Answers.Body: <p>A simple neural network (no hidden layer) with linear activation and MSE (mean squared error) as loss in the same as running a linear regression (OLS) and optimizing with gradient descent. So implementing a Poission style regression would be just changing the loss function from MSE to logit link i.e.</p>
  <p><a href="https://i.sstatic.net/kpamf.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/kpamf.png" alt="enter image description here" /></a></p>
  <p>where y is the target and y hat is the prediction</p>
  
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Answers.CreationDate: 2023-10-06T08:03:34.860Z
Answers.Text: Logit link isn’t the link function used for a Poisson GLM. It’s just a log link, since we need the mean of the Poisson distribution to be positive.
Answers.UserDisplayName: David
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Answers.CreationDate: 2023-10-06T10:29:11.990Z
Answers.Text: Welcome to the AI Stack! Yes, all of the theory works out: just use the Poisson loss and exponential activation (same as logarithmic link function). However, what work has been done with this? For instance, have there been any empirical success stories the way classification has found great success on the MNIST digits? Any catastrophes?
Answers.UserDisplayName: Dave
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Answers.CreationDate: 2023-10-06T06:24:12.213Z
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Answers.UserDisplayName: kaiser
Body: <p>The first neural net I wrote was a classifier. After that, I learned that neural nets can be used for regression tasks, even quantile regression.</p>
  <p>It has become clear to me that the usual games with extensions of OLS linear regression can be applied to neural networks.</p>
  <p>What work has been done with Poisson-style regression via neural networks with log link functions (exponential activation function)?</p>
  
Tags: <neural-networks><activation-functions><regression>
Title: What work has been done with Poisson-style regression via neural networks with exponential activation functions?
UserDisplayName: Dave
ThreadText: # What work has been done with Poisson-style regression via neural networks with exponential activation functions?
  
  (Asked by: username_0 on 2020-05-11)
  
  The first neural net I wrote was a classifier. After that, I learned that neural nets can be used for regression tasks, even quantile regression.
  
  It has become clear to me that the usual games with extensions of OLS linear regression can be applied to neural networks.
  
  What work has been done with Poisson-style regression via neural networks with log link functions (exponential activation function)?
  
  **Tags:** neural-networks, activation-functions, regression
  
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  ## 1 answers
  
  ### Answer by username_1 on 2023-10-06. Score: 0
  
  A simple neural network (no hidden layer) with linear activation and MSE (mean squared error) as loss in the same as running a linear regression (OLS) and optimizing with gradient descent. So implementing a Poission style regression would be just changing the loss function from MSE to logit link i.e.
  
  [![enter image description here](https://i.sstatic.net/kpamf.png)](https://i.sstatic.net/kpamf.png)
  
  where y is the target and y hat is the prediction
  
  > **Comments:**
  > **username_2**: Logit link isn’t the link function used for a Poisson GLM. It’s just a log link, since we need the mean of the Poisson distribution to be positive.  
  > **username_0**: Welcome to the AI Stack! Yes, all of the theory works out: just use the Poisson loss and exponential activation (same as logarithmic link function). However, what work has been done with this? For instance, have there been any empirical success stories the way classification has found great success on the MNIST digits? Any catastrophes?  
  
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