# 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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23 views

### Intuition on Mutual information in XAI

Following wikipedia, mutual information $MI(X,Y)$ is 'how much knowledge is in the output of one random variable about the other variable'. If MI between 2 variables is high, this does not mean I know ...
1 vote
64 views

### Conversion from FOL to CNF

To clarify, I am a newbie to this and am just doing some practice problems out of a text. Just looking for some clarification. The question is to convert \forall x \ \text{person}(x) \land [\exists ...
1 vote
61 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) ...
44 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 ...
115 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, ...
13 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 ...
24 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
85 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 ...
48 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
33 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 ...
40 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 ...
22 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 ...
20 views

### In Policy Iteration, why the successive value vector monotonically increases?

Let $\mathcal{X}=:\{x_1, x_2, x_3,...,x_n\}$ be the state space. Let $\mathcal{U}:=\{u_1, u_2, u_3,...,u_m\}$ be the set of actions. Let $A^{u_1}, A^{u_2}, A^{u_3},...,A^{u_m}$ be the state transition ...
1 vote
49 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 ...
8 views

### Constraint satisfaction problem

A perfect matching in an undirected graph is a subset S of the edges with the property that every vertex is contained in exactly one edge in S. Express the problem of finding perfect matching for a ...
408 views

### UNO Card Game and Game Theory

I've recently been trying to create a computer program which plays UNO against human opponents (and usually wins); however, because I have very little experience in game theory, I have been unable to ...
13 views

### Adjusting payoffs has unintuitive effect on optimal strategies in bimatrix games

Consider the game Rock-Paper-Scissors. If we award a win with $1$, a loss with $-1$ and a draw with $0$, we get the following bimatrix game (with rewards ordered as row player, then column player): R ...
1 vote
90 views

### Does "Iterative Policy Evaluation" Guarantee the "Optimal Policy"?

I am reading about "Iterative Policy Evaluation" algorithm in the context of Reinforcement Learning (http://incompleteideas.net/book/ebook/node41.html). If I have understood this correctly - ...
333 views

### Numerical Experiments: Definition and Examples

Could anybody define the "Numerical Experiment" and provide some examples? Does solving a problem using AI/Machine learning such as Artificial Neural Networks (ANN) or heuristic algorithm ...
128 views

### How to get a maximum and minimum score of dot product similarity metric?

I use this library (https://www.sbert.net/examples/applications/semantic-search/README.html) to perform an information retrieval task. There are two options for the similarity function: dot product ...
58 views

### Time Consumption by a super computer to solve a puzzle

I have a 4x3 cubic picture puzzle with 6 correct answers. Each piece in an inch^3 (l=b=h=inch=2.5cm). I can figure out the arrangements of this puzzle i.e. Each block in the puzzle can move in 24 ways ...
80 views

### Modelling a problem in Graph Theory language

I am trying to model the following problem that I found in the AI field in graph theory language, but I have limited experience in graphs. We consider a network of devices. If two devices are close ...
668 views

### Critic Loss in PPO

TL,DR: How precisely is the critic loss in PPO defined? I am trying to understand the PPO algorithm so that I can implement it. Now I'm somewhat confused when it comes to the critic loss. According to ...
319 views

### min max algorithm in Artificial Intelligence

How to understand the meaning of the image in Artificial Intelligence book in chapter 5?
150 views

### How can you find a 3-digit number "ABC", such that (ABC)/N = AxBxC ? Here, N=4. [closed]

How can you find a 3-digit number "ABC", such that (ABC)/N = AxBxC ? Here, N=4. Like, if abc/7= axbxc, answer is 735
22 views

### How to derive Slime Mould Equations

As shown in https://en.wikiversity.org/wiki/Slime_Mould_Algorithm, we have the Slime Mould equations for Approach food and Wrap food. I do not know how to derive these equations. Please help me or ...
595 views

### Reference: A rigorous mathematical approach to Deep Learning

I am searching for any reference that has a mathematical (and/or theoretical physics) rigorious approach to key principles in deep learning. while most books that I have came across with are heavily ...
34 views

### Which standard deviation for model averaging?

I hope math stack exchange is the right place for this question, even though it comes from an AI point of view. Say I have a machine learning model and for robustness of results, I initialize it with ...
33 views

### ReLU on a feature map

I have produced a feature map, that is 5x3, of a input layer which was 5x7. I have obtained "2:s" and "3:s" and also one "1". The aim is now to use the ReLU neuron on ...
1 vote
135 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 ...
93 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 ...
164 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 ...
116 views

### Removing Implication in the Conversion of WFF to Clausal Form

I understand the conversion algorithm, my concern is regarding the first step of 'Removing Implication'. Example: In the following figure when one removes implication, the negation comes before ...
67 views

82 views

### Mean of unormalized Gamma distribution

If $X$ follows a gamma distribution with parameters $\alpha$ and $\beta$ then: $p(x|\alpha,\beta) = \frac{\beta^{\alpha}x^{\alpha-1}e^{-\beta x}}{\Gamma(\alpha)}$ with $\Gamma(\alpha) = (\alpha - 1)!$...
434 views

### Introduction to AI

In the book Introduction to artificial intelligence Ertel asks this question (exercise 1.5(a)): Why is a deterministic agent with memory not a function from the set of all inputs to the set of all ...
359 views

### Saying either or both in first-order predicate logic?

I have a statement along the gist of "Each member of A is either Y, Z, or both" Would the appropriate way to write this using first-order logic be: ∀x (A(x) → (Y(x) ∨ Z(x))) Would it suffice ...
I'm learning about propositional logic and converting statements to conjunctive normal form. If I have a statement such as $t \leftrightarrow q$, a biconditional statement, and I apply apply ...