Mathematics Stack Exchange
Mathematics Stack Exchange

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 ($\triangle$)
97 questions
35
votes
4 answers

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…
Mountain_sheep
  • 469
14
votes
4 answers

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.
  • 388
6
votes
1 answer

Guessing a triple of digits by knowing if you got at least one of them right

Here is a rephrased version of problem $4$ in BMO $2016$ round $2$. I rephrased to make it clearer and shorter. Given is a triple of digits $(a,b,c)$, where $a$, $b$, $c\in\{0,1,\dots,9\}$. Each turn we guess a triple of digits $(m,n,p)$, and…
user1034536
6
votes
2 answers

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
  • 241
4
votes
2 answers

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
  • 43
3
votes
0 answers

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…
Ilya
  • 176
  • 1
  • 7
3
votes
0 answers

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
  • 301
3
votes
2 answers

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…
Han de Bruijn
  • 17,475
3
votes
2 answers

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…
Ruslan Mushkaev
  • 417
3
votes
1 answer

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
  • 145
2
votes
1 answer

Prove a lemma about permutations

Let $V$ be a set of $n$ permutations of $m$ numbers. Let $m
xavrojo
  • 21
2
votes
0 answers

Is this binary search tree correct?

I have made a binary search tree from this sequence: 4, 1, 7, 5, 6, 3, 0, 2, 9, 8 And I just want to make sure that it is correct. Starting with 4. Then 1 which is less than 4 so its placed on the left side. 7 is greater than 4 so it becomes the…
Peter
  • 67
  • 2
2
votes
0 answers

Formal definition of decision tree

I am looking for a reference that would provide a formal definition of a decision tree. I am mostly referring to combinatorial games, Markov decision processes and similar fields. It should be something more or less like: Let A be the set of…
alagris
  • 203
  • 1
  • 8
2
votes
1 answer

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
  • 669
2
votes
0 answers

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…
WeakLearner
  • 6,350
1
2 3 4 5 6 7