# Tagged Questions

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### 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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### 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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### 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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### 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 ...
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### 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 ...
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### 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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### 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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### 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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### “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 ...
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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### Markov Decision Process - Utility Function

Reward R(S) in a Markov Decision Process is a mapping from a State S -> Bounded number. I want to know how a Utility Function is defined for an MDP. I think it has to be a mapping from a sequence of ...
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### 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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### 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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### Memory of a neural network: is it forever?

As far as I remember a neural network cannot forget anything. Does this mean that no matters how evolved the network is, it's always going to throw me back the right output if I feed it an input? And ...
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### 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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### 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 ...