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.

A decision tree is a flowchart-like structure in which each internal node represents a "test" on an attribute (e.g. whether a coin flip comes up heads or tails), each branch represents the outcome of the test and each leaf node represents a class label (decision taken after computing all attributes). The paths from root to leaf represents classification rules.

A decision tree consists of $3$ types of nodes:

  • Decision nodes - represented by squares ($\square$)
  • Chance nodes - represented by circles ($\circ$)
  • End nodes - represented by triangles ($\triangle$)
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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, $$- \sum_{i=1}^6 \dfrac{1}{6} \log_2 \dfrac{1}{6} = \log_2 (6) = 2.5849...$$ However, the entropy…
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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 of how I calculated it: And from it I get that…
yt.
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Diminishing upper limit on Rubik's Cube solutions - why so long?

I distinctly remember the news in 2007 about how researchers at Northwestern University had established the upper bound on moves needed to solve a Rubik's Cube at 26. (I haven't been paying attention since, but it's obviously a lot lower…
pr1268
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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 drawn at 20-20. The final game will continue until…
Zavier
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Probability of a feature in a randomly permuted decision tree constrained that no feature is reached twice in any decision path

I have a (binary) decision tree consisting of nodes $N=\{N_i\}$ that take on boolean propositions/features $F=\{F_k\}$. Different decision paths can split on the same feature so $ |N| >> |F| $ Edit: and in addition the number of repeating features…
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Alice, Barb, and Claire each toss a fair die in that order until someone gets a 6 and wins. What are the probabilities of each player winning? ...

... Generalize this to $n$ players. Compute the probabilities $p_1, ..., p_n$ that each player wins. Proposed Solution: Let $p_k$ be the probability of player $k$ winning in the set $\{p_1, ..., p_n\}$ Then: $$p_k = (\frac{5}{6})^{k - 1} *…
Joshua Anderson
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Propositional Logic and Redundancy

The Dutch philosopher Emanuel Rutten wrote an article, titled Dissolving the Scandal of Propositional Logic?, about the philosophical problems with the material conditional. From his article, we quote the following as an example that is true in…
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How do I know when to use a Venn diagram or a probability tree? Also, when can I assume that the events are independent?

I have 2 specific problems, one 'requiring' me to use a probability tree, and the other a Venn diagram. I know that apparently the Venn diagrams can be converted into probability trees and vice versa, so I have attempted to use the probability…
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Have I Found an Error in "Game Theory" by Hans Peters?

I am reading the book Game Theory: A Multileveled Approach Second Edition by Hans Peters. It appears to be the most recent copy. I've search here and on Google for a list of known errors in the book, but couldn't find any. In section 1.3.3.1…
noel
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How can the number of times an event occurs a given number of times in a decision making tree be calculated when the odds of the occurrences is known?

stackexchangers I am attempting to calculate the probability that a subject will experience an event a minimum of 7 times over ten periods when the probability of the (independent) event occurring is 0.5. I think I need to sum the probabilities that…
duckegg
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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 examples on each side of the split, and moreover, the…
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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 that belong to a class c for a particular node t.…
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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: "A path is a sequence of moves such that at the…
Adolf Miszka
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How to cheapest test N people for an infection?

Say you have $N$ people each having a probability of $p$ for being affected (and, $p+q=1$, a probability of $q$ for being not infected). Say you have a test where you can combine the samples for any $n \leq N$ people and the test tells if any (at…
Gyro Gearloose
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Adaboost intuition

The intuition behind adaboost is that if a decision stump is performing well, i.e. $\alpha_t > 0$ by a significant amount, then we'll assign more weights to the misclassified instances and less weight to the correctly classified instances. We would…
Eli.Z
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