For questions about artificial intelligence.

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1answer
127 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 $\forall(xy)...
2
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1answer
991 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 ...
4
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2answers
96 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 ...
1
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0answers
55 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 ...
0
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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 ...
8
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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.
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0answers
77 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
344 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
480 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
498 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 ...
2
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1answer
234 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 ...
1
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1answer
2k 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 ...
2
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1answer
40 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
60 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
1k 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 ...
1
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1answer
1k 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 ...
4
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1answer
1k 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*} ...
0
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1answer
223 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 ...
0
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1answer
47 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 ...
1
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1answer
84 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) ...
3
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1answer
159 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, ...
0
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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 ...
3
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0answers
437 views

Modern Mathematical Theory for Neural Networks, Cellular Automata, Neuroscience

Is it possible for someone to do research on subjects like neural networks, cellular automata, or neuroscience as an applied mathematician? I have in mind the theoretical development of these fields,...
2
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1answer
264 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 ...
2
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2answers
830 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
105 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
vote
1answer
2k 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 ...
26
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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 ...
1
vote
2answers
173 views

Some Questions About Chess

I have to questions about the chess game: please help me to understand it. 1- How can a computer program know if this move or that move is better? It calculates all possbile continuation and examine? ...
3
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1answer
182 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. Either there are redundant values or I'm missing how the ...
10
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2answers
879 views

What would be the shortest path between 2 points when there are objects obstructing the straight path?

How would an algorithm find the shortest distance between 2 points on a horizontal 2d plane , especially when a straight path is not possible? Could it be something on the lines of calculating least ...
1
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4answers
447 views

Which books /tutorials will be good for these topics for AI computer science student

I have found from the internet that I need to know these topics for understanding Artificial Intelligence: Matrix algebra: most machine learning models are represented as matrices and vectors. ...
4
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1answer
735 views

Recursively Solving a Bellman Equation

Problem Overview I am to figure out $v_\pi$ of a certain Markov state. Given Information A set of actions, $a$ containing ${up, down, left, right}$ $v_\pi(12), v_\pi(13), v_\pi(14)$ (I am given ...
2
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1answer
347 views

Books on AI, programming, optimization

I'm studying math (just started) and I like programming as well (just started this too), is there a career or a branch of research including deep aspect of this two aspects? Is there someone among you ...
11
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4answers
2k views

Mathematics base for data mining and artificial intelligence algorithms. [closed]

Could you give me some clarification about data mining and artificial intelligence algorithms? What mathematics base they used for? Could you give me starting point, in mathematics, to understand ...
1
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2answers
150 views

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 ...
4
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3answers
775 views

First order logic.

In Artificial intelligence, I saw the following question and answer in website. Question: Politicians can fool some people all of the time, and they can fool all people some of the time, ...
2
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3answers
207 views

Games with human edge [closed]

Which are some two- or one-player games, where humans far outperforms the best computer programs? And how does the relative edge scale with time allowed to think? (In time frame 1 sec to 8 hours per ...
2
votes
1answer
358 views

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 ...
1
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1answer
1k views

Propositional Logic. Algorithm for Deciding Entailment [closed]

I start studying artificial intelligence and logic. There are many things I do not know. Reading about inference I found that a Knowledge Base KB entails a sentence a if and only if a is true in ...
6
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1answer
1k views

What about Genetic Algorithms from a mathematical point of view?

Last year I've attended an Artificial Intelligence course (it was very simple, just a summary of the main ideas); we've seen what a genetic algorithm is and the idea seems very interesting to me. Now ...