Questions tagged [math]
For questions about mathematics related to artificial intelligence.
168
questions
1
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0answers
8 views
How do I find the data-point with respect to a given frame?
I've been reading this paper that formulates invariant task-parametrized HSMMs. In section 3.1 (Model Learning), the task parameters are represented in $F$ coordinate systems defined by $\{A_j,b_j\}_{...
1
vote
1answer
37 views
The mathematics in the CBOW and Skip-Gram models
this is my first question on AI Stack Exchange. I am a mathematics student who is learning NLP so I have paid a high amount of attention on the mathematics used in the subject, but my interpretations ...
0
votes
1answer
47 views
Is it possible to know the distance objects are from camera based on only knowing one object's height?
I am doing a project where I have to know distance a particular object is from camera. In the photo I only know one of the object's height, but I don't know how far away that object is and I don't ...
2
votes
1answer
63 views
Why would the lookup table (of a table-driven artificial agent) need to store data at pixel precision?
While reading the book AI A modern approach, 4th ed, I came across the section of "Agent program" with following text:
It is instructive to consider why the table-driven approach to agent
...
0
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1answer
57 views
How to mathematically describe convolving operation of Gaussian kernel
I have build a model where I pre-process data with Gaussian kernel. The data are $n\times n$ matrix of one channel, but not an image, thus I cant reference to this matrix as image and to its elements ...
6
votes
2answers
118 views
Formal definition of the Object Detection problem
For many problems in computer science, there is a formal, mathematical problem defition.
Something like: Given ..., the problem is to ...
How can the Object Detection problem (i.e. detecting objects ...
2
votes
0answers
13 views
Mapping given probabilities to empirical probabilities
Consider following problem statement:
You have given $n$ actions. You can perform any of them. Each action gives you success with some probability. The challenge is to perform given finite number of ...
1
vote
1answer
36 views
Research paths/areas for improving the performance of CNNs when faced with limited data
I've been reading through the research literature for image processing, computer vision, and convolutional neural networks. For image classification and object recognition, I know that convolutional ...
0
votes
1answer
55 views
What does $r : \mathcal{S} \times \mathcal{A} \rightarrow \mathbb{R}$ mean in the article Hindsight Experience Replay, section 2.1?
Taken from section 2.1 in the article:
We consider the standard reinforcement learning formalism consisting of an agent interacting with an environment. To simplify the exposition we assume that the ...
0
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0answers
37 views
Could the neural network automatically calculate and get different one-to-many quantities relative to their parent quantity?
Let's say I have a primary dataset that its secondary dataset is hundreds to match and group like an one-to-many relationship.
I'm new in this world of the AI but my problem is that many child groups ...
0
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0answers
24 views
Confusion on Math Notation Definition
I attempt to understand the formulation of dictionary learning for this paper:
Depression Detection via Harvesting Social Media: A Multimodal Dictionary Learning Solution
Multimodal Task-Driven ...
0
votes
1answer
38 views
Do the rows of the design matrix refer to the observations or predictors?
I attempt to understand the formulation of dictionary learning for this paper:
Depression Detection via Harvesting Social Media: A Multimodal Dictionary Learning Solution
Multimodal Task-Driven ...
1
vote
2answers
92 views
The math behind PCA
I am trying to understand the math behind PCA. I can only solve it in the case of mapping vectors to 1 Dimensional space. How to solve the math in the case we reduce the number of dimension is greater ...
0
votes
1answer
33 views
Mathematical calculation behind decision tree classifier with continuous variables
Problem Description
I am working on a binary classification problem having continuous variables (Gene expression Values). My goal is to classify the samples as case ...
0
votes
0answers
52 views
Can a computer make a proof by induction?
Can a computer solve the following problem, i.e. make a proof by induction? And why?
Prove by induction that $$\sum_{k=1}^nk^3=\left(\frac{n(n+1)}{2}\right)^2, \, \, \, \forall n\in\mathbb N .$$
I'm ...
2
votes
1answer
73 views
Understand the DDPG algorithm in Keras
I'm trying to understand the DDPG algorithm using Keras
I found the site and started analyzing the code, I can't understand 2 things.
The algorithm used to write the code presented on the page
In the ...
1
vote
1answer
71 views
What is the definition of the “cost” function in the SVM's objective function?
In a course that I am attending, the cost function of a support vector machine is given by
$$J(\theta)=\sum_{i=1}^{m} y^{(i)} \operatorname{cost}_{1}\left(\theta^{T} x^{(i)}\right)+\left(1-y^{(i)}\...
1
vote
1answer
40 views
How to understand mapping function of kernel?
For a kernel function, we have two conditions one is that it should be symmetric which is easy to understand intuitively because dot products are symmetric as well and our kernel should also follow ...
1
vote
0answers
68 views
What is an auto-associator?
What is an auto-associator, and how does it work? How can we design an auto-associator for a given pattern? I couldn't find a clear explanation for this anywhere on the internet.
Here's an example of ...
1
vote
0answers
43 views
Simplifying Log Loss
I am reading through a paper (https://www.mitpressjournals.org/doi/pdf/10.1162/0891201053630273) where they describe logloss as a ranking function and can be simplified to the margin of the training ...
5
votes
1answer
140 views
Can deep learning be used to help mathematical research?
I am currently learning about deep learning and artificial intelligence and exploring his possibilities, and, as a mathematician at heart, I am inquisitive about how it can be used to solve problems ...
2
votes
0answers
69 views
Is this the correct gradient for log of softmax? [duplicate]
I am currently implementing the very basic version (REINFORCE) of the Monte Carlo policy gradient algorithm. I was wondering if this is the correct gradient for the log of softmax.
\begin{align}
\...
1
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0answers
56 views
Does Gödel's second incompleteness theorem put a limitation on artificial intelligence systems?
According to Brian Cantwell Smith
no calculation without representation
Therefore, computers depend on models. So, we can say that AI is limited internally by the model and external by the ...
4
votes
1answer
70 views
How is the Jacobian a generalisation of the gradient?
I came across these slides Natural Language Processing with Deep Learning CS224N/Ling284, in the context of natural language processing, which talk about the Jacobian as a generalization of the ...
1
vote
0answers
35 views
How do I approach this problem?
Let's say I have a dataset with multiple types of multiple ingredients (salt1,salt2, etc). Each n-th variation of each ingredient vs flavor may be represented by an n×k matrix that where an ingredient ...
2
votes
1answer
59 views
How is the log-derivative trick of a trajectory derived?
I am looking at this formula which breaks down the gradient of $P(\tau |\theta)$ the first part is clear as is the derivative of $\log(x)$, but I do not see how the first formula is rearranged into ...
4
votes
1answer
62 views
How can a single sample represent the expectation in gradient temporal difference learning?
I was reading the gradient temporal difference learning version 2(GTD2) from rich Sutton's book page-246. At some point, he expressed the whole expectation using a single sample from the environment. ...
0
votes
1answer
42 views
Why are all weights of a neural net updated and not just the weights of the first layer
Why are all weights of a neural net updated and not only the weights of the first hidden layer?
The error-influence of the prediction by the weights of a neural net is calculated using the chain rule....
1
vote
1answer
68 views
Understanding relation between VC Symmetrization Lemma and Generalization Bounds
I am new in the field of Machine Learning so I wanted to start of by reading more about mathematics and history behind it.
I am currently reading, in my opinion, a very good and descriptive paper on ...
2
votes
1answer
50 views
How can I implement policy evaluation when reward is tied to an action outcome?
I'm following Stanford reinforcement learning videos on youtube. One of the assignments asks to write code for policy evaluation for Gym's FrozenLake-v0 environment.
In the course (and books I have ...
2
votes
1answer
68 views
What are the challenges faced by using NLP to convert mathematical texts into formal logic?
From what I've figured
(a) converting mathematical theorems and proofs from English to formal logic is a straightforward job for mathematicians with sufficient background, except that it takes time.
...
1
vote
1answer
45 views
What does equation in the “related work” section of the GAN paper mean?
I was going through the paper on GAN by Ian Goodfellow. Under the related work section, there is an equation. I cannot decipher the equation. Can anyone help me understand the meaning of the equation? ...
3
votes
0answers
40 views
Is maximum likelihood estimation meaningless for a dataset of only outliers?
From my understanding, maximum likelihood estimation chooses the set of parameters for the estimator that maximizes likelihood with the ground truth distribution.
I always interpreted it as the ...
2
votes
1answer
44 views
Is the derivative of the loss wrt a single scalar parameter proportional to the loss?
I am wondering about the correlation between the loss and the derivative of the loss wrt a single scalar parameter, with the same sample. That means: considering a machine learning model with ...
1
vote
0answers
15 views
How do I decide which norm to use for placing a constraint on my adversarial perturbation?
I am performing an adversarial machine learning attack on a neural network for network traffic classification. For adding adversarial perturbations in features such as packet interarrival times and ...
2
votes
0answers
26 views
Is there any wrong in my focal loss derivation?
Assume $\mathbf{X} \in R^{N, C}$ is the input of the softmax $\mathbf{P} \in R^{N, C}$, where $N$ is number of examples and $C$ is number of classes:
$$\mathbf{p}_i = \left[ \frac{e^{x_{ik}}}{\sum_{j=...
2
votes
2answers
102 views
Is ReLU a non-linear activation function?
According to this blog post
The purpose of an activation function is to add some kind of non-linear property to the function
The sigmoid is typically used as an activation function of a unit of a ...
3
votes
1answer
83 views
Why does variational auto-encoder use the reconstruction loss?
VAE is trained to reduce the following two losses.
KL divergence between inferred latent distribution and Gaussian.
the reconstruction loss
I understand that the first one regularizes VAE to get ...
2
votes
0answers
41 views
Why are conics important in computer vision?
The book Multiple View Geometry in Computer Vision by Richard Hartley and Andrew Zisserman talks about lines, points and conics. A conic is a curve described by a second-degree equation in the plane, ...
0
votes
0answers
61 views
Derivation of regularized cost function w.r.t activation and bias
In regularzied cost function a L2 regularization cost has been added.
Here we have already calculated cross entropy cost w.r.t $A, W$.
As mentioned in the regularization notebook (see below) in ...
2
votes
1answer
78 views
Why is my derivation of the back-propagation equations inconsistent with Andrew Ng's slides from Coursera?
I am using the cross-entropy cost function to calculate its derivatives using different variables $Z, W$ and $b$ at different instances. Please refer image below for calculation.
As per my knowledge, ...
2
votes
1answer
113 views
In a single neuron output layer should the output be a scalar?
Given a neural network with 3 inputs, 4 hidden layers, and 1 output, should the output neuron be a vector or a scalar? I thought that at the end of the summation only one number between 0 and 1 would ...
3
votes
0answers
58 views
Interpretation of inverse matrix in mean calculation in Gaussian Process
The formula for mean prediction using Gaussian Process is $k(x_*, x)k(x, x)^{-1}y$, where $k$ is the covariance function. See e.g. equation 2.23 (in chapter 2) from Gaussian Processes for Machine ...
1
vote
1answer
127 views
Understanding the derivation of the first-order model-agnostic meta-learning
According to the authors of this paper, to improve the performance, they decided to
drop backward pass and using a first-order approximation
I found a blog which discussed how to derive the math ...
3
votes
2answers
102 views
Is there a possibility that there is no relationship between some inputs and outputs?
I'm doing machine learning projects. I took a look at many datasets I worked with, mostly there are already famous datasets that everyone uses.
Let's say I decided to make my own dataset. Is there a ...
2
votes
0answers
38 views
Expected duration in a state
I am going through Rabiner 1989 and he writes that the discrete probability density function of duration $d$ in state $i$ (that is, staying in a state for duration $d$, conditioned on starting in that ...
1
vote
1answer
41 views
What are the variables used in a Gaussian radial basis kernel in the context of SVMs?
If I have the Gaussian kernel
$$
k(x, x') = \operatorname{exp}\left( -\| x - x' \|^2 / 2\sigma^2 \right)
$$
What is $x$ and $x'$ in the context of training an SVM?
2
votes
1answer
99 views
How is the expected value in the loss function of DQN approximated?
In Deep Q Learning the parametrized Q-functions $Q_i$ are optimised by performing gradient descent on the series of loss functions
$L_i(\theta_i)= E_{(s,a)\sim p}[(y_i-Q(s,a;\theta_i))^2]$ , where
...
1
vote
2answers
50 views
What are the conditions for the convergence of SARSA to the optimal value function?
Is it correct that for SARSA to converge to the optimal value function (and policy)
The learning rate parameter $\alpha$ must satisfy the conditions:
$$\sum \alpha_{n^k(s,a)} =\infty \quad \text{and}...
1
vote
1answer
32 views
What is the equation of the separation line for this neuron with identity activation?
I have a single neuron with 2 inputs, and identity activation, where f is activation function and u is output:
$u = f(w_1x_1 + ...
