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.
81
questions with no upvoted or accepted answers
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Algebra & Artificial Intelligence (AI)
Artificial intelligence, especially deep learning & neural networks for image processing and classfication, are related to statistics and physics e.g. as decribed in below papers.
Statistics and ...
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4
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0
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80
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Advanced Math for Reinfrocement Learning - state space and state sequences (policies)
Reinforcement learning has two important notions and I am interested in advanced math that can investigate those notions:
State space - set of states. Apparently, deep structures should exist in this ...
- 1,353
4
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0
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838
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Modern Mathematical Theory for Neural Networks, Cellular Automata, Neuroscience
Is it possible for someone to do research on subjects like neural networks, cellular automata, or neuroscience as an applied mathematician?
I have in mind the theoretical development of these fields,...
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4
votes
1
answer
758
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$i,j,k$ Values of the $\Theta$ Matrix in Neural Networks
SO I'm looking at these two neural networks and walking through how the $ijk$ values of $\Theta$ correspond to the layer, the node number.
Either there are redundant values or I'm missing how the ...
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0
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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:/...
- 31
3
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0
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168
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How to Calculate Values from Incoming Messages? - Evidence Propagation in Bayesian Network
I'm currently trying to wrap my head around evidence propagation in bayesian network (simple tree propagation) but I'm having trouble finding information about the process.
As an example, let's take ...
- 513
2
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0
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477
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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 ...
- 249
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0
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33
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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
2
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0
answers
158
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The significance of odds and logs in Bayes Naive Classification
I do understand the concept of Naive Bayesian classification, as it tries to calculate the probability of an outcome of a class given multiple evidences. It comes from the Bayes theorem and it is ...
- 6,068
2
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0
answers
377
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feature selection for continuous variables
I wonder how exactly "feature selection" should be performed in case of continuous feature values. When feature values are discrete it is very straitforward to apply feature selection, but what to do ...
- 647
1
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0
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42
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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 ...
- 11
1
vote
0
answers
27
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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 ...
1
vote
0
answers
48
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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
1
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0
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124
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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
1
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0
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51
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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 (...
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1
vote
0
answers
46
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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:
$$\...
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0
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307
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Associative property in discrete 2D convolution
In CNN is tipically put on in cascade differents types of convolution layers, for example a 2D Convolution along with 2D Average Pooling. The convolution has the associative property:
$$(A*B)*C=A*(B*C)...
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1
vote
1
answer
33
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What's the fundamental difference between Tabular Q-learning and Q-learning (with off policy TD-control)
I have two equations.
Q-learning with off policy TD-control :
$$Q(S_t, A_t) \leftarrow Q(S_t, A_t) + \alpha[R_{t+1} + \gamma_{max}Q(S_t, A_t)]$$
Tabular Q-learning:
$$Q(s,a) \leftarrow (1-\alpha)...
- 27
1
vote
0
answers
28
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Implementing Actor-Critic with Experience Replay for Continuous Action Spaces
I have been trying to implement the ACER algorithm for continuous action spaces in reinforcement learning. The paper for the algorithm can be found here:
Sample Efficient Actor-Critic with Experience ...
- 43
1
vote
0
answers
25
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What are the differences between a linear logic based planner and a first order logic based planner
Linear logic based planners and first order logic based planners must have different strengths and weaknesses. I would appreciate help in understanding what these strengths and weaknesses are and ...
- 183
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0
answers
57
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mathematical proof of fast convergence of an nature-inspired algorithm
I am using the Moth-flame optimization algorithm to solve a problem. The algorithm uses logarithmic spiral to update the position of the moths. I have been asked to provide a mathematical proof to ...
- 11
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vote
2
answers
721
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First Order Logic to CNF for Knowledge Base
I am doing some Homework for an Artificial Intelligence Course, we are covering some First Order Logic and Conjuctive Normal Form.
Here are the questions that I have to answer that I am having ...
- 43
1
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0
answers
34
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Variable transformation for training a machine learning model
Suppose you have a train set $\mathbf{T}$ and you want to train some Machine Learning models. Each row of $\mathbf{T}$ consists in a set(vector) of attributes or variables $\mathbf{x} = (x_1, x_2...)$ ...
1
vote
0
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59
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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 ...
- 25k
1
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0
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56
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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
vote
0
answers
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
1
vote
0
answers
29
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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 ...
- 33
1
vote
0
answers
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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vote
1
answer
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.
- 11
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vote
0
answers
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 : ...
- 3,868
1
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0
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182
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AI Parameters for Tetris-like Game
I am building an AI to play a variation of Tetris. The rules are changed in that there are 19 different types of pieces, rotation is not allowed, and the pieces can be placed anywhere in a 10X10 grid. ...
- 131
1
vote
0
answers
840
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Maximizing alpha-beta pruning
A MiniMax tree is an arborescent structure generated by an AI role-playing game (e.g., tic tac toe) to simulate the player and its opponent turns, giving scores to each these turns.
In the image ...
- 746
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0
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2k
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How to calculate probabilities in a Bayesian network?
Consider the Bayesian network represented by the directed acyclic graph given below:
We are given the following probabilities:
P(tampering) = 0.02
P(fire) = 0.01
P(alarm | fire ∧tampering) = 0.5
P(...
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1
vote
0
answers
244
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Is normalized RBF always better than RBF
The question is as the title. Mathematically, I want to know does the following inequation always hold for any vector $\mathbf b$?
$\mathbf b^T \mathbf B \mathbf B^+ \mathbf b \, \ge \, \mathbf b^T \...
- 121
1
vote
0
answers
88
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Implicit feature space of Power Kernel
For the polynomial kernel, $K(x,y) = (x^Ty+c)^d$, the implicit feature space $\phi$ for which $K(x,y) = \phi(x)^T \phi(y)$ is of finite dimension and well known [1][2].
It is also well known that the ...
- 173
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vote
0
answers
220
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Improving Simulated Annealing based on Measure of Goodness
can anyone answer this question or direct me to a reference that can help?
Simulated Annealing returns the current state when the end of the annealing schedule is reached and if the annealing ...
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vote
0
answers
83
views
combine analysis and artificial intelligence
I'm sorry if I ask this question at the wrong place,
but I don't know a better one.
I am a Master's student and I am really interested in analysis, but I also
want to get into AI.
Does anyone know a ...
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1
vote
0
answers
157
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Solomonoff induction , Shannon Entropy, Kolmogorov Complexity.
If Expected Kolmogorov Complexity equals Shannon Entropy why can't Shannon Entropy be used as an approximation of Kolmogorov Complexity in Solomonoff Induction?
Regarding Kolmogorov Complexity and ...
- 83
1
vote
0
answers
811
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Estimating conditional probability as a function of time
My question relates to estimating from a time series a time dependent conditional probability without having a prior parametric model of anything.
Suppose I have two variables: r and I, and each can ...
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0
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10
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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 ...
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0
answers
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 ...
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0
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57
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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 ...
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0
answers
33
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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
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votes
1
answer
21
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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 ...
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0
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19
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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 ...
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0
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7
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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
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0
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329
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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 ...
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0
answers
12
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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
...
0
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0
answers
45
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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
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0
answers
106
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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 ...
