Summary statistics which don’t require you to keep all the data but which allow you to do inference nearly as well. e.g sufficient statistics in exponential families allow you to do do certain kind of inference perfectly without anything except summaries. Methods such as variational Bayes summarize data by maintaining a posterior density (usually a mixture models) as a summary of all the data, at some cost in accuracy.. I think of these as nearly sufficient statistics but there are other framings, as data summarization which I am going to note here for later reference.
- Approximate Bayesian Computation
- inducing sets, as seen in Gaussian processes
- coresets as seen in Bayesian linear models
- probabilistic deep learning possibly does this
- Bounded Memory Learning considers this from a computation complexity standpoint - which hypotheses can be learned from data subsets
Bayesian. Solve an optimisation problem to minimise distance between posterior with all data and with a weighted subset.
Directly approximate log likelihood
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