A message from our CEO about the future of Stack Overflow and Stack Exchange. Read now.

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.

134 questions with no upvoted or accepted answers
Filter by
Sorted by
Tagged with
7
votes
1answer
2k views

Why do people use Zero-Padding in Convolutional Neural Networks?

I am wondering why people usually pad with zeros instead of e.g., using the min-value. Zero-padding, in my opinion, makes sense if you have input images with a pixel range [0, 255] or [0, 1] (after ...
7
votes
0answers
453 views

Sum of absolute values of T random variables

Where X is a r.v. following a symmetric T distribution with 0 mean and tail parameter $\alpha$. I am looking for the distribution of the n-summed variable $ \sum_{1 \leq i \leq n}|x_i|$. $Y=|X|$ ...
6
votes
0answers
596 views

Two-sample bootstrap?

I have two independent samples of observations. From each sample I produce a statistic. Let's denote these as $\theta_1$ and $\theta_2$. I'd like to test the hypothesis that $H_0: \Theta_1=\Theta_2$, ...
5
votes
0answers
110 views

Finite sum of beta prime iid random variables

The beta prime distribution is infinitely divisible, as proved in Steutel and van Harn, 2003 (Appendix B). Sadly, in this book, there is no espression of the parameters of the distribution of n ...
4
votes
0answers
60 views

Multivariate stable distribution

I know that if $\pmb{X}_1$ and $\pmb{X}_2$ are independent copies of a $n \times 1$ random vector $\pmb{X}$, then $\pmb{X}$ is said to be sum stable in $\mathbb{R}^n$ if $a\pmb{X}_1 + b\pmb{X}_2 \...
4
votes
0answers
211 views

Deconvolution of sum results in negative numbers

Given $T=G+A$ where $A$ and $G$ are independent random variables, I'd like to estimate the distribution of $G$ given empirical (measured) distributions of $T$ and $A$. Of note: all three random ...
4
votes
2answers
515 views

Unlearning Neural Network? Prevent learning from a specific feature

Is it possible to train a NN to avoid the features that a different neural network finds? For example, let's train a simple 1 layer CNN with 1x1 kernels on a supervised binary classification problem. ...
3
votes
0answers
30 views

When (if ever) is the sum of two dependent geometric RVs negative binominal?

Imagine you have two random variables $X $ and $Y$, you know $$ X \sim \text{Geometric}(p) \\ X + Y \sim \text{Negative Binomial}(2, p) $$ I am interested in what if anything can be said about the ...
3
votes
0answers
15 views

Spectral graph convolutional network, re-assigning indices

This is a silly question for whom is familiar with the theory. I came across few papers that use a particular definition of convolution, designed to work with graphs, for example see section 2.1. of ...
3
votes
0answers
256 views

Why researchers use conv1d for embeddings instead of dense layers?

In some papers (like Reinforcement learning for Vehicle Routing Problem), researchers use conv1d to embed the problem input into a hyperspace; for example, in solving TSP, they use conv1d on the (x,y) ...
3
votes
0answers
148 views

Is this normal convolution or something special?

I am currently studying this paper (page 53) (mirror), in which the suggest convolution to be done in a special manner. This is the formula: \begin{equation} \tag{1}\label{1} q_{j,m} = \sigma \left(...
3
votes
0answers
197 views

What do the forward and backward propagation algorithms look like for convolutional neural networks

I've tried writing convolutional neural networks a few times and I always, always, always fail. It would be really useful if someone could write out the forward and back propagation algorithms in ...
3
votes
2answers
2k views

How to handle even and odd convolutional filter sizes and images

Is there a rule of thumb for determining the size of a convolutional filter given the shape of the input? Specifically, if you want to do a 1D convolution over an even-length vector, does the kernel ...
3
votes
0answers
129 views

polar analog of cartesian cross-correlation function

Background: The cross-correlation function, wrapped in frequency domain convolution, is used in particle image velocimetry to allow sub-pixel metrology. It is also used in convolutional neural ...
2
votes
0answers
19 views

Estimation of generalized gamma convolutions

How can i estimate on a data sample parameters of a generalised gamma convolution ? To be more specific, if my estimation gives me only a gamma convolution and not a generalised gamma convolution i'll ...
2
votes
0answers
863 views

Normalization of convolution kernel

I am trying to smooth a noisy one-dimensional physical signal, y, while retaining correspondence between the signal's amplitude and its units. I'm applying a ...
2
votes
1answer
879 views

Padding and stride in backpropagation of a conv net

I am trying to implement the back-propagation of a simple convolutional network. Specifically I understand that one of the steps is the convolution of the gradients coming from the next layer, with ...
2
votes
0answers
96 views

Flip Weights. How to change bias?

I am reading serialized weights and put them into a tensorflow network: tf.tanh(tf.nn.conv2d(t_im0, weights, strides=strides0, 'SAME') + bias) If I flip the ...
2
votes
0answers
332 views

How to define a loss function for discrete fourier series?

In each batch there are 8000 sample points, and I apply discrete Fourier transform on them. The original samples are real valued, so only the half of the result is needed. The end result is 4000 ...
2
votes
0answers
205 views

How to retrain a model (Inception) with 'prioritised' images in certain classifications

I am new to machine learning, and have constructed a basic CNN classifier by retraining the last layer of the Inception v3 model with my own image set into two classifications. I did this in Python ...
2
votes
0answers
78 views

Convolve Gamma distribution with Triangle distribution?

I am working on the use of distributed delay applied to pharmacometric models. Specifically, the delay kernel I am interested in is the Gamma distribution, with non-integer shape. The historical ...
2
votes
0answers
52 views

Proof Estimator is Locally Regular

In order to rely on Hajek-Le Cam Convolution Theorem, I tried to show that a given root-n consistent estimator was locally regular. In particular, suppose $\{T_n\}$ is a $\sqrt{n}$-consistent ...
2
votes
0answers
531 views

How to get continuous output with Convolutional network in Keras?

I'm a new user in using convolutional neural networks with keras. I have a code to classify set of images into 2 classes [0,1] using CNN in keras but I need to convert this code to get continuous ...
2
votes
0answers
281 views

Problems understanding “equivariance to translation” example in deep learning book by Goodfellow et al

I am trying to understand the following part about equivariance to translation from the deep learning book by Goodfellow, Bengio and Courville (chapter 9.2, page 338-339): To say a function is ...
2
votes
0answers
128 views

Would you interpret this image as a correct deconvolution process?

I'm applying the function conv2d_grad_wrt_inputs in theano to deconv a feature map into the original image. In the figure below the first image to the left is the ...
2
votes
0answers
56 views

Would whitening correlated inputs improve kernel estimates in a Volterra expansion?

I’m modelling a discrete-time 1-dimensional signal $y(t)$ as a sum of two input variables $x_1(t), x_2(t)$ convolved with their respective kernels plus noise $y=x_1*g_1+x_2*g_2+\eta$ and I’m ...
2
votes
1answer
170 views

Convolution equality

If $k$ is an squared or absolutely integrable kernel are the belo equalities true ? $$z(s)=\int_{R}^{} \! k(u-d) x(u).du \ \ =\int_{R}^{} \! k(u+d) x(u).du \ \ $$ and $$\int_{R}^{} \! k(u-d) k(u-d^{...
2
votes
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 ...
2
votes
0answers
434 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/...
2
votes
0answers
135 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 ...
2
votes
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 ...
2
votes
0answers
332 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 ...
2
votes
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 ...
2
votes
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 $g_2$, ...
2
votes
1answer
2k views

CNN: Details of Zeiler Fergus Net

I want to replicate the modified AlexNet by Zeiler and Fergus from 2013 (Visualizing and Understanding Convolutional Networks) but they spare some details. Hope someone here knows more about it. What ...
2
votes
0answers
59 views

Finding the normal divisor of a random variable

I have an iid sample $x_1, ..., x_n$ from a random variable $X$ which itself is a convolution $X = Z + \mathcal{N}(0, \sigma^2)$. Neither distribution of $Z$ nor parameter $\sigma^2$ are known (we ...
2
votes
0answers
233 views

How to explain certain patterns appearing after kernel averaging?

Having a 2D map filled uniformly by random values (Figure:top-left), the next maps are kernel averaged with a kernel of sizes ...
2
votes
0answers
156 views

About kernel based estimates

Kernel based operations are common in a variety of applications, such as image processing (e.g., blurring), generating smoothed estimation maps, and so on. A common approach is to select four ...
1
vote
1answer
13 views

Cropping input images Neural Networks

I'm creating a simple neural network for image classification,I had some doubts about the input images. Let's suppose i'm trying to classify (for example) a bear and i have an input image like this: ...
1
vote
0answers
24 views

Convolutions of joint random variables

I have two discrete dependent random variables $X,Y$, where both $X$ and $Y$ can take values either $0$ or $1$. Furthermore, I know their joint distribution $f_{X,Y}(X,Y)$. Now let's say I have an ...
1
vote
0answers
76 views

Question about the log-normal distribution

The main object of my question is this: if $X$ has a log-normal distribution, $Y = X + Z$ and $Y$ has the same distribution as that of $Z^2$ (in other words, $F_{Z^2} = F_{X+Z}$) and $X, Z$ are ...
1
vote
1answer
28 views

Does the model architecture of a CNN depend on the dimension of your input images?

By model architecture, I'm interested in knowing the following: Number of nodes in input layer Number of nodes in subsequent layers Number of layers in the architecture Number of filters and ...
1
vote
0answers
16 views

Solving discrete convolution linear functions

Consider we have samples $\mathbf{X} \in \mathcal{R}^{n\times p}$ and we aim to find a "regression" coefficients $\beta \in \mathcal{R}^{q \times 1}$ ($q>p$), but the regression is defined as a ...
1
vote
0answers
34 views

R: Calculating the convolution of two (multivariate) functions using FFT

I'm looking for a way to calculate: $$(f\ast g)(x) = \int_{\mathbb{R}^d}f(y)g(x-y)dy$$ in R. I have solved this problem using Monte-Carlo integration. However, ...
1
vote
0answers
113 views

How to pass from {Probability density function, convolution} to {Probability density function, characteristic function}?

In Forsman, W.C. (1986) "Polymers in solution: theoretical considerations and newer methods of characterization", Springer, New York. https://www.springer.com/la/book/9780306421464 page 24, it states:...
1
vote
0answers
41 views

Sum of two dependent random variables with copula

I'm trying to calculate sum of 2 random variables by using Copula Theory in R or Matlab. However, I have very limited knowledge about probability. Actually I read a lot of theoretical information ...
1
vote
0answers
53 views

What is the mode of the convoluted probability density function?

If I am aware of the distributions of both $V$ and $U$, is there general guiding principle in terms of the position of the mode of the distribution of $\varepsilon =V-U$. As I am not specifying the ...
1
vote
0answers
32 views

Distribution of 'DFSTAT'

Apart from the commonly applied "influence measures" in linear regression, i.e. dfbeta(s) / Cook's distance / covratio / dffit(s) / studentized residuals / leverage, there is one not so famous, ...
1
vote
2answers
349 views

1x1 convolution for inception module

When understanding inception module, I once saw the following statement from an online post. What's the calculation underline the "...
1
vote
0answers
162 views

How to add bias in convolution transpose?

My question is regarding the transposed convolution operation (also commonly called deconvolution or upconvolution). In TensorFlow, for instance, I refer to this layer. My question is, how / when do ...