For questions about artificial intelligence.

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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
29 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
13 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
94 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
20 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
27 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
14 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 ...
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1answer
36 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
66 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 ...
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0answers
13 views

Applying a Resolution to a Predicate with Substiutions

My professor handed us an exam review with the answers already filled in. On this one particular problem I have no idea how he came to the answers he did. Question: Apply a resolution to the ...
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0answers
30 views

Conjunctive normal form (~p->r) AND (~p->~r) <-> r

I need help converting following formula to conjunctive normal form. (~p->r) AND (~p->~r) <-> r By using equivalences i arrive to following result (((~p AND ~r) OR (~p AND r)) OR p) AND (~p OR ...
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0answers
5 views

What is a basic description of how diffusion mapping works?

I have been trying to get a basic understanding of diffusion mapping, and I think I understand the concept, but I am having trouble understanding the math behind it (I have knowledge of advanced math ...
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0answers
82 views

Concept Learning algorithm in Artificial Intelligence

Im going through Machine Learning in Artificial intelligence(Artificial Intelligence by George F Luger-Page 398) . Im going through the candidate elimination algorithm. There is this specific to ...
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1answer
41 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
41 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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0answers
22 views

How to transform one graph to a spectrum?

Recently, I studied a paper called "What Does Your Chair Know About Your Stress Level? It can be download at the link below. ...
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0answers
14 views

neural networks truth table uses of bias and weight

in a Truth table there are two additional columns for bias and weight, what is the correct purpose of the columns. i am having to build a randomiser application and would like to understand their ...
3
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2answers
45 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
33 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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0answers
41 views

An example shows the difference between inference in Bayesian network and Junction Tree

Why inference in Junction tree is more efficient? There are directed graph BN and the corresponded undirected graph transformed by Junction tree algorithm. The literature describes that inference in ...
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1answer
65 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
370 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
83 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
39 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
32 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 "?
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1answer
577 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
1k views

What Maths are the most important for Artificial Intelligence?

I am just curious about this. Please don't include anything about programming.
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0answers
48 views

Solomonoff induction , Shannon Entropy, Kolmogorov Complexity.

If Expected Kolmogorov Complexity equals Shannon Entropy why can't Shannon Entropy be used as an approximation of Kolmogorov Complexity in Solomonoff Induction? Regarding Kolmogorov Complexity and ...
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0answers
194 views

Estimating conditional probability as a function of time

My question relates to estimating from a time series a time dependent conditional probability without having a prior parametric model of anything. Suppose I have two variables: r and I, and each can ...
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4answers
434 views

Application of computers in higher mathematics

Currently the main application of computers in mathematics seems to be to compute things, i.e. to solve equations, evaluate integrals, etc. It is at all possible to delegate the thinking of a ...
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5answers
283 views

First Order Logic

Is it possible to represent the english sentence with numerical value in First order Logic. For example if the sentence is: Nobody has more than one mother. I am wandering who can i show the ...
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1answer
208 views

Testing critical points using newton-raphson method

I'm working on a homework assignment for my artificial intelligence course and I became a bit stuck on one part. The problem asks to retrieve the optima of the function and then to tell for each ...
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1answer
754 views

Proving that a Hessian Matrix is positive definite

I'm currently stuck on a problem for my Artificial Intelligence class. The assignment is provided at the following link: http://courses.engr.illinois.edu/cs440/HW1.pdf The problems that I'm stuck on ...
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1answer
32 views

Markov Decision Process - Optimal policy invariance to scaling in the Utility Function

The title says it all. If i use a discounted Utility Function, why is the optimal policy invariant with respect tot the scaling of the Utility Function by a positive Factor?
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2answers
52 views

Why this first-order logic formula is not correct?

I'm studing computer science at university, in specific Artificial Intelligence. We are using Otter as Theorem prover. I'm having some problems formalizing this: "John, Mary and Derek are three ...
8
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1answer
925 views

Applications of Differential Geometry in Artificial Intelligence

I am new to this wonderful site. I searched around a bit but I couldn't find any well-discussed posts on applications of differential geometry to artificial intelligence, or more generally to computer ...
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1answer
836 views

Using implication with the Universal quantifier

While reviewing my AI textbook, I came across a paragraph that baffled me. It attempts to explain why the truth table for implication turns out to be perfect, as ...
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1answer
577 views

Convert a WFF to Clausal Form

I'm given the following question: Convert the following WFF into clausal form: \begin{equation*} \forall(X)(q(X)\to(\exists(Y)(\neg(p(X,Y)\vee r(X,Y))\to h(X,Y))\wedge f(X))) \end{equation*} ...
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1answer
149 views

Is a traditional Multi Layer Perceptron Network capable of non-linear regression? Which activation function should be used for that purpose?

I need to use a Multi Layer Perceptron Network in order to perform some non-linear regression. Any ideas if it's possible to perform a task like that and how? Which activation function should be used ...
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1answer
44 views

probabilistic behaviour

I am trying to understand what 'probabilistic behaviour' in a 'deterministic model' means. I am reading this paper http://www.ulb.ac.be/sciences/use/publications/JLD/16.pdf but i find myself unable ...
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1answer
79 views

CHeck my proof of how I arrived at my answer

Show proof for: (P --> Q), P ^ (~ ~R & ~ ~ Q), (S --> ~ R), ~(P & Q) : (~S ^ ~Q) is this correct? (P --> Q) Premise P ^ ( ~ ~R & ~ ~Q) Premise (S --> ~R) ...
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1answer
150 views

Mathematics in cognitive sciences

Which areas of Maths can be formally studied in a cognitive sc major? Or: which areas of maths can support the study of brain. Some areas that seem relevant would be: mathematical logic, graph theory, ...
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1answer
12 views

Classification cost in growing a classification tree

This question is based in machine learning, but is heavily mathematic so I am posting here. This equation is used to estimate the class conditional probabilities of a certain leaf of data D in a ...
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0answers
329 views

Modern mathematical theory on Neural Networks, Cellular Automata, Neuroscience

Is it possible for someone to do research on Neural Networks/Cellular Automaton/Neuroscience as an applied mathematician, for its theoretical development, especially based on some modern mathematics, ...
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1answer
173 views

Gradient descent/ nonlinear optimization intuition needed

all. I'm taking an introductory AI class, and we're using the gradient descent algorithm to find the optimized/ lowest cost of a set of thetas (variable coefficients) to best fit a regression line. In ...
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2answers
599 views

Some doubts about the differences between logic implication and inference rule

I am studying for an Artificial Inteligence university exam that includes a section dedicated to mathematical logic. I am finding some difficulty in understanding the difference between logical ...
5
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1answer
100 views

AI strategies for losing positions [closed]

I have a card game that I am analyzing with Maple. Actually, it's a series of card games, one for every parameter k, where k is a natural number (representing the number of ranks of cards used in the ...
1
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1answer
1k views

Ranked Preference Matching Algorithm

first dropping the link that will serve as reference: NRMP Residency Matching I have a sort of side project (nothing riding on it, computational performance not an issue, so feel free to go wild, I ...
2
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1answer
66 views

Boolean Algebra Question

my problem is ,Please give the algorithm: how can rewrite an arbitrary propositional formula alfa(α) into a proposional formula beta(β) so that beta does not contain disjunction(∧) and alfa ...
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3answers
1k views

Mathematical preparation for postgraduate studies in Linguistics

I am an undergraduate student in Mathematics and I would like to continue my postgraduate studies in the harder, more mathematical aspects of Linguistics. What exactly would that include is unknown ...