Row 66038

Row ID: 66038 | Dataset Entry | Axioma AXP Content Repository

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I understand the intuition about the I-projection and M-projection approximating the posterior over latents differently and how that would be desirable/non-desirable for different models. My question is about the consequences of the different objectives on the predictive distribution of the data.

Ok, so being more specific. Model is given as p(x,z) = p(z)p(x|z) where x is 'data' and z is 'latent' variable. Given x, I approximate the intractable posterior p(z|x) with q(z) by either minimizing KL(q(z)||p(z|x)) or KL(p(z|x)||q(z)) wrt q. My predictive distribution over x is then given as p(x) = ∫q(z)p(x|z)dz.

Question: what is the difference in p(x) when approximating q(z) w/ either rKL or fKL? Anything we can say about the variance of p(x) that generally holds for certain models? Any works that study this question? For example for sparse GP models, where z is a latent function, \[4\] finds that the rKL overestimates the variance of p(x).

FieldValue
text I understand the intuition about the I-projection and M-projection approximating the posterior over latents differently and how that would be desirable/non-desirable for different models. My question is about the consequences of the different objectives on the predictive distribution of the data. Ok, so being more specific. Model is given as p(x,z) = p(z)p(x|z) where x is 'data' and z is 'latent' variable. Given x, I approximate the intractable posterior p(z|x) with q(z) by either minimizing KL…
label r/machinelearning
dataType comment
communityName r/MachineLearning
datetime 2024-05-23
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{
  "text": "I understand the intuition about the I-projection and M-projection approximating the posterior over latents differently and how that would be desirable/non-desirable for different models. My question is about the consequences of the different objectives on the predictive distribution of the data.\n\nOk, so being more specific. Model is given as p(x,z) = p(z)p(x|z) where x is 'data' and z is 'latent' variable. Given x, I approximate the intractable posterior p(z|x) with q(z) by either minimizing KL(q(z)||p(z|x)) or KL(p(z|x)||q(z)) wrt q. My predictive distribution over x is then given as p(x) = ∫q(z)p(x|z)dz. \n\nQuestion: what is the difference in p(x) when approximating q(z) w/ either rKL or fKL? Anything we can say about the variance of p(x) that generally holds for certain models? Any works that study this question? For example for sparse GP models, where z is a latent function, \\[4\\] finds that the rKL overestimates the variance of p(x).",
  "label": "r/machinelearning",
  "dataType": "comment",
  "communityName": "r/MachineLearning",
  "datetime": "2024-05-23",
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