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.
225
questions
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0
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8
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Hough voting or RANSAC voting, which strategy is better for pixel-wise object's center location estimation?
If we know all the pixels of the object in an image and draw a unit vector from all the known pixels of the object body towards the center direction of the object, and then apply some voting ...
-1
votes
0
answers
20
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How do I detect which of N objects appears in an image, and classify it's "state"? [closed]
Suppose I have a finite number of N objects O.
In every image I, strictly 1 of these objects exist.
And each object is in 1 of M states S. You can think of Q as a set R positions P, where each ...
- 1
1
vote
1
answer
38
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 - ...
- 533
0
votes
0
answers
8
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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
24
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
33
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
27
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 ...
- 303
0
votes
0
answers
80
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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
34
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
4
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
53
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
0
answers
59
views
McDermott about Skolemization
I am a beginner in AI. In a paper by McDermott (titled "A critique of pure reason") I found the following passage: "A goal containing a variable is interpreted as a request to find ...
- 73
0
votes
1
answer
52
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
108
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 ...
- 109
0
votes
0
answers
17
views
How do I get $P(A|C,!B)$ with the following probability distributions?
I have the following probability distributions table:
I know that $P(B)=0.6$ and that:
A may or may not have B
Some A have C
How do I get $P(A|C,!B)$?
I built the following baysiean network:
I ...
- 19
0
votes
1
answer
29
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
72
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
10
views
Uniform Cost Search - 2 paths to the goal
I'm working through a rather peculiar UCS problem:
Assume the start node is A, and the goal node is G. There are 2 paths from the start to the goal - both through E. I get stuck here:
When I expand ...
0
votes
0
answers
45
views
n queen problems state space is at least 3√n!?
Im at the beginning of my ai journey. Im reading the book and Im stuck at the problem.
Consider the n queens problem using the efficient incremental formulation. Explain why state space size is at ...
0
votes
0
answers
14
views
Find optimal Vector for a dataset equation problem
Is there an algorithm or an efficient way to solve the following equation?
$S=
\frac{
\begin{bmatrix}
R_{1} & . & . & R_{n}\\
\end{bmatrix}
\begin{bmatrix}
P_{1}\\
. \\
. \\
P_{n}\\
\end{...
- 1
0
votes
0
answers
19
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 ...
0
votes
0
answers
15
views
Is vector quantization belonging to the extention of K-means clustering
In unsupervised learning, vector quantization belongs to the extension of K-means clustering? since K-means tries to develop clusters with corresponding chose optimized centers to represent and find ...
- 71
2
votes
0
answers
97
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 ...
- 229
0
votes
0
answers
21
views
Vapnik-Chervonenkis-dimension of a set of specific functions
Good evening,
I'm struggling with calculating a few things in a task:
Given: $\mathbb{C}=\{f_{a,b} :\mathbb{R} ^2 \to \{0,1\}|a,b \in \mathbb{R}\}$, where $f_{a,b}(x,y) = a\cdot (x^2 + y^2) - b$. Let $...
- 23
0
votes
0
answers
32
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
23
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
91
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
59
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
139
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 ...
- 3,244
0
votes
1
answer
70
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
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votes
1
answer
46
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
86
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 ...
- 1,823
0
votes
1
answer
198
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 ...
- 127
0
votes
1
answer
125
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 ...
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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
48
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
59
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 ...
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0
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0
answers
37
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
28
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 $S_i^x$ ...
- 1,309
0
votes
0
answers
34
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
45
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 $\Gamma(\alpha) = (\alpha - 1)!$...
- 41
0
votes
1
answer
303
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
130
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 ...
0
votes
1
answer
497
views
Ways to write CNF for an implication with disjunction?
I have the following statement before it's converted to CNF: p → (s ∨ q). When I initially convert this to a CNF, I get the following: ¬p ∨ (s ∨ q).
I'm wondering if I could use laws of associativity ...
0
votes
1
answer
267
views
Biconditional elimination and implication elimination rules canceling statement out?
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 ...
1
vote
4
answers
122
views
Why $A \rightarrow B \Leftrightarrow \textrm{( A is False or B is True )} $
I am reading a book about Artificial intelligence and Knowledge representation and there is a logic formula that I cannot explain
Why $A \rightarrow B \Leftrightarrow \textrm{( A is False or B is True ...
- 41
1
vote
1
answer
147
views
Calculate a formula using back-propagation algorithm
English isn't my first language, so I'm sorry if I am unable to clearly describe the problem. Recently I have encountered a question in my artificial intelligence course that I am unable to wrap my ...
1
vote
0
answers
39
views
What is the parameter update rule for neural networks
I am currently taking a machine learning course and had a question about the update rule for $\theta$ in neural networks. In the discussion of previous learning algorithms, the professor defined:
$$\...
