# 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.

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### How much should i delve deeper in a subject? [closed]

I'm currently studying for my AI and machine learning course and I've found myself more and more interested in the mathematical concepts underlying the subject. Though exams are still far, I more and ...
1 vote
52 views

### Conditional Probability with four variables [closed]

In the book A First Course in Machine Learning, second edition, by Simon Rogers, page 322, the author states that the joint posterior density over f and y is given by: p(f, y | t, X) = p(t|y) * p(y|f) ...
1 vote
42 views

### Can You Help Me Interpret the Meaing of an Relationship between a Vector, Element Symbol, the All Real Values Symbol, and a Variable?

I'm reading a research paper and I'm trying to decipher some mathematical text. It looks like this: $[y_1,...,y_T] \in \mathbb{R}^T$ My best guess is it is saying, "This set contains all real ...
148 views

### Can I interpret $\models$ as $\implies$ while proving logical expressions using different techniques?

In the book by Artificial Intelligence by Norvig and Russel, I came across following problem: Prove if correct: $(A ∧ B) \models (A ⇔ B).$ I quickly interpreted $\models$ as $\implies$ and tried to ...
1k views

### 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: $A =$ {$\text {car I }0.5,\text{ truck I }0.9,\text{ bus I }0.7,\text{ scooter }10,\text{ bike I }0.2$}...
102 views

### Determining the Degree of Counter-Clockwise Rotation at Which a Rectangle's X Coordinate Becomes Non-Negative [closed]

I've been asked to provide context to my original question, so here's the context: The rectangle in the problem below represents a pool table whose "pool table light" cannot be easily moved, ...
10 views

### Is it Possible to calculate probabilities on a Node, if one or two of Probabilities of the node on Bayes network not Given?

I just curious is it possible to calculate a Probabilities of something, if one of their nodes doesnt have the probabilities? For example, i want to calculate probabilites of Storm. I know the ...
1 vote
48 views

### Viterbi algorithm for object-tracking

I have a sequence of images, and I need to find and track the creation of the objects, then their movement and then their disappearance. There can be up to $3$ objects overall, and sometimes there are ...
1 vote
214 views

### how to calculate number of states for this logistics problem?

Consider a logistics problem with 3 cities, 5 trucks and 3 packages. Each truck can be at any of the locations. A package can either be at one of the locations or in one of the trucks. What would the ...
1 vote
248 views

### Can an artificial neural network with only one hidden layer suffice for all applications?

I have heard that only a single layer is needed for an artificial neural network to fit any possible function (input to output). Is this true and where is this shown? If this is true, then what is ...
21 views

### Can we unify 3 different First Order Logic sets/expressions?

Wherever I searched about unification in first-order logic (FOL) expressions, I could only find it as the unification of "two different logical atomic expressions identical by finding a ...
1 vote
80 views

### Good books on mathematics of information?

Are there any good books on the mathematics of information, under whose umbrella would fall cryptography, information storing, data processing (i.e. data to information), mathematics of artificial ...
46 views

### what's the best way of Inferring chance of heads with a coin of Unknown Bias

hi what would be the best strategy to infer the range of probabilities of getting heads with a coin of Unknown Bias that is variable? Thanks EDIT: Problem specification I'm working on a similar ...
57 views

### How can I calculate this repeating power?

I'm considering the stochastic tree. When root node is activated, the $n$ child nodes get the signal. But the probability of activation is $p$. $d$ is index of layer and starts from 1 that is ...
1 vote
27 views

### Breakdown question of single node hidden layer neural networks

I am working on writing a paper about neural networks and have been doing research and I seem to be getting conflicting answers from different articles. For the paper process we are required to submit ...
34 views

### Data distribution definition and notation, what is wrong or right?

My work area is machine learning but since I am not from a math background I am struggling a lot to do the right job. I wanna define the data distribution which is defined for data points. I have ...
21 views

### Is there a condition that guarantees that hill climbing will find the optimal solution?

I am studying intro to AI with shortest-path algorithms like A* and hill climbing. I learned that A* is guaranteed to find the optimal solution if the heuristic function ...
255 views

185 views

### Derivation Contrastive Divergence

I am trying to follow the original paper of GE Hinton: Training Products of Experts by Minimizing Contrastive Divergence However I can't verify equation (5) where he says:  -\frac{\partial}{\...
1 vote
124 views

### Help with Resolution Refutation Problem

I'm trying to convert Solve a Resolution Refutation problem. The problem states: Knowledge Base is ∀𝑥𝑦 𝐹(𝑥, 𝑦). Prove using resolution-refutation that ∀𝑥𝑦 𝐹(𝑦, 𝑥). Note: β = F(y, x) This ...
91 views

### water jug problem [closed]

The original version of water jug problem is that we have two empty jugs and an infinite source of water and the goal is to find a way to reach a state so that one of the jugs contains a specific ...
160 views

### Gödel's Incompleness Theorems and the "Minds vs. Machines" conundrum

As a part of my self-learning about Gödel's Incompleness Theorems, I try to dive a little bit into their different interpretations and (possible) philosophical implications. One that immediately ...