For questions about artificial intelligence.

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2answers
80 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 ...
4
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1answer
897 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*} ...
3
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1answer
158 views

i,j,k values of the theta matrix in neural networks

SO I'm looking at these two neural networks and walking through how the ijk values of Theta correspond to the layer, the node number, and either there are redundant values or I'm missing how the ...
1
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1answer
215 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 ...
0
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1answer
26 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. ...
0
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1answer
87 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 $L_1$ ...
0
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1answer
45 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
45 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 ...
2
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0answers
18 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 ...
2
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0answers
385 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, ...
1
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0answers
21 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 ...
1
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0answers
31 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
12 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 ...
1
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0answers
33 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 ...
1
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0answers
45 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 ...
1
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0answers
64 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 ...
1
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0answers
287 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 ...
0
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0answers
15 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 ...
0
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0answers
54 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 ...
0
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0answers
21 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 $9$ ...
0
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0answers
30 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, ...
0
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0answers
25 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 ...
0
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0answers
11 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
16 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 ...
0
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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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0answers
35 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 ...
0
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0answers
25 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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0answers
15 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 ...