I am struggling to understand how the decoder of variational autoencoder (VAE) works, and there is a question still making me confused after reading some papers and doing some researches, which is as following :
why the decoder of a trained VAE can generate reasonable outputs just using the samples from Normal distribution instead of the samples from distribution generated by the encoder,which is denoted by q(z|x) in most academic papers.
in other words, The KL divergence does his job by pulling the q(z|x) towards the Normal distribution during the VAE training. Nevertheless, there is no way that the q(z|x) is strictly identical to the Normal distribution when the training is done.
so in the procedure of training, the inputs of decoder are the samples from distribution q(z|x),which is the output of encoder.
My question is : why the decoder can generate the outputs reasonably just using the samples from the Normal distribution, insteading of using ones from the distribution q(z|x),when the training is done.
Any tips and hints will be appreciated. thank you.
The question was asked more than a year ago but in the spirit of better late than never here is how to reason about it based on use cases -
a) If your use case is to re-construct your input then you would go the route of first feeding your image to the encoder, get the approximate posterior, then sample from it and feed that latent sample to the decoder. If you have a well-trained network then you would get the output which is similar/same as your input. But then what is the utility of this in the first place? See use case (c) to see when having an encoder is important/interesting.
b) Let's remove the encoder from VAE. You have a trained decoder that accepts z. In other words, it is capable of mapping the z to an image. Since the z that it was trained with earlier was approximately standard normal, the decoder will generate the corresponding image. This generated image will now be considered synthetic and wouldn't necessarily match any of your training data.
c) There is another VAE called CVAE (Conditioned Variational Encoder) which has the same flow as regular VAE with the addition that you can supply extra input (i.e besides the latent sample). This additional input would then influence the generation/reconstruction of the input. For e.g. you pass in an image to the encoder to get the z, you then supply a (learned) vector that represents the addition of glasses and pass this vector and z to the decoder. Now the result will be the same/similar to the image you passed as input to the encoder but with the addition of glasses.
My question is: why the decoder can generate the outputs reasonably just using the samples from the Normal distribution
I have answered in use case (b) but to be very explicit here - The reason decoder can generate the outputs reasonably because it was trained with input (z in this case) that is sampled from a distribution closer to standard normal.
Related
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.
If I use the trained RNN(or LSTM) to generate series data(name the network with generated-RNN), then I use the series data to train the RNN(i.e. the same structure with the generated-RNN) from scratch, is it possible to get the same trained network(the same trained weights) with the generated-RNN?
You take series with X as input and Y as output to train a model, then with that model you generate series O.
Now you want to recreate the Ws from O=sigmoid(XWL1+b)...*WLN+bn with O as input and X as output.
Is it possible?
Unless X=O, then most likely not. I can't give a formal mathematical proof but multiplying forward through a network isn't equal to multiplying backwards, mainly due to the activation function. If you removed the activation function or took the inverse of the activation function you would more likely approach the Ws you desired, though another set of weights might also get you the the same output for a given input.
Also, this question would be better received in stats.stackexchange than stackoverflow.
I am trying to cluster a dataset using an encoder and since I am new in this field I cant tell how to do it.My main issue is how to define the loss function since the dataset is unlabeled and up to know, what I have seen from bibliography they define as loss function the distance between the desired output and the predicted output.My question is since that I dont have a desired output how should I implement this?
You can use an auto encoder to pre-train your convolutional layers, like it described in my question here with usage of convolutional autoencoder for images
As you can see form code, loss function is Adam with metrics accuracy and dice coefficient, I think you can use accuracy only, since dice coefficient is image-specific
I’m not sure how it will work for you, because you hadn’t provided your idea how you will transform your bibliography lists to vector, perhaps you will create a list for bibliography id’s sorted by the cosine distance between them
For example, you can use a set of vector with cosine distances to each item in a bibliography list above for each reference in your dataset and use it as input for autoencoder
After encoder will be trained, you can remove the decoder part from your model output and use as an input for one of unsupervised clustering algorithms, for example, k-mean. You can find details about them here
I was reading this particular paper http://www.robots.ox.ac.uk/~vgg/publications/2011/Chatfield11/chatfield11.pdf and I find the Fisher Vector with GMM vocabulary approach very interesting and I would like to test it myself.
However, it is totally unclear (to me) how do they apply PCA dimensionality reduction on the data. I mean, do they calculate Feature Space and once it is calculated they perform PCA on it? Or do they just perform PCA on every image after SIFT is calculated and then they create feature space?
Is this supposed to be done for both training test sets? To me it's an 'obviously yes' answer, however it is not clear.
I was thinking of creating the feature space from training set and then run PCA on it. Then, I could use that PCA coefficient from training set to reduce each image's sift descriptor that is going to be encoded into Fisher Vector for later classification, whether it is a test or a train image.
EDIT 1;
Simplistic example:
[coef , reduced_feat_space]= pca(Feat_Space','NumComponents', 80);
and then (for both test and train images)
reduced_test_img = test_img * coef; (And then choose the first 80 dimensions of the reduced_test_img)
What do you think? Cheers
It looks to me like they do SIFT first and then do PCA. the article states in section 2.1 "The local descriptors are fixed in all experiments to be SIFT descriptors..."
also in the introduction section "the following three steps:(i) extraction
of local image features (e.g., SIFT descriptors), (ii) encoding of the local features in an image descriptor (e.g., a histogram of the quantized local features), and (iii) classification ... Recently several authors have focused on improving the second component" so it looks to me that the dimensionality reduction occurs after SIFT and the paper is simply talking about a few different methods of doing this, and the performance of each
I would also guess (as you did) that you would have to run it on both sets of images. Otherwise your would be using two different metrics to classify the images it really is like comparing apples to oranges. Comparing a reduced dimensional representation to the full one (even for the same exact image) will show some variation. In fact that is the whole premise of PCA, you are giving up some smaller features (usually) for computational efficiency. The real question with PCA or any dimensionality reduction algorithm is how much information can I give up and still reliably classify/segment different data sets
And as a last point, you would have to treat both images the same way, because your end goal is to use the Fisher Feature Vector for classification as either test or training. Now imagine you decided training images dont get PCA and test images do. Now I give you some image X, what would you do with it? How could you treat one set of images differently from another BEFORE you've classified them? Using the same technique on both sets means you'd process my image X then decide where to put it.
Anyway, I hope that helped and wasn't to rant-like. Good Luck :-)
I am studying Support Vector Machines (SVM) by reading a lot of material. However, it seems that most of it focuses on how to classify the input 2D data by mapping it using several kernels such as linear, polynomial, RBF / Gaussian, etc.
My first question is, can SVM handle high-dimensional (n-D) input data?
According to what I found, the answer is YES!
If my understanding is correct, n-D input data will be
constructed in Hilbert hyperspace, then those data will be
simplified by using some approaches (such as PCA ?) to combine it together / project it back to 2D plane, so that
the kernel methods can map it into an appropriate shape such a line or curve can separate it into distinguish groups.
It means most of the guides / tutorials focus on step (3). But some toolboxes I've checked cannot plot if the input data greater than 2D. How can the data after be projected to 2D?
If there is no projection of data, how can they classify it?
My second question is: is my understanding correct?
My first question is, does SVM can handle high-dimensional (n-D) input data?
Yes. I have dealt with data where n > 2500 when using LIBSVM software: http://www.csie.ntu.edu.tw/~cjlin/libsvm/. I used linear and RBF kernels.
My second question is, does it correct my understanding?
I'm not entirely sure on what you mean here, so I'll try to comment on what you said most recently. I believe your intuition is generally correct. Data is "constructed" in some n-dimensional space, and a hyperplane of dimension n-1 is used to classify the data into two groups. However, by using kernel methods, it's possible to generate this information using linear methods and not consume all the memory of your computer.
I'm not sure if you've seen this already, but if you haven't, you may be interested in some of the information in this paper: http://pyml.sourceforge.net/doc/howto.pdf. I've copied and pasted a part of the text that may appeal to your thoughts:
A kernel method is an algorithm that depends on the data only through dot-products. When this is the case, the dot product can be replaced by a kernel function which computes a dot product in some possibly high dimensional feature space. This has two advantages: First, the ability to generate non-linear decision boundaries using methods designed for linear classifiers. Second, the use of kernel functions allows the user to apply a classifier to data that have no obvious fixed-dimensional vector space representation. The prime example of such data in bioinformatics are sequence, either DNA or protein, and protein structure.
It would also help if you could explain what "guides" you are referring to. I don't think I've ever had to project data on a 2-D plane before, and it doesn't make sense to do so anyway for data with a ridiculous amount of dimensions (or "features" as it is called in LIBSVM). Using selected kernel methods should be enough to classify such data.