Body: <p>I am faced with a problem which I bet was already solved before, but that I had never seen. Perhaps by discussing it abstractly, someone can point me to relevant literature.</p>
  <p>It goes like this: I have a dataset of images <span class="math-container">$I_j$</span> and numerical features <span class="math-container">$f_{1,j}, f_{2,j}, ..., f_{k, j}$</span>. In production, I don't have access to the features <span class="math-container">$f_{i,j}$</span>, which I know to be more relevant to my learning problem than the images.</p>
  <p>However, theses features <span class="math-container">$f_{i,j}$</span> are also very hard to obtain, and there is a known correlation (informal) between the images and the numerical features <span class="math-container">$f_{i,j}$</span>. So the whole point of using the images is to avoid using the <span class="math-container">$f's$</span>.</p>
  <p>Know comes the question: is there any useful way I could learn a representation of the images that &quot;exposes&quot; the maximum information about the features <span class="math-container">$f_{i,j}$</span>? Perhaps some form of autoencoder with a regularization term that penalizes uncorrelated codings?</p>
  <p>Any ideas are welcome. Thanks!</p>
  <p>Edit:</p>
  <p>In the problem that I have, the images <span class="math-container">$I_j$</span> are <span class="math-container">$(64,64)$</span> images of tumor nuclei, and the <span class="math-container">$f_{i,j}$</span> are genetical information about each cell, such as the expressivity of certain biomarks (HER2, ER, etc.).</p>
  <p><a href="https://i.sstatic.net/RmHCc.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/RmHCc.png" alt="enter image description here" /></a></p>
  
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2023-08-16T12:12:01.623Z
Comments.Text: can you please provide a practical example of what $f_{i,j}$ is?
Comments.UserDisplayName: Alberto
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2023-08-16T12:39:26.233Z
Comments.Text: @AlbertoSinigaglia Done.
Comments.UserDisplayName: Alek Fröhlich
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2023-08-16T13:19:24.080Z
Comments.Text: It looks like the features you are wanting to learn are explanatory for some other classification that you don't say? And that you want to train a model that predicts the classification from an image as the primary task, whilst also having these features expressed within the model? Could you please clarify
Comments.UserDisplayName: Neil Slater
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2023-08-16T13:53:35.883Z
Comments.Text: @NeilSlater A first example could be to classify a cell as HER2+ or HER2- based only on the image data. (During training the autoencoder would have access to reliable HER2 score for each nuclei)
Comments.UserDisplayName: Alek Fröhlich
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2023-08-16T23:09:10.177Z
Comments.Text: I'm not really an expert on this field so i still don't get what are the $f$, but I think that you can formulize this as a contrastive problem, using biomarks to attract of pull away latent vectors
Comments.UserDisplayName: Alberto
Tags: <regularization><representation-learning><correlation>
Title: Does this learning scenario have a name? If so, can someone point me to relevant literature?
UserDisplayName: Alek Fröhlich
ThreadText: # Does this learning scenario have a name? If so, can someone point me to relevant literature?
  
  (Asked by: username_0 on 2023-08-16)
  
  I am faced with a problem which I bet was already solved before, but that I had never seen. Perhaps by discussing it abstractly, someone can point me to relevant literature.
  
  It goes like this: I have a dataset of images $I\_j$ and numerical features $f\_{1,j}, f\_{2,j}, ..., f\_{k, j}$. In production, I don't have access to the features $f\_{i,j}$, which I know to be more relevant to my learning problem than the images.
  
  However, theses features $f\_{i,j}$ are also very hard to obtain, and there is a known correlation (informal) between the images and the numerical features $f\_{i,j}$. So the whole point of using the images is to avoid using the $f's$.
  
  Know comes the question: is there any useful way I could learn a representation of the images that "exposes" the maximum information about the features $f\_{i,j}$? Perhaps some form of autoencoder with a regularization term that penalizes uncorrelated codings?
  
  Any ideas are welcome. Thanks!
  
  Edit:
  
  In the problem that I have, the images $I\_j$ are $(64,64)$ images of tumor nuclei, and the $f\_{i,j}$ are genetical information about each cell, such as the expressivity of certain biomarks (HER2, ER, etc.).
  
  [![enter image description here](https://i.sstatic.net/RmHCc.png)](https://i.sstatic.net/RmHCc.png)
  
  **Tags:** regularization, representation-learning, correlation
  
  > **Comments:**
  > **username_1**: can you please provide a practical example of what $f_{i,j}$ is?  
  > **username_0**: @AlbertoSinigaglia Done.  
  > **username_2**: It looks like the features you are wanting to learn are explanatory for some other classification that you don't say? And that you want to train a model that predicts the classification from an image as the primary task, whilst also having these features expressed within the model? Could you please clarify  
  > **username_0**: @username_2 A first example could be to classify a cell as HER2+ or HER2- based only on the image data. (During training the autoencoder would have access to reliable HER2 score for each nuclei)  
  > **username_1**: I'm not really an expert on this field so i still don't get what are the $f$, but I think that you can formulize this as a contrastive problem, using biomarks to attract of pull away latent vectors  
  
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  ## 0 answers
  
  