Questions tagged [convolution]

Convolution is a function-valued operation on two functions $f$ and $g$: $\int _{-\infty }^{\infty }f(\tau )g(t-\tau )d\tau$. Often used for obtaining the density of a sum of independent random variables. This tag should also be used for the inverse operation of deconvolution. DO NOT use this tag for convolutional neural networks.

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2
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1answer
319 views

Sampling from a Convolutional Restricted Boltzmann Machine's Visible Gaussian Real-valued Units

I am trying to confirm whether or not I am understanding the process described in the title. I am implementing a CRMB (with Real Valued Gaussian Visible units and Binary hidden units) as outlined in ...
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1answer
62 views

Known univariate unimodal analytical convolution with gaussian

I have data that are distributed with an unknown distribution. The data are from one continuous variable and unimodal. The shape looks like a gaussian, but it is asymmetric and with more long tails. ...
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0answers
83 views

Should initial filters for a 1-layer convolutional neural net converge to a smaller set of solution filters if the singular values are dissimilar?

I am experimenting with a 1 layer convolutional neural net and am seeing a pattern that I'd like some help explaining (this is personal interest, I am not a student). I have picked a single 3x3 ...
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6answers
19k views

Convolutional Layers: To pad or not to pad?

AlexNet architecture uses zero-paddings as shown in the pic: However, there is no explanation in the paper why this padding is introduced. Standford CS 231n course teaches we use padding to ...
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0answers
435 views

What is the architecture of a Variational Recurrent Autoencoder and Convolutional RNN?

So I am trying to do pretraining on MIDI (music input) of humans using recurrent neural networks. I read the papers https://arxiv.org/pdf/1412.6581v6.pdf and http://www.hexahedria.com/2015/08/03/...
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0answers
136 views

Generalization of the Irwin-Hall distribution for general linear combinations of uniform variables?

Consider the random variable $Z$, defined by: $$Z = \sum_{k=1}^n c_k X_k$$ where $X_k \sim U[0,1]$ is a real random variable with continuous uniform distribution between 0 and 1, and the $c_k$ are ...
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2answers
117 views

Does $X+Y$ having the same distribution as $X\implies $ $P(Y=0)=1\ ?$

If $X $ and $Y$ are independent random variables such that $X+Y$ has the same distribution as $X$ then is it always true that $P(Y=0)=1\ ?$ [This is actually a fact that a researcher used (without ...
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1answer
328 views

Is the sum of two independent non-overlapping uniforms uniform?

Suppose $X_1\sim U[a,b]$ and $X_2\sim U[c,d]$ with $a<b<c<d$ and suppose they are independent. I guess that the sum must be a uniform but I don't know how to show it [EDIT: I was wrong]. I ...
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1answer
12k views

How to get continuous output with Convolutional network? (Keras) [closed]

I'm new in using convolutional neural networks with keras. I can train a CNN for classify somethings and in other words for discrete output, but I can't find an example for getting continuous output (...
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1answer
702 views

What do the dimensions of a convolutional layer represent?

My understanding is that the width and the height represents a kernel (convolution matrix) that is convolved over the image. The depth is the number of these kernels. If that is the case, how would ...
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0answers
92 views

CRF message passing as convolution operation

I was reading this particular paper: Efficient Inference in Fully Connected CRFs with Gaussian Edge Potentials, and I didn't understand this equation (eq 5) in the paper: I understand the first ...
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1answer
3k views

Manually writing code for a Simple CNN using Backpropagation?

Are there any resources online that offer examples of how to write a CNN from scratch? Specifically, I am looking to understand the inner-workings of the backpropagation steps within a 1-D or 2-D ...
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0answers
305 views

Convolution of Pareto Random Variables [duplicate]

Define $X$ ~ Pareto($a$) and $Y$ ~ Pareto($b$), meaning $f_X (x) = ax^{-a + 1}$ for $x \geq 1$ and $f_Y (y) = by^{-b + 1}$ for $y \geq 1$. Assuming that $X$ and $Y$ are independent random variables, ...
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4answers
16k views

The sum of independent lognormal random variables appears lognormal?

I'm trying to understand why the sum of two (or more) lognormal random variables approaches a lognormal distribution as you increase the number of observations. I've looked online and not found any ...
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2answers
892 views

Does the property of equivariance to translation of convolution layers help to learn translation-invariant features?

In some texts, people mention that the reason why convolutional neural networks are able to learn translation-invariant features are related to the property that convolution layers are equivariant to ...
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1answer
379 views

Maximum of a probability vector distributed as a Dirichlet variate

Let $p_1, p_2, \ldots \sim \text{Dirichlet}(\alpha_1, \alpha_2, \ldots)$. What is the distribution of $\max(p_1, p_2, \ldots)$? I have searched for the order statistics of the Dirichlet distribution ...
6
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1answer
276 views

Sum of truncated Gammas

I have a set of i.i.d. variables $X_i$ that are distributed according to a truncated $\text{Gamma}(\alpha,\beta)$ distribution, with support on $[0,w)$ where $w$ is a known constant. What's the ...
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1answer
23 views

Sum of N four-component mixture variates

I asked a similar question with two-component mixture variates, and I was wondering how it extends to a four-component mixture variate. In other words, I have a list of random variables, $X_1$, $X_2$, ...
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1answer
71 views

Sum of N two-component mixture variates

I have a list of random variables, $X_1$, $X_2$, ..., $X_N$, associated with binary random variables $A_i$ such that $P(A_i) = \pi$ is known. I also know that, for all $i$ $$X_i|A_i\sim f(x)\\ X_i|\...
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2answers
2k views

How to work multiple filter region sizes: 2, 3 and 4 in CNN?

I mention learn convolutional neural networks (CNN) for classification of sentences made by Yoonkim. I am still confused about the size of the filter and how convolution works . What do ...
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1answer
108 views

How to get array of pixels from image [closed]

I read article about learning to segment. I am wondering how to get the same array of numbers as in the picture. Do I understand correctly that it is RGB? If possible, write an example in Python.
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0answers
66 views

Is deconvolution commutative?

Convolution is commutative: $f \star g = g \star f$ where $f$ and $g$ are functions, and $\star$ the convolution operator. Does deconvolution possess this commutative property?
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1answer
275 views

Convolutional Neural Networks trained with vital data eg. EKG?

I am wondering if CNN are a right tool for classification of human vital data. My data base consists of vector measurements and has a dimension of $$ \mathsf{3000 \times 1 \times 1 \times ...
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2answers
1k views

general solution sum of two uniform random variables aY+bX=Z?

is there a general solution to that? I have seen simple examples for Y+X=Z but I was wondering how this would be with rescaling?
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0answers
333 views

How to find the density of a sum of multiple dependent variables

Can one use convolutions to construct the density of a sum of dependent variables, and if so, how? I understand that to construct the density of the sum of two possibly dependent random variables, it ...
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2answers
4k views

Do convolutional neural networks flip the kernel?

After reading various examples of CNNs it doesn't look like the kernel used for convolution is flipped. Can anybody explain why?
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0answers
385 views

Convolutional neural network fails at the easiest task

This is my first attempt at making a convolutional neural network, and I'm having trouble making it perform the easiest task. Even though each separate part of the algorithm seems to work as expected (...
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1answer
221 views

regarding computing output size for convolutional layer

I am following up the lecture notes posted on http://cs231n.github.io/convolutional-networks/ I am sort of confusing about one example given in the notes. It says ...
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1answer
94 views

Convolution to find Pr(X +Y >1)

I have been hunting around on the internet for days to find an example I can easily relate to but without successes. It would really appreciate some help with the following; Joint pdf; $f(x,y)=2(x+y)...
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1answer
420 views

Distribution of Quotient of 2 dependent random variables

Well , I have the following problem.. Let $X_1,\cdots ,X_{2n}$ be iid $N(0,1)$ random variables. Define $$U_n=\left({X_1\over X_2}+{X_3\over X_4}+\cdots +{X_{2n-1}\over X_{2n}}\right)$$ $$V_n=X_1^...
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0answers
486 views

Is it possible to use Caffe to classify text?

I'm trying to build a sentence classifier using Caffe, for example the following dataset: 1 -> 'Fell energy at my home' 2 -> 'I liked the city's new buses' 3 -> 'It has a hole in the road in front ...
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1answer
2k views

How to normalize data for VGG-16 pretrained model?

I can't really find any data on how to go about normalizing the input for the following VGG-16 model I am using https://gist.github.com/baraldilorenzo/07d7802847aaad0a35d3 Right now I am inputting a ...
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0answers
98 views

Heuristics for modeling a convolutional network

Is there some good heuristics to choose: Number of filters in a Convolutional layer Size of the filters Number of Convolutional layers I have 250k small images (28x28), and I have 37 outputs. So I ...
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1answer
4k views

AlexNet implementation in Tensorflow not converging, huge loss

I implemented the AlexNet Oxford 17 Flowers example from the tensorflow API tflearn using the CIFAR10 source code from TensorFlow. Like described in the paper of Alex Krizhevsky ("ImageNet ...
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2answers
839 views

A dynamical systems view of the Central Limit Theorem?

(Originally posted on MSE.) I have seen many heuristic discussions of the classical central limit theorem speak of the normal distribution (or any of the stable distributions) as an "attractor" in ...
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1answer
88 views

How and what do I train in my Convolutional Neural Network [closed]

I have been trying to research and implement a convolution neural network in c++, and I think I understand the basic architecture of it. My problem is that I am incredibly confused as to what is ...
39
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4answers
34k views

What is translation invariance in computer vision and convolutional neural network?

I don't have computer vision background, yet when I read some image processing and convolutional neural networks related articles and papers, I constantly face the term, ...
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0answers
542 views

Cross correlation of gaussian signals with its mean signal gives non-gaussian distributed scores

The following is my question: I have signals that contains noise, they are of the following form see the figure below.. Then I take the mean signal of all these signals (identical in length and shape)....
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0answers
253 views

Sum of uniformly distributed random variables over different intervals?

Let $\{X_i\}_{i=1}^N$ be $N$ random variables uniformly distributed over the intervals $[a_i, b_i]$ respectively. How does the sum: $$\sum_{i=1}^N X_i$$ distribute? This is a generalization of the ...
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1answer
55 views

How to obtain the inverse of a matrix while solving an equation?

Given a matrix $A$, let us assume there is a equation: $Ax = b$ To solve for $x$, we can write: $x = A^{-1} b$ One way to obtain the inverse of A is by single value decomposition: Decomposition of ...
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1answer
958 views

Tikhonov regularization in the context of deconvolution

I came across "Tikhonov regularization" and I have bare knowledge on it. It seems that it is a type of regularization that is important for deconvolution. Are there any good resources and examples? ...
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0answers
63 views

PDF of sums, products of iid Normals

I've recently taken to looking at the distribution of a financial time series of the form $$X_t = X_{t-1}(1+W_t)$$ where $W_t$ is iid $N(0,\sigma^2)$. Expanding the equation out we get $$X_t = X_0\...
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3answers
1k views

What makes neural network a *convolutional* neural network?

What is the difference between a Convolutional Neural Network (CNN) and an ordinary Neural Network (NN)? What does convolution mean in this context?
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0answers
458 views

How to calculate the per-pixel uncertainties of an image after convolving it with a 2D kernel?

I have one 2D image (let's call it "model image"), which is generated by evaluating a particular analytic model for each of its pixels. Since this is just a simple analytic model, there is no error/...
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0answers
260 views

Deconvolution - two transfer functions applied to the same signal

I'm observing two timeseries, $\hat{h_1}$ and $\hat{h_2}$. I believe that both are products of convolution of the same underlying signal $f$ with a two different transfer functions, $g_1$ and $g_2$, ...
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2answers
338 views

Sum of independent binomials is binomial

My question is related to the question Sum of Independent Binomials How is it possible to sum X from 0 to w? I see two potential problems: Since $X\sim$Binomial(n,p), $X$ can maximally be $n$, and ...
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2answers
1k views

Why does multiplication in the frequency domain equal convolution in the time domain?

This question came in the context of understanding how to get a distribution of a sum of two iid random variables. I'm working through the top answer to this question Consider the sum of $n$ uniform ...
113
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6answers
76k views

What does 1x1 convolution mean in a neural network?

I am currently doing the Udacity Deep Learning Tutorial. In Lesson 3, they talk about a 1x1 convolution. This 1x1 convolution is used in Google Inception Module. I'm having trouble understanding what ...
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1answer
104 views

Probability the next draw from a distribution is greater than some number given a previous draw

I'm working on a game theory model of incomplete information, where players observe certain attributes via noisy signals. I am looking to solve for two different probability functions, though I think ...
3
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1answer
1k views

Deconvolution of two Gaussians

Assuming $X$ and $Y$ are two Gaussians with parameters of $\mu_X,\Sigma_X$ and $\mu_Y,\Sigma_Y$ then for their convolution we know that (reference) : $Z=X*Y$ is also a Gaussian with parameters of $\...