Questions tagged [decision-tree]

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How to convert a decision tree to an automaton?

From what I know, a problem can be transformed to a yes/no answer, which can be described by a decision tree. Solution to a problem also can be represented by a set of strings (a language), which ...
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60 views

Why decision tree method for lower bound on finding a minimum doesn't work

(Motivated by this question. Also I suspect that my question is a bit too broad) We know $\Omega(n \log n)$ lower bound for sorting: we can build a decision tree where each inner node is a comparison ...
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25 views

Lower bound on comparison-based sorting

I have a question from one of the exercises in CLRS. Show that there is no comparison sort whose running time is linear for at least half of the $n!$ inputs of length $n$. What about a fraction of $1/...
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27 views

Problems about Decision Tree

Do any one give me some hints to solve this problem. Explain is steps by steps.Thanks
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24 views

Longest palindrome substring in logarithmic runtime complexity

In a palindrome of size N, the amount of candidates for the longest palindrome is N^2. Therefore, the information theoretic lower bound (IBT) should be lg(N^2), which is equivalent to a runtime ...
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33 views

Decision tree and information-theoretic lower bound

Consider the following problem : ...
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17 views

Finding the lower bound through decision trees

One way to find the lower bound of a comparison based algorithm is to use the decision tree. U have two questions regarding this method : 1) We know that the height of the tree is path that connects ...
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2answers
64 views

Lower bound and worst case scenario

We know that the lower bound is the minimum amount of work needed to solve a problem. So for a given problem say x it has the best algorithm ( the most efficient algorithm to solve this problem ) say ...
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122 views

How to convert a decision table to a consistent decision tree?

I am working from presentation from school, but I am not able to understand how they go from one step to the other. This is the decision table that I have. From it, the first thing we have to do is ...
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22 views

Decision tree: how to decide the next node?

I have to decide for which value of "Klasse" How do i do it? I know that I have to decide on maximum information gain So first off I've calculated the entropy of "Klasse" That is E(Klasse)= -(3/11*...
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91 views

vc dimension of binary decision trees of depth d?

how do i find the vc dimension of the hypothesis space H ,of the binary decision trees of depth d-2? will the hypothesis space H consist of{0,1} and the vc dimension is the number of ways in which we ...
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2answers
122 views

In information theory, why is the entropy measured in units of bits?

In information theory, we have the quantity "information". Suppose we have some discrete random variable $X$, that can take values $\{{a,b,c\}}$ with corresponding probability distribution $\{{\frac{...
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1answer
46 views

How to handle missing attribute's value with ID3 algorithm?

i am working with ID3 algorithm, and i know that classic ID3 basically can handle missing data. But i am trying to code this algorithm, so what should i do if there is missing attribute's value in ...
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87 views

Decision Tree for searching an element in an n*n matrix

I just learnt decision tree concept in class. I have a question for homework. It says to prove that for searching an element in n*n matrix the lower bound is logn and prove it using decision tree. My ...
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1answer
35 views

Lower bound for merging $m$ sorted arrays (decision tree leaves count - permutations)

I need some help understanding how to calculate the lower bound on the time complexity of merging $m$ sorted arrays of length $n$. The bound should be $nm \lg(m)$. I need to prove this using a ...
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1answer
142 views

How to calculate information gain in ID3?

I am trying to implement a decision tree classifier using ID3 algorithm. According to Aritificial Intelligence - A Modern Approach, information gain of attribute A ...
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379 views

Random Forest - Conditional Permutation Importance

I've been looking for the most unbiased algorithm to find out the feature importances in random forests if there are correlations among the input features. Besides the most commonly preferred ...
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1answer
35 views

Finding maximum takes at least $\lceil n/2 \rceil$ comparisons

We are given an array $A$ with $n$ elements, $n \in \mathbb{N}$ and all elements are in the set $\{1,2,3, \cdots, n \}$. I want to prove that finding the maximum in $A$ (that is, outputting the index ...
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20 views

decision trees and numeric attributes

I have been reading a book about Decision Trees and it caught my attention the following part: In case of numeric attributes, decision trees can be geometrically interpreted as a collection of ...
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30 views

Classify/Distinguish between 8008 binary grids, with 13 queries

I have $8008$ binary grids of size $6 \times 10$ (they are all grids with the property described below), which I want to distinguish between with at most $13$ queries. A query will determine if the ...
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34 views

Attribute Selection for minimum number of clusters

I have a table consisting of some headers $P, Q, R, S$ (shown in blue in Table 1). According to the headers, the column $T$ is populated using some predefined logic. Now, any of the headers $P,Q,R,S$ ...
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1answer
57 views

What do Arora and Barak mean by $x|_S$ in their definition of certificate complexity?

I am having much trouble understanding the following definition (of certificate complexity - for decision trees) from Arora and Barak's book Computational Complexity: A Modern Approach. Perhaps there ...
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29 views

Avoiding collisions in space and time

Say I have an image, represented as a 2D array of pixel values. Also, say I have a set of points on that image where each has a current (x, y) position and a Destination (x, y) associated with it. I ...
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1answer
2k views

What machine learning training algorithm to use for this kind of string dataset?

I am working on a project where I have to train the following data-set using machine learning algorithm. One of my friend suggested decision tree, but I have never seen a situation where independent ...
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1answer
57 views

Decision Tree Learning Deviation - Russell and Norvig

I am working through the Russell and Norvig AI book and came across the following on the top of page 706. The section concerns Decision Tree pruning and testing a given attribute against the null ...
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1answer
638 views

What is the main difference between binary decision tree and binary decision diagram(BDD)?

What is the main difference between binary decision tree and binary decision diagram(BDD)? From what I can tell I only understand that a binary decision diagram is a more compact representation ...
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1answer
38 views

Connected Components - Linear Decision Trees

What does connected components mean in the context of non-graphs? Graphs have vertices and the vertices are connected by edges. Hence, you can build a spanning tree (for example) by systematically ...
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1answer
37 views

Decision tree complexity of finding parameters of “zigzag” array

I am currently studying for a test on data structures. I have to find the lower and upper bounds for the following problem: An array is called a zigzag array if there are $1 \leq i \leq j \leq n$ so ...
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1answer
114 views

Decision tree complexity of deciding whether array is “zigzag”

I am currently studying for a test on data structures. I have to find the lower and upper bounds for the following problem: Input: an array with $n$ numbers. Output: boolean answer for the ...