Subject: [icnrg] Sotchastic Analysis

From: Sitaraman Vilayannur <[email-masked]>
Date: Sat, 15 Jun 2013 14:44:18 +0530

I was listening in to PGM and Expander Graphs course on Courseera and
Daphne had a cartoon wherein the hero(ine) sweeps down to solve a great
problem with a newly learnt skill....though why not sweep dowon on this
list if not with a solution, at least with a question...easier done.... for
it has a designated research flavor....hope it is ok. Could the below be
applied to control and in ICN networks?

Any pointers appreciated...

>From the last lecture on missing data, and related to what i posted in the
general discussion earlier, the following thought/question occurred. Any
pointers to related work in the literature and especially its applications
is most appreciated.

The missing data, especially the non MAR ones, perhaps, is reminscent of
what the communications folks daily bread. Digital sampling of a continuous
wave form, once you sample, you essentially end up with Missing Data in the
signal.  In this field, the Fourier Transform revolutionized analysis.

I wish i could cross post this to Expanders group...I am nervous about
earning the wrath of the very rigorous Mathematicians there!  I am  taking
the liberty to handwave relatively in this group! Thanks for that.**

Iam wondering if in the field of Probability and Stochastic analysis, is
there an equivalent to the transform. Looking at transforms, in the
communications field it is between the time and frequency domain.

A) A question i have is, is it true in nature that an entity/function/
characterized in one domain is invariably deterministic in one and
probabilistic in the other.   Certainly this is true in position momentum
uncertainty.

B) Are transforms viewed more generally the characterization of the
entity/function [Discrete or otherwise] in one domain where its transform
being the characterization of the same entity/function in its derivative of
the domain?

Can we combine A) and B) together  to explore if typically nature prefers
duality in deterministicity between a domain and its transform?  If so, is
the wealth of knowledge with the communication folks reusable in here?

Now this seems to make intuitive sense, at least in a handwaving way.   One
could think of stochastic nature occurring essentially due to the loss of
infinitesimality in the observability of the characterising variable(s) of
the function/entity. For, if you can observe upto the inifinitesimal limit
you are certain of what you are observing. Now is it then typically true
that if you can observe to the infinitesimal limit in one domain, it is
impossible to do so in its transform domain which in itself is a derivative
(and therefore an infinitesimal in itself) as mentioned above...

As an aside, could this type of phenomenon, in where it exists,  then be
exploited reusing concepts of primal-dual method of combinatorial
optimization or the converse.

 Specific to the interplay of the PGM and Expanders course...could we look
at the transform of a Graph as the inverse of its Adjacency matrix,   if so
is there an PGM transform for a Graphical model and its inverse and if so,
is there a probabilistic-deterministic duality between them?

Extending this further,  i am wondering if there is such a thing as a
continnum of EigenValues of the Adjacency matrix that moves a graph from
being a graph to a topological space....and could we think of PGMs on a
continuum of topological space, where the model is based on nodes (which
are say "flat"  regions and edges are the more "interesting" regions in the
topology)

A formalism application i want to hazard a guess is correlations between a
large number of variables... wherein there is not a natural map to a
discrete  structure such as a graph and analysis based on them, we could
possibly map it more naturally to a continuous topological space, and as
usual leech upon the Mathematicians hard, rigorous arcane work (for me at
least) to draw quick benefits..

An application for the above in the field of Networking i see is
Information based networking and traffic management of the same.  Questions
arise such as can we characterize information in various "domain spaces"
are there transforms to these spaces and can these be formalized for
analysis and control either deterministically or stochastically.

There could be applications in pattern recognition analytics and Root Cause
Analysis also...

Any pointers to existing literature in related areas  appreciated....

 I will pester the SDNRG and ICNRG list to see if someone gives me further
pointers in areas related...

Sitaraman

---

From: Sitaraman Vilayannur <[email-masked]>
Date: Sat, 15 Jun 2013 18:03:29 +0530

Not sure of applications to Networking, but related to above looknig at the
Riemann hypothesis the numbers raised to the expnent of a complex seem to
be characterizing the behavior of the function, in both the domain and its
transform, and if the expectation is zero then then due to the said
duality, the zero lies always in probability 0.5 ...
Sitaraman

On Sat, Jun 15, 2013 at 2:44 PM, Sitaraman Vilayannur <
[email-masked]> wrote:

> duality in deterministicity between a domain and its transform?  If so,
> is the wealth of knowledge with the communication folks reusable in here?
>
>  Specific to the interplay of the PGM and Expanders course...could we
> look at the transform of a Graph as the inverse of its Adjacency matrix,
>   if so is there an PGM transform for a Graphical model and its inverse
> and if so, is there a probabilistic-deterministic duality between them?
>
> are say "flat"  regions and edges are the more "interesting" regions in
> the topology)
>
> There could be applications in pattern recognition analytics and Root
> Cause Analysis also...
>
>  I will pester the SDNRG and ICNRG list to see if someone gives me
> further pointers in areas related...
>
> Sitaraman
>