Questions tagged [decision-tree]

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How to prove that the lower bound of the Huffman coding problem is $\Omega(n \log n)$?

how to prove that the lower bound of the Huffman coding problem is $\Omega(n \log n)$? Here Huffman coding problem is Huffman encoding. For example, ...
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1answer
40 views

Intersection of Decision Tree Boundaries in Higher Dimensions

I have trained two binary decision tree classifiers with splits in $\mathbb{R}^4$. Same data, but from two different patches. Now, I want to find the exact intervals where the two trees disagree. The ...
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1answer
22 views

What is beta and k parameter in Incremental Decision Tree

I have read this paper https://arxiv.org/pdf/1803.03674v1.pdf for outlier detection problem with real data (online training) In this paper, the authors used Incremental Decision Tree to build ...
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1answer
44 views

Basic exercises on decision trees

I am a pure math person doing some ML self-study and I am pretty lost. I am trying to solve the following exercises on decision trees: Exercise 1. Consider the following training set where $X_1,X_2,...
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1answer
38 views

Can inputs in the decision tree model be computed?

The Wikipedia definition of the decision tree model says that it allows the sign functions of certain classes to be computed in constant time (and presumably also memory). My questions, still ...
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174 views

how does the shap algorithm work in polynomial time?

I'm trying to understand how the shap algorithm calculates in polynomial time an estimation to the feature attribution function that satisfies the shapely value attributes (specifically for tree based ...
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23 views

Communication complexity and query complexity model

I have some doubts for the relationship between communication complexity model and query complexity model. In my understanding, query complexity model are same as decision tree complexity model. Let $...
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1answer
38 views

SMO, Random forest and Bayes net algorithms: why does Random forest perform better?

I analyzed a dataset using those 3 different algorithms. As I can see, Random forest performs better in most cases. My dataset is composed of 4000 instances of two classes (class A 2000 elements, ...
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31 views

Rummy Card Game Bot

in my beginner’s computer science class, we are asked to create an bot for a variant of rummy. It has to make logical moves as it needs to beat other very simple bots. I wanted to know how you would ...
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1answer
115 views

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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176 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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1answer
45 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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28 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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1answer
28 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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1answer
137 views

Decision tree and information-theoretic lower bound

Consider the following problem : ...
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2answers
418 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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370 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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482 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
77 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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89 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
96 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
192 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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559 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
36 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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1answer
30 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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47 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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111 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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30 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
67 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
779 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
44 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
39 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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124 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 ...