Questions tagged [artificial-intelligence]
For questions about artificial intelligence, the intelligence of machines and robots and the branch of computer science that aims to create it.
230
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Machine of maximum number of support vectors (SVM)?
I have learned a thing or two about Support Vector Machines (SVM) and it seems to me that maximum margin machines are popular. I came to wonder if there exist any flavour of SVM which not only strive ...
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How to convert an English sentence that contains "can't take more than 2" into predicate calculus sentence? [closed]
The example is :
A student can’t take more than 2 courses with the same instructor
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1
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167
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What is the set of models of the empty set?
We have that :
$Mod (\emptyset) = \{ I \in Int_{At} / I \vDash \emptyset \}.$
My question is, what is the set of interpretations that satisfty the empty set?
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236
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Why is the Error surface for a 2 input neural network with 2 weights a parabolic bowl
I am new to machine learning and AI in general and had a quick question regarding the error function surface regarding a simple neural net:
2 input neural net
After reading the following wiki: https:/...
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1
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452
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Sample covariance matrix notation
I do not understand this notation for the sample covariance matrix (from Artificial Intelligence: A Modern Approach, Peter Norvig and Stuart J. Russell, Section 20.3, EM algorithm):
$\Sigma_{i} = \...
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Payoff matrix of a scenario and the Schelling point.
Consider the problem of two people trying to drive safely on a two lane road. Each player can drive on their right or left. If players follow the same convention, they’ll drive safely. If they do not, ...
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1k
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Convert sentence into First order predicate logic.
a) rabin likes only CSit Course
b)science course are hard.
c)all courses in CSIT are easy
d)CSC 101 is a csit course.
4
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2
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348
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Regarding Research in Artificial Intelligence [closed]
Which mathematical areas are important for research purposes in artificial intelligence? Specifically, If I have Masters in Statistics how much it will be beneficial for research in artificial ...
- 243
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1
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149
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Optimizing a function through reinforcement learning.
I want to know if reinforcement learning can be used for such optimization problems:
\begin{align}
& \max_{p_1^t, p_2^t}\quad\log_2(1+ p_1^t h_1^t)+\log_2(1+ p_2^t h_2^t) \\[6pt]
\text{s.t. } &...
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4
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What areas of math can be tackled by artificial intelligence?
Artificial intelligence is nearing, with image/speech recognition, chess/go engines etc. My question is, what areas of math that are interesting to mathematicians, is likely to be the first to be able ...
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269
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How to First order logic procedure convert Convert to Conjunctive Normal Form ?
How to below this First order logic procedure convert Convert them into Conjunctive Normal Form ?
Ɐx [[employee(x) ꓥ ¬[PST(x) ꓦ PWO(x)]] → work(x)]
I strive to do this below step ,
i. S1: ...
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2
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238
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How to write the below paragraph in First Order Logic and Convert them into Conjunctive Normal Form
I tried to do this. but this is uncertain. see this below my answer. Please kindly help for me. how do you do this.
Any employee who does not participates for the strike or work in
contract basis ...
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0
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57
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Bayesian Network Probability
Question # 1: On the network which I posted above, I am having trouble determining what the probability of:
P(A,F)
is and how it is derived?
My thinking was that if you have this event (A) that is ...
- 11
1
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1
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181
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Minimize the maximum value returned by paths of an oriented graph in a minimum of transformations
I'm definitely not a math expert so please forgive me in advance for not using the proper vocabulary or conventions. I'm kind of stuck with the following situation in a project of mine:
I have been ...
- 113
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0
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62
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Understanding the definition of general knowledge between agents
Background
Consider a set of possible states, $W$. An agent, $i$ has knowledge of a fact $E\subseteq W$, $K_iE=\{w|\sim_i[w]\subseteq E\}$, where $w\in W$ and $\sim_i[w]=\{w'|(w, w')\in\sim_i\}$ is ...
- 209
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Find boolean function without brute force truth table?
I have the following homework (AI-related):
Which boolean function does the following TLU (threshold logic unit) implement? The TLU (threshold logic unit) has five inputs. Its weight vector is (1.1, 3....
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327
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Grounded vs. Preferred Semantics (Dung) [closed]
How does Dung's Grounded Semantics framework work in practice? I got this from slides of an AI course but can't figure it out:
Grounded Semantics is said to minimize amount of arguments IN (green) ...
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23
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In Dempster-Shafer theory, is it possible for a BPA to be equal to 0(zero) or 1?
Can a Basic probability assignment for an event A, m(A)=1 or 0.
m(A) could be a decision output for any classifier.
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Clustered Regions by Each Neuron in Self Organizing Map (SOM)
I was given a question about SOM.
There is a SOM which have 4x4 neurons and each neuron's x1 and x2 values (coordinates) given. Also neighborhood function and weight update rule given. How can i find ...
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489
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How to find the conditional independence?
I reviewing some AI books and recently i found the following question that i would like to solve:
In the given Bayes network, decide the conditional independence of the nodes.
Justify ...
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1
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88
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Bayesian network
I have this following question and i would like to know if anyone can answer it.
For a given Bayesian network where $P(a) =.6, P(b|a) =.8, P(b|-a)=.4, P(c|a)=.4$ and $P(c|-a) = .3$, compute $P(c|b)$. ...
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82
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Weird logarithm rules in an attempt to proof an upper bound of JSD between two Gaussian distribution
I'm currently working on my thesis in Deep Learning and stumbled upon one paper that I think is really related to my topic. In short, I could not understand some parts of its computation process. Here'...
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659
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How to prove this using resolution theorem or resolution refutation?
I need to prove P v (Q ^ R), S : (S ^ P) v Q using resolution theorem or resolution refutation. This is my proof:
Convert P v (Q ^ R) to (P v Q) ^ (P ^ R)
Convert ...
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2
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85
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De morgan quantifers prove
prove ∃x (P(x) => Q(x)) = ∀x P(x) => ∃x Q(x)
∃x (P(x) => Q(x))
= ∃x (¬P(x) ∨ Q(x)) ----- (1)
= ∃x(¬P(x)) ∨ ∃xQ(x) ----- (2)
= ¬∀xP(x) ∨ ∃xQ(x) ----- (3)
= ∀x P(x) => ∃x Q(x) ----- (4)
From line ...
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0
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151
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how to get decision tree and calculate the error of tree?
Recently i start to read the artificial intelligent book written by David poole and i am trying to solve some exercise from there.
In exercise that "Suppose we have a system that observes a person’s ...
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1
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82
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Calculating probability using Bayes rule.
I've been searching through posts on this web about how to apply Bayes' rule on the question on my assignment. I've came across many useful tips and advices. However, not all of my questions are ...
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1
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466
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greedy best first search
What heuristic functions transform greedy best-first search into breadth-first search, depth-first search, and uniform-cost search?
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2
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348
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Perceptron and gradient descent
Let imagine the simpliest case where we have a set of point with some label in $\{1,-1\}$ such that the two group of point (respectively to their label) are perfectly well separated by an hyperplane ...
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546
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Why was the resolution method so important to AI/theorem proving?
I have read that the resolution method was literally a "miracle" for AI. So far, from what I understand, there are 2 things differentiating from other systems of inference rules:
Only a single ...
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1
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118
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Evolving Neural Network using both genetic algorithm and back propagation
I didn't find any literature on this matter; I want to build an RNN that uses both Genetic algorithms and back propagation to evolve a network. So my idea is to use GA and BP for training, though in a ...
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68
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Program / web service to connect a number with known constants?
Say I have a number, that I know to a certain precision:
$$c = 1.46342 ...$$
where $...$ denote unknown digits. I want to find a simple formula connecting this number to a known mathematical ...
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434
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How to solve $Ax = b$ using Simulated Annealing?
I have an idea how the Simulated-Annealing algorithm works w/ TSP, but I have no idea how to solve $Ax = b$, given an $n \times n$ matrix $A$ and a vector $b$. I know that it might sound stupid, but I ...
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Determine the concentration and normalization of a fuzzy set
Could you help determine this?
Concentration and Normalization of a Fuzzy set $A$ as given
below:
$A =$ {$\text {car I }0.5,\text{ truck I }0.9,\text{ bus I }0.7,\text{
scooter }10,\text{ bike I }0.2$}...
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1
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166
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Transform a wff to a prenex normal form
Could you help solve this problem. I need to convert the following wff to a PNF
∀x(L(x)->∃x M(x,y))
I do not understand how universal quantifier and existential quantifier on same variable operate. ...
0
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1
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156
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What is the significance of a graph exhibiting the delta property?
In class about AI we are studying graph searches. Here, we defined the "delta" property to mean that c(n,m)≥δ>0 for each (n,m)...
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40
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Solving linear system of equations with three variables to obtain ranked prestige: how to?
Whatever I do, I can't grasp it. The letters confuses me, as I don't know exactly what I need to do.
For example, I get z = 14 / 15 y, but what's next? Should I plug the whole y function once again ...
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120
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Can this given set be unified?
Assuming a,b,c are constant, and the rest are variables, what is the result of unification to the following sets?
P(f(x,z),r,t) , P(w,f(g(w),h(t),b)
The obvious solution would be to do the ...
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0
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461
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Derivation of P(MB(X)) where MB(X) is the Markov Blanket of X in a Bayesian Network
Given the Markov Blanket $\mathit MB(X)$ I am told that $$P(\mathit MB(X)) = \alpha P(X \vert U_{1}, \cdots , U_{n}) \prod_{Y_{i}} P(Y_{i} \vert P(Y_{i} \vert Z_{i1} \cdots)$$
where $\alpha$ is the ...
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365
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Estimate the parameters of the Laplacian distribution using Bayesian Distribution
I have the following zero-mean Laplacian distribution, and I am trying to estimate its parameters using Bayesian Estimation.
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How to find A and k constants of the equation y_n = A cos(x_n + k) using Numerical method
How to find A and k
constants of the equation $y_n = A cos(x_n + k)$ when $y_1 ... y_n$ and $x_1 ... x_n$ is available in a iterative process. Data is received iteratively. All data is not available ...
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77
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What does the following function mean?
The following is the mathematical definition of a Artificial Neuron,
$$\textbf{Activation function } f: \qquad y = f(w^t x) = f\left( \sum_{i=1}^n w_i x_i \right)$$
Given that $W$ is a vector, what ...
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What's the difference between y(x) and a in the cost function from neuralnetworksanddeeplearning.com book
I'm reading Neural Networks and Deep Learning book of Michael Nielsen from http://neuralnetworksanddeeplearning.com/chap1.html#learning_with_gradient_descent
The definition of the cost function is:
\...
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2
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260
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Self-similarity in mathematical sequences
Can any mathematical sequence be considered self-similar after some predefined number of terms similar to the initial sequence?
Such a function could be something crazy or simply every second term, ...
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1
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715
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Given a Knowledge Base use resolution to prove ∃x¬B(x)
¬B(x) ∨ C(x), ¬C(K) ∨ D(L), ¬C(M) ∨ E(N), ¬D(w) ∨ ¬E(y).
Given this knowledge base, use resolution to prove ∃x¬B(x).
I am really stuck with this one.
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Need help calculating full joint probability distribution
I need help calculating P(alarm) from this setup:
This problem is similar to that in this link:
http://www.cs.tut.fi/~elomaa/teach/AI-2012-7.pdf
However, the sum of all probabilities in that link ...
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1
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93
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Is there any mathematical work on formalizing problems and their solutions as mathematical objects?
Problems (tasks?) are an important part of life, science, math, basically everything. Do people study them as mathematical objects? Theorem proving seems close, however, I'm interested more in the ...
- 121
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1
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52
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A* tree search at the start node and goal node
I want to know if i'm understand the idea behind A* tree search correctly. My understanding is that the path is given by:
$f(n) = g(n) + h(n)$
and that
$h(n) \leqslant h^*(n)$
Where $g(n)$ is ...
- 91
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0
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23
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Search on graphs, finding the best way for more than one driving object
I know about algorithms like A*, Breadth-First, Depth-First , and so on. These algorithms are based on a very bad assumption which makes them not working on actual situations. I give you an example : ...
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1
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67
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First Order Logic question using moels
I've got the following expression and I want to know its truth value. What confuses me is the fact that False implies Truth is True. So, what happens if there's NO "a" value in the domain of some ...
1
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1
answer
216
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How to estimate two unknown parameters of a equation
The equation is
$$
y(x) = ab^2x^2 + abx + g(x)
$$
I know $x$, $y(x)$ and $g(x)$, I want to estimate $a$ and $b$.
And I want to optimize $a$ and $b$ with future data of $x$ and $y(x)$.
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