Passing a message along for my colleague Waheed Bajwa:
As the US Liaison Chair of IEEE SPAWC 2019, I have received NSF funds to support travel of undergraduate and/or graduate students to Cannes, France for IEEE SPAWC 2019. Having a paper at the workshop is not a prerequisite for these grants and a number of grants are reserved for underrepresented minority students whose careers might benefit from these travel grants. Please share this with any interested students and, if you know one, please encourage her/him to consider applying for these grants.
-node graph (c.f. a graphical model) representing the joint distribution on 
or 
. At each time you get to observe the data from only one node of the graph. You can either observe the same node as before, explore by observing a different node, or make a decision about whether the data from from 
, where 
(say a Bernoulli-Gaussian prior). The question is what happens when we do estimation assuming a different prior 
. The main result of the paper is an analysis of the excess MSE using a decoupling principle. Since I don’t really know anything about the replica method (except the name “replica method”), I had a little bit of a hard time following the talk as a non-expert, but thankfully there were a number of pictures and examples to help me follow along.
targets 
uniformly distributed in the unit interval, and what we can do is query at each time ![S_n \subseteq [0,1]](https://s0.wp.com/latex.php?latex=S_n+%5Csubseteq+%5B0%2C1%5D&bg=ffffff&fg=333333&s=0&c=20201002)
and get a response 
where 
and 
where 
is the Lebesgue measure. So basically you can query a set and you get a noisy indicator of whether you hit any targets, where the noise depends on the size of the set you query. At some point 
you stop and guess the target locations. You are 
successful if the probability that you are within 
of each target is less than 
. The targeting rate is the limit of ![\log(1/\delta) / \mathbb{E}[\tau]](https://s0.wp.com/latex.php?latex=%5Clog%281%2F%5Cdelta%29+%2F+%5Cmathbb%7BE%7D%5B%5Ctau%5D&bg=ffffff&fg=333333&s=0&c=20201002)
as 
(I’m being fast and loose here). Clearly there are some connections to group testing and communication with feedback, etc. They show there is a significant gap between the adaptive and nonadaptive rate here, so you can find more targets if you can adapt your queries on the fly. However, since rate is defined for a fixed number of targets, we could ask how the gap varies with 
and 
if the corresponding entry 
in the inverse covariance matrix. They show a relationship between the KL divergence of two distributions and their corresponding graphs. The divergence is lower bounded by a constant if they differ in a single edge — this indicates that estimating the edge structure is important when estimating the distribution.![\mathbb{E}[ \ell(W, \hat{W}) ]](https://s0.wp.com/latex.php?latex=%5Cmathbb%7BE%7D%5B+%5Cell%28W%2C+%5Chat%7BW%7D%29+%5D&bg=ffffff&fg=333333&s=0&c=20201002)
of a 
-dimensional parameter 
which is observed noisily by separate encoders. Think of a CEO-style problem where there is a conditional distribution 
such that the observation at each node is a 
matrix whose columns are i.i.d. and where the 
. Each sensor gets independent observations from the same model and can compress its observations to 
bits and sends it over independent channels to an estimator (so no MAC here). The main result is a lower bound on the expected loss as s function of the number of bits latex 
. The key is to use the strong data processing inequality to handle the mutual information — the constants that make up the ratio between the mutual informations is important. I’m sure Max will blog more about the result so I’ll leave a full explanation to him (see what I did there?)
An Ergodic Walk 