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.

Filter by
Sorted by
Tagged with
0
votes
1answer
24 views

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 ...
0
votes
0answers
8 views

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 ...
0
votes
0answers
70 views

Is it possible to prove this conjecture about Collatz sequences?

I have constructed a tree that looks something like this: $$ 1,2,4,8,16, \begin{cases} 32,64,\begin{cases} 128, 256, \begin{cases} 512...\\ 85... \end{cases}\\ 21, 42, 84... \end{cases}\\ 5, 10, \...
0
votes
0answers
9 views

Prove that a split at a node in a decision tree reduces the RSS

Problem: let $m_1, m_2 \in \mathbb{Z}_+$ and $m = m_1 + m_2$ and let $y_1, ... , y_m$ be m real numbers. Define: $\mu = \frac1m\sum_{i=1}^m y_i,\ \ \mu_1 = \frac{1}{m_1}\sum_{i=1}^{m_1} y_i, \ \ \...
0
votes
0answers
14 views

confusion matrix

I need to construct a ROC curve for this decision tree, so I need to construct a confusion matrix first, but I am not sure which numbers are true positive and false negative? So, how can I find true ...
0
votes
0answers
31 views

Upper bound for the VC-dimension of a random forest with k trees where each tree has n leaves

Consider using decision trees/forests to implement Boolean functions. How to get a good upper bound for the VC-dimension of a random forest with k trees where each tree has n leaves.
1
vote
1answer
44 views

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 ...
0
votes
0answers
14 views

How to get the best combination from a set of variables without testing all of the combinations (user perspective)?

Giving a little bit of context: I have 3 variables which each of them can have 3 different values, where the best combination of the variables depends on user preferences (i.e. the user has to find ...
0
votes
1answer
32 views

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 ...
0
votes
0answers
15 views

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?
0
votes
0answers
14 views

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. ...
0
votes
0answers
14 views

pairwise variable importance (VIMP) in regression trees

I'm studying a little bit about detecting pairwise variable interactions in (survival) trees. But I'm struggling to understand one thing about the pairwise VIMP, defined as: $VIMP(x_i,x_j) := PIMP(...
0
votes
0answers
9 views

Logical alternative to random forest for one variable?

I have a large dataset I am analysing with a random forest regression. Part of my analysis aims to show that combining all features is better than subgroups. To highlight improvement, I want to run a ...
3
votes
0answers
57 views

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, ..., ...
0
votes
0answers
136 views

Decision Tree- Surgeory

Can someone please confirm if the decision tree I made for this Question is correct James McGill, age 68, was recently diagnosed with a particular type of brain tumor, and was referred to Dr. ...
0
votes
1answer
31 views

Nearest-neighbour classifier

Given a dataset $\mathcal D =\{x_i, y_i\}$ where $i$ runs from $1$ to $N$ and a new sample $x$, we simply assign to $x$ the label of the nearest sample to $x$ in $\mathcal D$, i.e. $f(x)=y_i$ such ...
1
vote
1answer
54 views

𝛾-rule in semantic tableaux of first-order logic

I'm a novice and I'm trying to understand semantic tableaux in First-Order Logic. 𝛿 - existential rule makes sense to me, if ∃x A(x) is true, saying "let c by ...
3
votes
1answer
125 views

Propositional Logic and Redundancy

There are Philosophical problems with the Material conditional. The Dutch philosopher Emanuel Rutten has written an article about it, titled: Dissolving the Scandal of Propositional Logic? From that ...
2
votes
0answers
20 views

Markov decision process structural properties

I am trying to prove a structural property of a Markov Decision Process (MDP), but I have not been able to do so. I am wondering if someone can give me some insight in how to prove it or give me some ...
0
votes
0answers
37 views

Decision tree construction

I recently failed a university exam in Decision theory. The question is as follows: 2. A car manufacturer wishes to market its latest design. They have already performed the minimum mandatory level ...
0
votes
0answers
23 views

Split Information vs Information Gain

I am reading about Decision Tree and Gain Ration To get Gain Ratio which is $Gain Ratio = \frac{Information Gain}{Split Information}$ But from the document I am reading they are actually the same ...
0
votes
0answers
14 views

Dynamic Multiple Variable Decision Support Probability Help

All, I'm faced with an unfamiliar, conceptual problem (at least to me). I'm sure there are a number of ways to execute, but I'm curious as to the best or most intuitive approach to achieve the ...
1
vote
0answers
30 views

Decision Trees - Regression trees weighting of child nodes?

I'm familiar with how classification trees weight the impurity measure of a potential split by the proportion of observations that would fall into each child node, such as: $$ loss = \frac{n_1}{N_m} ...
1
vote
0answers
26 views

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 ...
1
vote
0answers
34 views

Compute conditional probability for a decision analysis network

I have to resolve an exercise for decision analysis network. I have the following decision tree for that decision analysis network: $$\begin{array}{l} G&\to&Y&\to&D&\to&X&...
0
votes
0answers
35 views

Compute conditional probability

I have to solve this problem for a decision analysis network: "There is a genetic trait present in 20% of the population that makes that, for men over 65 years, the probability of suffering the ...
0
votes
2answers
51 views

Is this expected utility correct?

I'm learning Bayesian Networks and Decision Making but I'm not very good with notation. I have written down this expected utility (more info here): $$UE=\sum_s\max_b\sum_{s,r}\max_q\sum_tP(t)P(s|t)P(...
1
vote
0answers
31 views

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 $\mathbf{x} = (x_1, x_2...)$ ...
0
votes
2answers
73 views

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 ...
0
votes
1answer
44 views

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 ...
0
votes
0answers
106 views

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 ...
0
votes
1answer
27 views

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” ...
0
votes
1answer
75 views

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 ...
0
votes
1answer
41 views

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 ...
3
votes
2answers
600 views

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 ...
2
votes
1answer
1k views

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 ...
1
vote
1answer
294 views

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 ...
27
votes
4answers
8k views

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}...
0
votes
2answers
88 views

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 ...
-1
votes
1answer
100 views

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 $n!$
2
votes
0answers
47 views

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. ...
1
vote
1answer
77 views

Calculating the GINI impurity

I have a question regarding the GINI impurity that we use while building decision trees. From the wiki page on gini impurity, Gini impurity can be computed by summing the probability ${\...
0
votes
1answer
34 views

Decision tree and stopping the splitting process

I've have this question and I'm completely lost. Would really appreciate an answer to this question. Thank you. Let $D_a$ denote the training data set and let $T$ be a decision tree trained on $D_a$ ...
0
votes
0answers
111 views

how to get decision tree and calculate the error of tree?

Recently i start to read the artificial intelligent book written by David poole and i am trying to solve some exercise from there. In exercise that "Suppose we have a system that observes a person’s ...
0
votes
1answer
29 views

Event tree - can I add and mulitply the probabilities like this

If I have an event tree such as the following: Is the following solution then correct to get to B or to D: $(0.1 \times 0.4) + (0.1 \times 0.6 \times 0.7) = 0.082$ Or should I only use the first ...
0
votes
1answer
184 views

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 ...
0
votes
1answer
158 views

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 ...
15
votes
4answers
5k views

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 ...
1
vote
0answers
286 views

Perfect recall, Absent-minded driver,behavior strategy, equivalent mixed strategy

I wonder if a behavior strategy in an extensive form game has always an equivalent mixed strategy. There is no consensus in the literature I've read on this: in the chapter in the Handbook of game ...
1
vote
1answer
66 views

'ordered' set of rules

I have the following decision tree: ...