Body: <p>This is a naive question... But I realized that auto-regressive predictions can be inherently unstable due to previous prediction error monotonically accumulating in the inputs: <span class="math-container">$M(h_{t-n},...,h_{t-m},p_{t-m+1},...,p_{t})=p_{t+1}$</span> (e.g. LSTM/GRU type models). And I can only think of one application where auto-regressive predictions' &quot;self-consistency&quot; would be worth it: text generation (...otherwise text would be gibberish).</p>
  <p>But for regular time series: <em>Why not directly predict/query time-step(s) <strong>independently</strong>, given only historical observations?</em> That is, independent of any potential <em>intermediate predictions</em>: <span class="math-container">$M(h_{t-n},...,h_{t},q)=p_{q}$</span>.</p>
  <p>Context:
  This auto-regressive instability is a big problem (for statistical models/surrogates) in the computational physics community and it seems they prefer to avoid the problem altogether in exactly the way I described.</p>
  
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2024-02-02T19:50:49.187Z
Comments.Text: it's valid in other areas, for example in reinforcement learning... however, if you are only interested in a pointwise prediction, and wiht prediction i mean "that output wont effect the rest of the outputs", then don't do that
Comments.UserDisplayName: Alberto
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2024-02-02T20:00:17.577Z
Comments.Text: @Alberto I'm confused because, standard RL is Markov (depends on only current state). Could you elaborate?
Comments.UserDisplayName: profPlum
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2024-02-02T20:04:22.947Z
Comments.Text: I'm essentially looking for examples where this auto-regressive prediction approach is necessary aside from text-generation.
Comments.UserDisplayName: profPlum
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2024-02-02T23:41:50.037Z
Comments.Text: In case you are in a partially observable environment, you have to build a "belief", which is your recurrent latent value.. in that case, you don't want to tell to the agent only the (partial) state in which is, but also the action that you have sampled at each timestep (the same holds in what is known in meta reinforcement learning/knowledge distillation RL)
Comments.UserDisplayName: Alberto
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2024-02-05T17:44:04.863Z
Comments.Text: Fair enough. Do you also have any examples for standard time-series problems?
Comments.UserDisplayName: profPlum
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2024-02-05T18:27:28.937Z
Comments.Text: you want to do this only when $p(y_i|x_0,...,x_n) \not\!\perp\!\!\!\perp p(y_{i+1}|x_0,...,x_n)$ therefore if the decision at time $i$ influences the future classification you do this, otherwise is useless... in case of time series, i don't see how this might be useful tbh... but maybe i'm wrong
Comments.UserDisplayName: Alberto
Tags: <recurrent-neural-networks><time-series><gated-recurrent-unit>
Title: Why use auto-regressive models for time-series?
UserDisplayName: profPlum
ThreadText: # Why use auto-regressive models for time-series?
  
  (Asked by: username_0 on 2024-02-02)
  
  This is a naive question... But I realized that auto-regressive predictions can be inherently unstable due to previous prediction error monotonically accumulating in the inputs: $M(h\_{t-n},...,h\_{t-m},p\_{t-m+1},...,p\_{t})=p\_{t+1}$ (e.g. LSTM/GRU type models). And I can only think of one application where auto-regressive predictions' "self-consistency" would be worth it: text generation (...otherwise text would be gibberish).
  
  But for regular time series: *Why not directly predict/query time-step(s) **independently**, given only historical observations?* That is, independent of any potential *intermediate predictions*: $M(h\_{t-n},...,h\_{t},q)=p\_{q}$.
  
  Context:
  This auto-regressive instability is a big problem (for statistical models/surrogates) in the computational physics community and it seems they prefer to avoid the problem altogether in exactly the way I described.
  
  **Tags:** recurrent-neural-networks, time-series, gated-recurrent-unit
  
  > **Comments:**
  > **username_1**: it's valid in other areas, for example in reinforcement learning... however, if you are only interested in a pointwise prediction, and wiht prediction i mean "that output wont effect the rest of the outputs", then don't do that  
  > **username_0**: @username_1 I'm confused because, standard RL is Markov (depends on only current state). Could you elaborate?  
  > **username_0**: I'm essentially looking for examples where this auto-regressive prediction approach is necessary aside from text-generation.  
  > **username_1**: In case you are in a partially observable environment, you have to build a "belief", which is your recurrent latent value.. in that case, you don't want to tell to the agent only the (partial) state in which is, but also the action that you have sampled at each timestep (the same holds in what is known in meta reinforcement learning/knowledge distillation RL)  
  > **username_0**: Fair enough. Do you also have any examples for standard time-series problems?  
  > **username_1**: you want to do this only when $p(y_i|x_0,...,x_n) \not\!\perp\!\!\!\perp p(y_{i+1}|x_0,...,x_n)$ therefore if the decision at time $i$ influences the future classification you do this, otherwise is useless... in case of time series, i don't see how this might be useful tbh... but maybe i'm wrong  
  
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  ## 0 answers
  
  