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.
231
questions
-4
votes
2
answers
84
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, ...
- 95
0
votes
0
answers
9
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 ...
0
votes
0
answers
20
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
1
vote
1
answer
73
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 ...
- 11
-1
votes
1
answer
45
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 ...
- 1
0
votes
0
answers
56
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 ...
- 11
1
vote
0
answers
26
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 ...
0
votes
0
answers
24
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 ...
- 111
0
votes
1
answer
20
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 ...
- 717
0
votes
0
answers
15
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
0
answers
46
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 ...
- 11
0
votes
0
answers
7
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 ...
0
votes
0
answers
288
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 ...
- 139
0
votes
0
answers
12
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
1
answer
79
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 - ...
- 2,464
0
votes
0
answers
37
views
alpha beta pruning for multiple players
I have just finished implementing the min-max algorithm for a three-player game. I currently want to implement alpha-beta pruning but I, unfortunately, am unable to find any clear methods on how to ...
0
votes
0
answers
86
views
Converting First-Order Logic to CNF
I am having a lot of trouble using the rules of converting First-Order Logic to CNF. I have this statement:
∀x∃y : ([P(x, y) → Q(y, x)] ∧ [Q(y, x) → S(x, y)]) → ∃x∀y : [P(x, y) → S(x, y)]
After ...
0
votes
1
answer
235
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 ...
0
votes
0
answers
44
views
Book recommendation for introduction to symbolic logic motivated by AI
I am a second year mathematics undergraduate that has taken real and complex analysis, linear algebra, group and ring theory, general topology, probability theory and statistical inference. I am ...
- 343
0
votes
0
answers
84
views
Monte Carlo Tree Search
You are to manually run the MCTS algo-
rithm for the navigation example covered in class for 10
iterations. For this, you will need simulation results for
nodes at tree depth up to 2, which is ...
- 23
0
votes
0
answers
113
views
multiple losses with L-BFGS in torch
I am using the torch iimplementation of L-BFGS to minimize a loss function, which is given as the sum of $n$ loss function
loss = loss_1 + loss_2 + ... + loss_n
Computing each of the losses loss_i is ...
- 183
0
votes
0
answers
9
views
Heuristic search problem in a directed tree
I am learning about heuristic search algorithms and am trying to find a non-trivial admissible heuristic for the problem linked below.
Problem
Note: Let V(n) be the value in node n. There are 3 ...
0
votes
1
answer
106
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 ...
- 1
0
votes
0
answers
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 ...
0
votes
1
answer
79
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 ...
- 307
0
votes
1
answer
449
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 ...
- 209
0
votes
1
answer
281
views
min max algorithm in Artificial Intelligence
How to understand the meaning of the image in Artificial Intelligence book in chapter 5?
- 21
0
votes
1
answer
134
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
0
votes
0
answers
20
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 ...
2
votes
0
answers
403
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 ...
- 239
0
votes
0
answers
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 ...
- 1
0
votes
1
answer
26
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 ...
- 25
1
vote
0
answers
112
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 ...
- 11
0
votes
1
answer
81
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 ...
- 1
4
votes
1
answer
156
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 ...
- 3,277
0
votes
1
answer
98
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 ...
- 129
-1
votes
1
answer
60
views
Solve this by converting sentences to clausal form? [closed]
If:
$E\land R \implies B$
$E\implies R\lor P\lor L$
$K\implies B$
$\lnot(L\land B)$
$P\implies \lnot K$
Which of the following can't be deducted?
$E\land P$
$K \land E \implies R$
$L \land P \implies\...
- 9
3
votes
1
answer
113
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 ...
- 1,943
0
votes
1
answer
363
views
Does empty set entails everything?
I am new to propositional logic, and I am trying to figure out whether the below statement is correct:
[a |= c] or [ b |= c] → [a^b |= c]
First of all, it is ...
- 137
0
votes
1
answer
168
views
Determining Independence in Bayesian Network
Consider the Bayesian Network Structure Below, decide whether the statements are true or false.
b) $G \perp \!\!\! \perp A$ (G is independent of A)
c) $E \perp \!\!\! \perp H | \{D,G\}$ (E and H are ...
- 873
0
votes
1
answer
65
views
You know the probability that an object is dirty. An unreliable sensor tells you its true state. What is the new probability that the object is dirty?
I have encountered a statistics related problem for an AI project that I don't know how to solve, but I'm also nearly statistically illiterate so I'm not sure where to look. Hoping I can get a tip ...
- 3
1
vote
0
answers
50
views
Why does k-means have more bias than spectral clustering and GMM?
I ran into a 2019-Entrance Exam question as follows:
Which of the following algorithm has the higher bias?
GMM
GMM (identity covariance matrix)
spectral clustering
k-means
The answer mentioned is (...
- 53
0
votes
0
answers
126
views
T-algebra and a matrix paradigm over the algebra
We established a novel semisimple commutative algebra called t-algebra, which is backward-compatible to the field of complex numbers. Many notions of complex numbers and matrices are generalized. The ...
- 29
1
vote
1
answer
65
views
Is this textbook's combinatorial reasoning for $n \times n! / (b!(n - b)!)$ incorrect?
I recently asked this question on cs.stackexchange.
I am currently studying the textbook Artificial Intelligence: A Modern Approach, 4th Edition, by Russell and Norvig. Chapter 3 Solving Problems by ...
- 4,334
0
votes
0
answers
45
views
Updating probability distribution for decision making in game AI.
I'm programming an AI simulation where a car is randomly driving around a area. Within this area there are 5 repair shops. While driving, the car get's damaged (1% for every step). Once the damage of ...
2
votes
0
answers
31
views
Using Bayesian Networks to solve this localization problem?
I'm reading this paper, which I'll summarize here:
Let a sensor network (in this case, a network of radio receivers)
consist of $N$ sensor nodes at locations $S = \{ S_1 \cdots S_N\}$.
Let $S_i^x$ ...
- 1,281
0
votes
0
answers
39
views
Non continuous Fuzzy Set
I stuck in this question for a few hours now. Can anyone help me?
$ A ̃ $ is a non continuous fuzzy set and is defined by:
$ A ̃ = \{0.6/x_1 +0.5/x_2 + 1/x_3 + 0.75/x_4 + 0.7/x_5 + 0.8/x_6 + 1/...
- 33
0
votes
3
answers
73
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 $\Gamma(\alpha) = (\alpha - 1)!$...
- 141
0
votes
1
answer
420
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 ...
-1
votes
1
answer
292
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 ...
- 149