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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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26 views

how is local minima possible in gradient descent?

gradient descent works on the equation of mean squared error, which is an equation of a parabola y=x^2 we often say weight adjustment in a neural network by ...
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1answer
17 views

Markov Decision Process - Discounted return

I was reading this article about Discounted return (in the context of MDP): http://deeplizard.com/learn/video/a-SnJtmBtyA I got the section: ...
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0answers
19 views

Inference can be the goal of an unsupervised learning method?

I am new to machine learning, and I am reading a pair of machine learning books. Those references talk about 2 different learning approaches: Prediction and inference, I understand the difference ...
1
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1answer
45 views

Policy gradient reinforcement learning for continuous state and action space

I am a novice in the field of machine learning, I have a moderate level understanding of linear/non-linear regression, support vector machines, neural networks, and q-learning (for discrete finite ...
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1answer
18 views

Different order of insertion - different Bayesian network ? how to prove formally?

I have some Bayesian network which i constructed from some data, say it consists of nodes A, B, C and D and that was the initial order of insertion. If i ...
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2answers
42 views

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 ...
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0answers
31 views

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 $\mathbf{x} = (x_1, x_2...)$ ...
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1answer
31 views

MGU - most general unifier for skolem functions?

I have trouble understanding MGU for functions, especially skolem functions. Is it correct that in order to find MGU for 2 functions, say f(x) and g(y) then they ...
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0answers
12 views

Minimal Explanations for an observation in a given knowledge base

Given the following knowledge base: a := e b := f a := f b := g c := g c := h d := h false := h & g false := i & a assumables: e,f,g,h And the following ...
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0answers
19 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}{\...
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0answers
63 views

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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1answer
165 views

Category Theory & Artificial Intelligence (AI)

Category theory turns out to be useful in more and more areas. (see e.g. MSE - Category Theory & Biology) Question. Does anyeone know of some connection of category theory to (convolutional) ...
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1answer
58 views

Are neural networks with bounded parameters a compact subset of the Banach space of continuous functions?

Let $d, n \in \mathbb{N}$. Moreover, let $D \subset \mathbb{R}^d$ be compact and denote with $\mathcal{C}(D, \mathbb{R}^n) $ the set of continuous functions from $D$ to $\mathbb{R}^n$. Then $\mathcal{...
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1answer
33 views

What is the output in a RNN?

I have recently been looking for some information about recurrent neural networks. Some people use a layer between the hidden state and the output and other ones use the hidden state as output. What ...
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0answers
39 views

What's going on in this sum?

This is part of a slope calculation example to update the new weight of a neural network from the slope. From a Deep Learning course on DataCamp My math is a bit dodgy and what I don't understand is ...
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1answer
31 views

reverse mapping of SVM kernel into original feature space

I am experimenting with support vector machines (SVM) following this book Without a kernel, it is very easy to "summarize" the SVM optimal solution, as you only need the separator hyperplane w, equal ...
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0answers
16 views

What is the meaning of stochastic sampling?

I came across this term in the context of Kernel Methods for Supervised Learning. Subsampling is the selection of a subset from the training set. But what is stochastic subsampling, I understand that ...
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1answer
108 views

Turn into Proposition logic

I am new to logic. I am suffering to turn one of the following sentences from normal form into propositional logic. Paragraph as follows: ...
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0answers
44 views

What courses should I take in my Masters for PhD in mathematics - artificial intelligence? [closed]

I am currently enrolled in a masters programme in mathematics and I am taking mostly courses in mathematical statistics, but also dynamical systems and analysis. And I'm wondering if I want to go ...
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0answers
23 views

Is it possible to output vectors/scalars from a neural network that are of a different type than the input

I have just begun researching convolutional neural networks on images and I see that they are useful for processes such as feature recognition and de noising etc. as they apply transformations to the ...
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1answer
24 views

Back propagation equation proof

I am trying to prove this equation (from the backpropagation equations in AI). $$\frac{\partial C}{\partial b_j^l} = \delta_j^l$$ C is the cost function: $C = \frac{1}{2}||y - a^L||^2$ Where the ...
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0answers
23 views

Matrix valued function theory for neural networks

Is there matrix valued function theory for neural networks (for optimal learning of weights and biases, for optimal meta-learning of architecture, for learning rate estimation)? I have found only ...
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0answers
85 views

Project ideas on Chaos theory, Cellular Automata, Fractals, Games, IA [closed]

I'm a computer science student and I need to find a final year project. What interests me the most is Chaos, IA, Games, Fractals, CA.. Something I liked was the chaos theory within sudoku. The ...
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0answers
54 views

Applications of Stochastic Dynamical Systems in Artificial Intelligence

It is my first post here but I have come to ask a question that will, hopefully, clear the ambiguity I have regarding the subject. A bit of a background about myself - I am a physics undergraduate ...
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0answers
89 views

What are some current best practices for function approximation using neural networks?

There are lots of guides out there for current best practices for using neural networks for classification tasks. However, these guides don't always apply to function approximation. What are some of ...
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0answers
42 views

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 ...
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1answer
47 views

How to convert an English sentence that contains “can't take more than 2” into predicate calculus sentence? [closed]

The example is : A student can’t take more than 2 courses with the same instructor
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1answer
43 views

What is the set of models of the empty set?

We have that : $Mod (\emptyset) = \{ I \in Int_{At} / I \vDash \emptyset \}.$ My question is, what is the set of interpretations that satisfty the empty set?
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0answers
68 views

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:/...
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1answer
206 views

Sample covariance matrix notation

I do not understand this notation for the sample covariance matrix (from Artificial Intelligence: A Modern Approach, Peter Norvig and Stuart J. Russell, Section 20.3, EM algorithm): $\Sigma_{i} = \...
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0answers
76 views

Using ANNs to solve Polynomials

Is it possible to train a neural network to solve a polynomial equation? What about any non-linear single variable equation? Has it been done before I am thinking of training a neural network to ...
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1answer
46 views

Payoff matrix of a scenario and the Schelling point.

Consider the problem of two people trying to drive safely on a two lane road. Each player can drive on their right or left. If players follow the same convention, they’ll drive safely. If they do not, ...
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1answer
267 views

Convert sentence into First order predicate logic.

a) rabin likes only CSit Course b)science course are hard. c)all courses in CSIT are easy d)CSC 101 is a csit course.
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2answers
119 views

Regarding Research in Artificial Intelligence [closed]

Which mathematical areas are important for research purposes in artificial intelligence? Specifically, If I have Masters in Statistics how much it will be beneficial for research in artificial ...
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1answer
60 views

Optimizing a function through reinforcement learning.

I want to know if reinforcement learning can be used for such optimization problems: \begin{align} & \max_{p_1^t, p_2^t}\quad\log_2(1+ p_1^t h_1^t)+\log_2(1+ p_2^t h_2^t) \\[6pt] \text{s.t. } &...
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4answers
585 views

What areas of math can be tackled by artificial intelligence?

Artificial intelligence is nearing, with image/speech recognition, chess/go engines etc. My question is, what areas of math that are interesting to mathematicians, is likely to be the first to be able ...
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1answer
170 views

How to First order logic procedure convert Convert to Conjunctive Normal Form ?

How to below this First order logic procedure convert Convert them into Conjunctive Normal Form ? Ɐx [[employee(x) ꓥ ¬[PST(x) ꓦ PWO(x)]] → work(x)] I strive to do this below step , i. S1: ...
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2answers
86 views

How to write the below paragraph in First Order Logic and Convert them into Conjunctive Normal Form

I tried to do this. but this is uncertain. see this below my answer. Please kindly help for me. how do you do this. Any employee who does not participates for the strike or work in contract basis ...
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0answers
46 views

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 ...
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1answer
40 views

Minimize the maximum value returned by paths of an oriented graph in a minimum of transformations

I'm definitely not a math expert so please forgive me in advance for not using the proper vocabulary or conventions. I'm kind of stuck with the following situation in a project of mine: I have been ...
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0answers
56 views

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 ...
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1answer
353 views

Find boolean function without brute force truth table?

I have the following homework (AI-related): Which boolean function does the following TLU (threshold logic unit) implement? The TLU (threshold logic unit) has five inputs. Its weight vector is (1.1, 3....
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1answer
139 views

Grounded vs. Preferred Semantics (Dung) [closed]

How does Dung's Grounded Semantics framework work in practice? I got this from slides of an AI course but can't figure it out: Grounded Semantics is said to minimize amount of arguments IN (green) ...
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0answers
13 views

In Dempster-Shafer theory, is it possible for a BPA to be equal to 0(zero) or 1?

Can a Basic probability assignment for an event A, m(A)=1 or 0. m(A) could be a decision output for any classifier.
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0answers
25 views

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 ...
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1answer
253 views

How to find the conditional independence?

I reviewing some AI books and recently i found the following question that i would like to solve: In the given Bayes network, decide the conditional independence of the nodes. Justify ...
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1answer
50 views

Bayesian network

I have this following question and i would like to know if anyone can answer it. For a given Bayesian network where $P(a) =.6, P(b|a) =.8, P(b|-a)=.4, P(c|a)=.4$ and $P(c|-a) = .3$, compute $P(c|b)$. ...
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1answer
36 views

Weird logarithm rules in an attempt to proof an upper bound of JSD between two Gaussian distribution

I'm currently working on my thesis in Deep Learning and stumbled upon one paper that I think is really related to my topic. In short, I could not understand some parts of its computation process. Here'...
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1answer
431 views

How to prove this using resolution theorem or resolution refutation?

I need to prove P v (Q ^ R), S : (S ^ P) v Q using resolution theorem or resolution refutation. This is my proof: Convert P v (Q ^ R) to (P v Q) ^ (P ^ R) Convert ...
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2answers
57 views

De morgan quantifers prove

prove ∃x (P(x) => Q(x)) = ∀x P(x) => ∃x Q(x) ∃x (P(x) => Q(x)) = ∃x (¬P(x) ∨ Q(x)) ----- (1) = ∃x(¬P(x)) ∨ ∃xQ(x) ----- (2) = ¬∀xP(x) ∨ ∃xQ(x) ----- (3) = ∀x P(x) => ∃x Q(x) ----- (4) From line ...