For questions about artificial intelligence.

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0answers
19 views

Boosting v. weighted average

I have been watching an MIT online Artificial Intelligence lecture by Prof. Winston about boosting. The boosting technique uses complicated maths to combine the results from several weak predictors to ...
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1answer
75 views

Does this equation my professor wrote actually work? [closed]

Does this make sense to you? Peter's classroom example $\frac{1}{2^{(\text{any power})}} = \frac{1^{(\text{any power})}}{2^{(\text{any power})}} = (\frac{1}{2})^{(\text{any power})}$ If that's the ...
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0answers
7 views

How do I use resolution refutation in backward reasoning

Suppose I have the following facts in my KB: ∀a,b: g(a,b)→ p(a,b) ∀x: ¬p(x,x) ∀x,y,z: p(x,y)∧ p(y,z)→ p(x,z) ∀w,r: p(w,r)→ g(w,r) I have a questions: If I want ...
2
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1answer
39 views

What aspects of convex optimization are used in artificial intelligence, if any?

I work on convex optimization with Stephen Boyd's book. As an example, support vector machines are mentioned as an application of separating hyperplanes theorem. I am wondering if there is any other ...
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0answers
27 views

hamiltonian graph problem (sitting problem)

Hello guys sorry for noob question but i am learning graph theory and i am solving a question . in book it says it have only four solution but i founded that it can more than four so i am confused . ...
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56 views

The mathematics behind Google Deepmind

I'm aware of the following question: The mathematics behind AlphaGo AI and Google Deepmind I'm aware of math behind Perceptron and several other AI concepts: ...
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0answers
13 views

Uniform cost search algorithm on given graph

I am having an issue understanding this problem and how to apply the uniform cost search on a given graph (the London metro) which is given here: http://tubephotos.dannycox.me.uk/stationsbyline.html ...
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1answer
222 views

The mathematics behind AlphaGo AI and Google Deepmind [closed]

in case you are following the tech news, Google's AlphaGo beat the world Go champion Lee Sedol, not once but twice. Here is the link of the game 2 review: ...
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1answer
20 views

Formulas of propositional logic, two sets and refutation.

Let $\alpha$ and $\beta$ be two formulas of propositional logic and set $S_\alpha$ and $S_\beta$ be the sets of clauses representing $\neg \alpha$ and $\neg \beta$, respectively. Show that if ...
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1answer
21 views

How to find the optimal linear basis functions of an MDP?

Given a set of basis functions, there are many papers on finding a weight vector to linearly approximate the value function. Is there any paper on how to find the basis functions? Is it possible to ...
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1answer
66 views

How to apply negation to a term?

EDIT: Maybe page 18 of this paper can help. This is a follow up from this question, where I am using ALCQ and I have this: $\lnot(3 \le \exists \text{hasPet}.\text{Animal})$ How to apply the ...
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1answer
46 views

Make individuals distinct

I am trying to construct an ALCQ knowledge base (KB) for some sentences. Here is what I have: Abox (Yiannis is a person and he drinks only one kind of a coffee, frappe): Person(YIANNIS) $\forall$ ...
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1answer
170 views

State space for 8-queen problem

While reading Artificial Intelligence a Modern Approach I came across the following formulation for the 8-queen problem: Initial state: No queens on the board. States: Arrangements of n queens (0 ...
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0answers
22 views

Use of activation derivative in back propagation algorithm

I'm a little confused how the activation derivative in back propagation work. Firstly, when I remove the activation derivative from the back propagation algorithm and replace it with a constant the ...
2
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1answer
32 views

Comparing two textbooks for machine learning

I am a Ph.D student in Electrical Engineering. I am going to study the field of machine learning and I found some textbooks to study this field. 1) Probabilistic Graphical Models: Principles and ...
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0answers
29 views

How to calculate probabilities in a Bayesian network?

Consider the Bayesian network represented by the directed acyclic graph given below: We are given the following probabilities: P(tampering) = 0.02 P(fire) = 0.01 P(alarm | fire ∧tampering) = 0.5 ...
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1answer
53 views

LOGIC - Completeness vs Consistent

One of my exams questions were the following (translated from Hebrew) Course is in Artificial Intelligence, and is about Logic in this question. What is a consistent logic system? What is a ...
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2answers
105 views

Neural network cost function - why squared error?

Question: Why is the squared error most often used for training neural networks? Context: Neural networks are trained by adjusting the link weights. The key factor that informs these adjustments is ...
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1answer
27 views

who is lying? - by using Knowledge Base by resolution

I found this question online, and tryied to solve. However, I have trouble with the methods Here question Three children Allison, Jack, and Frank were playing “hide and seek” game in an apartment. ...
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0answers
25 views

The significance of odds and logs in Bayes Naive Classification

I do understand the concept of Naive Bayesian classification, as it tries to calculate the probability of an outcome of a class given multiple evidences. It comes from the Bayes theorem and it is ...
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0answers
36 views

Is normalized RBF always better than RBF

The question is as the title. Mathematically, I want to know does the following inequation always hold for any vector $\mathbf b$? $\mathbf b^T \mathbf B \mathbf B^+ \mathbf b \, \ge \, \mathbf b^T ...
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0answers
17 views

Implicit feature space of Power Kernel

For the polynomial kernel, $K(x,y) = (x^Ty+c)^d$, the implicit feature space $\phi$ for which $K(x,y) = \phi(x)^T \phi(y)$ is of finite dimension and well known [1][2]. It is also well known that the ...
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0answers
76 views

Solving differential equation using artificial intelligence

Hellow, I want to do my phd on the topics solving differential equation using artificial intelligence. At first I want to read some introductory books on artificial intelligence and then on the topic ...
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0answers
27 views

State space complexity of $2d$ and $3d$ tic tac toe

So for a 2d tic tac toe game, we know that the space complexity can be represented as follows. A naive upper bound will be $3^9$ as there is $3$ possibilities (X, Y or blank) in each of the $9$ ...
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1answer
36 views

Dung's Argumentation Framework

Given an extension of Dung's argumentation framework, and all definitions therein, let $$AF_1 = \langle A,Def \rangle$$ be a framework where $$A = \{ A, B, C, D, E, F, G, H \}$$ and $$Def = \{A def G, ...
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0answers
36 views

Improving Simulated Annealing based on Measure of Goodness

can anyone answer this question or direct me to a reference that can help? Simulated Annealing returns the current state when the end of the annealing schedule is reached and if the annealing ...
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1answer
134 views

binary resolution rule proof

I want to proof the binary resolution rule that is, if we For any two clauses $C_1$ and $C_2$, if there is a literal $L_1$ in $C_1$ that is complementary to a literal $L_2$ in $C_2$, then delete $L_1$ ...
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0answers
33 views

Complexity analysis of alpha beta pruning of a full tree

I am trying to understand the derivation of a time complexity for an alpha-beta pruning algorithm but up till now have not found any reasonable recourse. Many recourses claim that if you take a full ...
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0answers
14 views

Using differential evolution to evaluate weights

I have an equation I am attempting to optimise of the form: w1x1 + w2x2 + w3x3 Using a pre defined fitness function. Unlike any of the original papers, I also have the constraint: Sum of the ...
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0answers
22 views

How does Best First Search Calculate the Heuristic Values in the Graph

I understand that Best First Search uses a sorted open list based on Heuristic Values of the Nodes (priority queue) and a closed list.But how are these Heuristic values of the Nodes calculated? The ...
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3answers
289 views

Reducing TIC-TAC TOE State Space by using Symmetry in Artificial Intelligence

Im learning Heuristics in AI.I see that for brute force search there are 9! states.But the textbook says that first 3 levels are reduced by symmetry.How does that work?
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0answers
15 views

What would linear neurons be able to model in artificial neural nets

Is it true that linear neurons are only useful in single layer neural nets because adding multiple layers will not allow the net to learn any interesting features because of the linear neurones?
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1answer
107 views

Math replacing natural language [closed]

Before reading any further. I ask yous to think creatively on this subject. I was in shower and was pondering over A.I. (Strong A.I. both at human level and beyond human level) as I do from time to ...
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0answers
44 views

combine analysis and artificial intelligence

I'm sorry if I ask this question at the wrong place, but I don't know a better one. I am a Master's student and I am really interested in analysis, but I also want to get into AI. Does anyone know a ...
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1answer
75 views

Can you give a simple CDCL example?

I am trying to understand how Conflict-Driven Clause Learning works. After reading through the lecture slides, wikipedia article and some additional slides I found online I realized that I still can't ...
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0answers
29 views

Lattice of a Fuzzy Number?

Can somebody define what is a fuzzy lattice? How to computer lattice of a fuzzy number? Please try to be generic and basic in the explanation as I'm a beginner in studying fuzzy theory and soft ...
0
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1answer
44 views

Calculating Entropy

Hi there kind people, I'm studying for an Artificial Intelligence test in a week or so, and this question is from a past paper - and it has really stumped me. Any help would be appreciated. Thank ...
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0answers
93 views

How does Godel Escher Bach support Artificial Intelligence? [closed]

Typically, Godel's Incompleteness theorems have been used to argue against the possibility that the human mind is essentially equivalent to a formal system. However, in Daniel Dennett's book "Darwin's ...
2
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0answers
83 views

How to Calculate Values from Incoming Messages? - Evidence Propagation in Bayesian Network

I'm currently trying to wrap my head around evidence propagation in bayesian network (simple tree propagation) but I'm having trouble finding information about the process. As an example, let's take ...
2
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1answer
50 views

Finding the best fit of 3 categories ( restaurants/meal/person analogy problem )

I have this problem that sounds tedious and long and I'm not sure if there exist an intuitive way to solve it. The problem is related to image recognition but I will try to give an analogy to it You ...
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1answer
59 views

What does the notation ab1, ab2, etc. refer to in predicate logic?

I'm trying to decipher a set of relations from a John McCarthy paper: $$ specializes(c1,c2) \land \neg ab1(p,c1,c2) \land ist(c1,p) \supset ist(c2,p) $$ and $$ specializes(c1,c2) \land \neg ...
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2answers
61 views

Find sectors in a racing line.

Consider the following photo: To magnify image, right click and select open-image in new tab or something similar The photo above is a random race circuit data I've collected. What I'm trying to ...
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1answer
63 views

Bayesian Nets. No active path from X to Y, versus No inactive paths from X to Y

I am learning d-seperation in Bayes nets for my A.I. class. What this involves is considering all paths from some node X to Y (representing random variables) and seeing whether such paths are active ...
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1answer
121 views

“Anything anyone eats and is not killed as a result is food” - First order logic representation

Given the required predicates: eats(x,y) : x eats y food(x) : x is food killed(x) : x is killed I am confused as to how to represent this statement in First Order Logic Would it be ...
2
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1answer
931 views

How to calculate Full joint probability distribution

This is a past exam question, I did it wrong in the exam, I'm reviewing it right now. The question is to compute the full joint probability of the problem below: I draw the full joint ...
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2answers
92 views

Are there some functions that cannot be optimized using calculus?

I've been working on a project to maximize a functions output using a genetic algorithm. However, from the limited calculus I know I thought there were methods to find the maximum of a mathematical ...
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0answers
53 views

feature selection for continuous variables

I wonder how exactly "feature selection" should be performed in case of continuous feature values. When feature values are discrete it is very straitforward to apply feature selection, but what to do ...
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1answer
39 views

Ellipsoidal Covariance Matrix

What does it mean when you say "Covariance matrix are highly ellipsoidal"? I am reading a paper and it uses this term very often "Covariance matrices are all equal and Highly ellipsoidal "?
2
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1answer
1k views

What is the sigmoid *squashing* function?

I've just read the following The basic unit ("neuron" i) performs the following computation to update its state $y_i$: it computes a weighted sum $v_i$ of its inputs $x:j$ which is passed ...
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3answers
2k views

What Maths are the most important for Artificial Intelligence?

I am just curious about this. Please don't include anything about programming.