Questions tagged [latent-variable]

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Why does $E_q[\log p(\mathbf{w}|\mathbf{z},\beta)]=\sum_{n=1}^{N}\sum_{i=1}^{k}\sum_{j=1}^{V}\phi_{ni}w_n^j\log \beta_{ij}$ hold in LDA?

I'm having trouble understanding an equality that comes up in the original LDA paper by Blei et al.: Consider the classical LDA model, i.e. for every document $\textbf{w}=(w_1,\ldots,w_N)$ in a text ...
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2answers
106 views

Is it possible to have a variable-length latent vector in an autoencoder?

I'm trying to have a simple autoencoder but with variable latent length (the network can produce variable latent lengths with respect to the complexity of the input), but I've not seen any related ...
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1answer
58 views

What is meant by degrees of freedom of latent variables?

...Designing such a likelihood function is typically challenging; however, we observe that features like spectrogram are effective when latent variables have limited degrees of freedom. This motivates ...
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0answers
23 views

How to find difference between topics in two languages using NLP

I want to analyze queries and their differences between two different languages English and Spanish in this case. I'm aware of topic modeling. I'm in search of any corpus available or any algorithm to ...
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0answers
20 views

Why do hypercube latent spaces perform poorer than Gaussian latent spaces in generative neural networks?

I have a quick question regarding the use of different latent spaces to represent a distribution. Why is it that a Gaussian is usually used to represent the latent space of the generative model ...
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0answers
16 views

Does bottleneck size matter in Disentangled Variational Autoencoders?

I suppose that picking an appropriate size for the bottleneck in Autoencoders is neither a trivial nor an intuitive task. After watching this video about VAEs, I've been wondering: Do disentangled ...
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1answer
44 views

In this VAE formula, why do $p$ and $q$ have the same parameters?

In $$\log p_{\theta}(x^1,...,x^N)=D_{KL}(q_{\theta}(z|x^i)||p_{\phi}(z|x^i))+\mathbb{L}(\phi,\theta;x^i),$$ why does $p(x^1,...,x^N)$ and $q(z|x^i)$ have the same parameter $\theta?$ Given that $p$ is ...
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1answer
188 views

Why is the evidence equal to the KL divergence plus the loss?

Why is the equation $$\log p_{\theta}(x^1,...,x^N)=D_{KL}(q_{\theta}(z|x^i)||p_{\phi}(z|x^i))+\mathbb{L}(\phi,\theta;x^i)$$ true, where $x^i$ are data points and $z$ are latent variables? I was ...
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1answer
113 views

What are some new deep learning models for learning latent representation of data?

I know that autoencoders are one type of deep neural networks that can learn the latent representation of data. I guess there should be several other models like autoencoders. What are some new deep ...
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2answers
118 views

Do we also need to model a probability distribution for the decoder of a VAE?

I'm working on understanding VAEs, mostly through video lectures of Stanford cs231n, in particular lecture 13 tackles on this topic and I think I have a good theoretical grasp. However, when looking ...
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4answers
5k views

What is the difference between latent and embedding spaces?

In general, the word "latent" means "hidden" and "to embed" means "to incorporate". In machine learning, the expressions "hidden (or latent) space" ...
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165 views

How can VAE have near perfect reconstruction but still output junk when using random noise input

I am creating a VAE for time series data using CNNs. The data has 4800 timesteps and 4 features. It is standardized and normalized. The network I am using is implemented in Keras as follows. I have ...
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0answers
54 views

What kind of distributions can be used to model discrete latent variables?

If we take the vanilla variational auto-encoder (VAE), we $p(z)$ is a Gaussian distribution with zero mean and unit variance and we approximate $p(z|x) \approx q(z|x)$ to be a Gaussian distribution as ...