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| -rw-r--r-- | posts/2019-03-14-great-but-manageable-expectations.md | 10 |
1 files changed, 8 insertions, 2 deletions
diff --git a/posts/2019-03-14-great-but-manageable-expectations.md b/posts/2019-03-14-great-but-manageable-expectations.md index 9315844..a886e08 100644 --- a/posts/2019-03-14-great-but-manageable-expectations.md +++ b/posts/2019-03-14-great-but-manageable-expectations.md @@ -328,8 +328,6 @@ assumptions. ACGMMTZ16 --------- -**Warning**. This section is under construction. - What follows is my understanding of this result. I call it a conjecture because there is a gap which I am not able to reproduce their proof or prove it myself. This does not mean the result is false. On the @@ -352,6 +350,14 @@ $$D_\lambda (p || q) \le D_\lambda (r \mu_1 + (1 - r) \mu_0 || \mu_0)$$ where $\mu_i = N(i, \sigma^2)$. +**Remark**. +<!--- +Conjecture 1 is heuristically reasonable. +To see this, let us use the notations $p_I$ and $q_I$ to be $q$ and $p$ conditioned on +the subsampling index $I$, just like in the proof of the subsampling theorems (Claim 19 and 24). +--> +[A more general version of Conjecture 1 has been proven false](https://math.stackexchange.com/a/3152296/149540). + <!--- **Conjecture 1** \[Probably [FALSE](https://math.stackexchange.com/a/3152296/149540), to be removed\]. Let $p_i$, $q_i$, $\mu_i$, $\nu_i$ be probability densities on the same space for $i = 1 : n$. If |