Frequently linear interpolation is used with a Gaussian or uniform prior which has unit variance and zero mean where the size of the vector can be defined in an arbitrary way e.g. 100 to generate initial random vectors for generator model in Generative Adversarial Neural (GAN).
Let's say we have 1000 images for training and batch size is 64. Then each epoch, need to generate a number of random vectors using prior distribution corresponding to each image given small batch. But the problem I see is that since there is no mapping between random vector and corresponding image, the same image can be generated using multiple initial random vectors. In this paper, it suggests overcoming this problem by using different spherical interpolation up to some extent.
So what will happens if initially generate random vectors corresponding to the number of training images and when train the model uses the same random vector which is generated initially?
In GANs the random seed used as input does not actually correspond to any real input image. What GANs actually do is learn a transformation function from a known noise distribution (e.g. Gaussian) to a complex unknown distribution, which is representated by i.i.d. samples (e.g. your training set). What the discriminator in a GAN does is to calculate a divergence (e.g. Wasserstein divergence, KL-divergence, etc.) between the generated data (e.g. transformed gaussian) and the real data (your training data). This is done in a stochastic fashion and therefore no link is neccessary between the real and the fake data. If you want to learn more about this on a hands on example, I can recommend that you train to train a Wasserstein GAN to transform one 1D gaussian distribution into another one. There you can visualize the discriminator and the gradient of the discriminator and really see the dynamics of such a system.
Anyways, what your paper is trying to tell you is after you have trained your GAN and want to see how it has mapped the generated data from the known noise space to the unknown image space. For this reason interpolation schemes have been invented like the spherical one you are quoting. They also show that the GAN has learned to map some parts of the latent space to key characteristics in images, like smiles. But this has nothing to do with the training of GANs.
Related
The calculation of NMSE is not changing even after changing the latent dimension from 512 to 32
the normalized mean square error values should change after changing the latent dimension.
Variational autoencoder is different from autoencoder in a way such that it provides a statistic manner for describing the samples of the dataset in latent space. Therefore, in variational autoencoder, the encoder outputs a probability distribution in the bottleneck layer instead of a single output value.
Variational autoencoders were originally designed to generate simple synthetic images. Since their introduction, VAEs have been shown to work quite well with images that are more complex than simple 28 x 28 MNIST images. For example, it is possible to use a VAE to generate very realistic looking images of people.
When we use the convolutional autoencoder for new image generating,
does the model generate the same image every time we run the model? or does it rather generate images with random variation?
I think that the autoencoder (AE) generates the same new images every time we run the model because it maps the input image to a single point in the latent space. On the other hand, the variational autoencoder (VAE) maps the the input image to a distribution. Therefore, if we need images with some random variation we need to use VAE and if we need the same generated images every time we run the model we use AE. Is this true?
My question is:
Does AE generate images with random variation?
Autoencoders first encode the input data into some latent representation and then use that representation (bottleneck layer) to reconstruct the same input.
I trained an autoencoder on MNIST data and encoded the digits into a two-dimensional vector. The network learned quite a useful representation of the data that I plotted.
Latent representation of MNIST digit
You can see for each digit the latent representation has some range of values for example zero's latent representation has nearly range from -2 to 4 on the x-axis and 4 to 8 on the y axis.
Now if you sample a random two-dimensional random vector in that range and run it through a decoder, you will get a random image of zero.
Now the problem is this is a very simple case. How about latent vector has 64 dimensions or even higher and a number of categories are also more. In that case, we need to model the distribution of the latent vector in order to sample valid vectors. Otherwise, we would never know that which latent vector is valid.
So autoencoder may give random samples, but it needs to know the distribution of data and that point we cover in VAE.
I have a set of data. I want to build a one class distribution from that data. Based on the learned distribution I want to get a probability value for each of the data instance.
Based on this probability values (thresholding) I want to build a classifier to classify a particular data instance is comming from that distribution or not.
In this case, lets say I have a data of 50x100000 where 50 is the dimension of each data instance, the number of instances are 100000. I am leaning a Gaussian mixture model based on this distribution.
When I try to get the probability values for instances I am getting very low values. So in this case how can I build a clssifier?
I don't think this makes sense. For example, suppose your data is 1 dimensional, and suppose the truth is that it has been sampled from a bimodal distribution. But suppose you haven't worked out that it's from a bimodal distribution and you fit a normal distribution. You'd still have the best possible fit, but it would be the best possible fit to the wrong distribution, and the truth is that none of the points come from that distribution or from any distribution that looks like it.
I have a set of data in a vector. If I were to plot a histogram of the data I could see (by clever inspection) that the data is distributed as the sum of three distributions;
One normal distribution centered around x_1 with variance s_1;
One normal distribution centered around x_2 with variance s_2;
Once lognormal distribution.
My data is obviously a subset of the 'real' data.
What I would like to do is to take a random subset of my data away from my data ensuring that the resulting subset is a reasonable representative sample of the original data.
I would like to do this as easily as possible in matlab but am new to both statistics and matlab and am unsure where to start.
Thank you for any help :)
If you can identify each of the 3 distributions (in the sense that you can estimate their parameters), one approach could be to select a random subset of your data and then try to estimate the parameters for each distribution and see whether they are close enough (according to your own definition of "close") to the parameters of the original distributions. You should repeat this process several time and look at the average difference given a random subset size.
I have to write a classificator (gaussian mixture model) that I use for human action recognition.
I have 4 dataset of video. I choose 3 of them as training set and 1 of them as testing set.
Before I apply the gm model on the training set I run the pca on it.
pca_coeff=princomp(trainig_data);
score = training_data * pca_coeff;
training_data = score(:,1:min(size(score,2),numDimension));
During the testing step what should I do? Should I execute a new princomp on testing data
new_pca_coeff=princomp(testing_data);
score = testing_data * new_pca_coeff;
testing_data = score(:,1:min(size(score,2),numDimension));
or I should use the pca_coeff that I compute for the training data?
score = testing_data * pca_coeff;
testing_data = score(:,1:min(size(score,2),numDimension));
The classifier is being trained on data in the space defined by the principle components of the training data. It doesn't make sense to evaluate it in a different space - therefore, you should apply the same transformation to testing data as you did to training data, so don't compute a different pca_coef.
Incidently, if your testing data is drawn independently from the same distribution as the training data, then for large enough training and test sets, the principle components should be approximately the same.
One method for choosing how many principle components to use involves examining the eigenvalues from the PCA decomposition. You can get these from the princomp function like this:
[pca_coeff score eigenvalues] = princomp(data);
The eigenvalues variable will then be an array where each element describes the amount of variance accounted for by the corresponding principle component. If you do:
plot(eigenvalues);
you should see that the first eigenvalue will be the largest, and they will rapidly decrease (this is called a "Scree Plot", and should look like this: http://www.ats.ucla.edu/stat/SPSS/output/spss_output_pca_5.gif, though your one may have up to 800 points instead of 12).
Principle components with small corresponding eigenvalues are unlikely to be useful, since the variance of the data in those dimensions is so small. Many people choose a threshold value, and then select all principle components where the eigenvalue is above that threshold. An informal way of picking the threshold is to look at the Scree plot and choose the threshold to be just after the line 'levels out' - in the image I linked earlier, a good value might be ~0.8, selecting 3 or 4 principle components.
IIRC, you could do something like:
proportion_of_variance = sum(eigenvalues(1:k)) ./ sum(eigenvalues);
to calculate "the proportion of variance described by the low dimensional data".
However, since you are using the principle components for a classification task, you can't really be sure that any particular number of PCs is optimal; the variance of a feature doesn't necessarily tell you anything about how useful it will be for classification. An alternative to choosing PCs with the Scree plot is just to try classification with various numbers of principle components and see what the best number is empirically.