data

I have a set of vectors $V = (v_1, v_2, \cdots, v_i, \cdots, v_n), v_n \in \mathbb{R}^d$ and a partition annotation $L_i$ for each vector $L_i \in \{1, 2, \cdots, K \}$. My goal is to partition $V$ ...
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1 vote
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I have a probability question which I would appreciate some help with. a) Complete the values in the tree diagram b) The probability that Terry will not be the champion is 0.58. Find the value of p c)...
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### Prove that the average height of a full binary tree is greater or equal to the logarithm of its leaf count [closed]

The average height of a full binary leaf (a node is either a parent with 2 childs or a leaf) is: $$h_m(T) = \frac{1}{|B(T)|}\sum_{b\in B(T)}\operatorname{depth}(b)$$ B(T) is the set of leaves. Now I ...
1 vote
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### Metric for partitions of a topological space

Let $X$ be a topological space. Consider the set $B_X$ of partitions of $X$ such that every block of the partition is simply connected. How can one define a metric $d$ on $B_X$? To help answer this, ...
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### Understanding the $\alpha$-regularity assumption for trees

In this paper, definition 4 claims that a tree grown by recursive partitioning is $\alpha$-regular for some $\alpha>0$ if each split leaves at least a fraction $\alpha$ of the available training ...
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### Why is $\sum x(1-x)$ equal to $1-\sum x^2$?

I'm going through Python Machine Learning and I'm at the Gini impurity sections, where they define Gini Impurities as $I_g(t) = \sum_{i=1}^c p(i|t) (1 - p(i|t))$ where p is the proportion of samples ...
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### If $4$ distinct integers $a, b, c, d$ are randomly selected from $n$ distinct integers, what is the probability that $a \lt b \lt c \lt d$?

a. If $i$ distinct integers $r_1, r_2, \ldots,r_i$, i $\leq n$, are randomly selected (one after other) from n distinct integers, what is the probability that $r_1 < r_2 < \cdots < r_i$? b. ...
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### Decision based on decision tree

Based on a text I created a decision tree. This decision tree shows options A, B and C. I calculated the value that could be expected for each decision and the highest one would be that of option C ...
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### Probability of disease transmission to future generations

Assume disease D is transmitted through a father (male) to his children. Let us assume that every family in a society have $C\geq1$ children. Let the father of a family have the disease D. What is the ...
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### What is the difference between P(W1,W2) vs P(W2|W1) in this context

What is the conceptual difference between the probability of winning two successive games in a playoff series vs winning the second game given that you won the first game? I understand P(W2|W1) as the ...
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### Complete path of a decision tree

The task is to prove that a complete path starts at the root and ends at the leaf. For me is quite obvious, but I should write a mathematical proof, so, need some help with it. I found a definition: &...
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### Decision Tree Problem: Evaluate probabilities and determine in terms of C, all the optimal decisions.

I'm struggling with this decision tree question: A part of an aircraft engine can be given a test before installation. The test has only a 75 % chance of revealing a defect if it is present, and the ...
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### Need help understand this theorem of decision trees

A version of the game of Nim is used to illustrate the minmax strategy in Rosen's Discrete Mathematics and Its Applications, 3ed, chapter 11 p. 768. I understand the ...
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### in machine learning’s impurity measures. Where does the word Gini originate from? Why entropy is represented with an H? Where does this H come from?

Where does the word Gini originate from? Why entropy is represented with an H? Where does this H come from?
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### Looking for a counterfactual approach to interpreting classification decisions

Suppose you're a surgeon and you are making a decision based on the output of a model. The variables in this model $x_1, x_2,...$ are clinically interpretable, like age, blood sugar, or hemoglobin. ...
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