Re: Question
Reginald Beardsley <[email protected]> Tue, 20 May 2025 02:59:22 +0000 (UTC)
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FWIW Below is my attempt at disambiguating the problem. I have *some* confi=
dence it is an accurate description, but assert no more. I've not had a rep=
ly from Federico yet, but expect one soon.
Translating a word problem into a mathematical problem is fraught with peri=
l. Much of my career was spent helping people convert their word problem in=
to a mathematical problem. Most of the time they immediately knew how to so=
lve the problem after I asked some questions and gave them the proper mathe=
matical formulation. My English lit BA degree had broad application to PhD =
level mathematics. Go figure. I'd never expected that.
From a series of emails with Federico, I *think* this is an accurate descri=
ption:
Given phoneme frequencies for all of a language, e.g. Spanish, how does one=
select the best combination of repetitions of a subset of the entire lexic=
on to best match the phoneme distribution of the entire language? The goal =
being evaluating verbal intelligibility in speech communication. It looks t=
o me to be a straight forward linear error minimization problem.
This seems to me a classic sparse L1 program as described in a paper by Ema=
nuel Candes which he called it "The Dantzig Selector" in the early 2000s as=
an application of sparse L1 pursuits. I am acutely interested in whether t=
hat is correct. Not merely in the solution of Federico's problem, but my ow=
n understanding of sparse L1 pursuits as I learned from Focuart and Rauhut'=
s "A Mathematical Introduction to Compressive Sensing." Having worked for 3=
years without almost no one with whom to converse, I'm less than confident=
I have all the nuances correct. If I am wrong, I should very much apprecia=
te an explanation. I no longer have the pleasure of doing this as an occupa=
tion, but money was never what motivated me.
My perception is that the solution is straight forward, but tedious to impl=
ement because of size. The obvious solution to me is, write a program to ge=
nerate a GMPL file. I *think* it is a mixed integer problem, but not yet co=
nvinced that's the best formulation.
I am very grateful for the assistance provided by this list 8-10 years ago =
and should very much enjoy contributing something useful. GLPK is a true "t=
our de force". Many thanks to Andrew et al.
Have Fun!
Reg
----- Forwarded Message ----- From: Reginald Beardsley <pulaskite@yahoo=
.com>To: Federico Miyara <[email protected]>Sent: Monday, May 19, 20=
25 at 12:10:37 PM CDTSubject: Re: Question
Federico,
Is this a correct statement of your problem?
You have a dictionary of N words composed of various elements from a set of=
M symbols each of which has a certain number of occurrences in the N words=
. The number of symbols from M which form an word in the set N varies but i=
s small.
You wish to determine the number of recurrences of a smaller subset of P wo=
rds which have the same proportion of the M symbols as the entire set of N =
words, but with P << N. Further, you wish to be able to select different su=
bsets of P words that all have the best matched frequency of occurrence of =
the M symbols in P as in N with Q selections from P. The particular sets of=
P words in each case being chosen independently based on other criteria un=
related to the frequency of occurrence of the M symbols in N.
The desired output is a list of the number of occurrences of each word in t=
he set P which best approximates the number of occurrences of the M symbols=
in the set N for Q selections from the list M for the case Q >=3D P.=20
The fundamental problem is then constructing Ax=3Dy where y is the vector o=
f probabilities of each element in M in N. The vector x is a integer valued=
number of repetitions of words in P. The hard part is creating the correct=
A matrix.
Have Fun!
Reg
On Friday, May 16, 2025 at 04:55:34 PM CDT, Federico Miyara <fmiyara@f=
ceia.unr.edu.ar> wrote: =20
=20
=20
I need to solve the following problem:
I have an alphabet of n symbols and a dictionary with N words of m
symbols (n in the order of tens, N in the order of tens of thousands, m
=3D 4, say)
Assuming each symbol has a definite probability, I need to generate a
list of M words (M in the order of 100) taken from the dictionary in
which the proportion of each symbol matches as best as possible the
required probability.
Is this a problem that can be solved using GLPK?
Thanks.
Bes regards,
Federico Miyara
--
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<div> <br>FWIW Below is my attempt at disambiguating the pro=
blem. I have *some* confidence it is an accurate description, but assert n=
o more. I've not had a reply from Federico yet, but expect one soon.<b=
r><br>Translating a word problem into a mathematical problem is fraught wit=
h peril. Much of my career was spent helping people convert their word pro=
blem into a mathematical problem. Most of the time they immediately knew h=
ow to solve the problem after I asked some questions and gave them the prop=
er mathematical formulation. My English lit BA degree had broad applicatio=
n to PhD level mathematics. Go figure. I'd never expected that.<br><b=
r>From a series of emails with Federico, I *think* this is an accurate desc=
ription:<br><br>Given phoneme frequencies for all of a language, e.g. Spani=
sh, how does one select the best combination of repetitions of a subset of=
the entire lexicon to best match the phoneme distribution of the entire la=
nguage? The goal being evaluating verbal intelligibility in speech communi=
cation. It looks to me to be a straight forward linear error minimization =
problem.<br><br>This seems to me a classic sparse L1 program as described =
in a paper by Emanuel Candes which he called it "The Dantzig Selector&=
quot; in the early 2000s as an application of sparse L1 pursuits. I am acu=
tely interested in whether that is correct. Not merely in the solution of =
Federico's problem, but my own understanding of sparse L1 pursuits as I=
learned from Focuart and Rauhut's "A Mathematical Introduction to=
Compressive Sensing." Having worked for 3 years without almost no on=
e with whom to converse, I'm less than confident I have all the nuance=
s correct. If I am wrong, I should very much appreciate an explanation. I=
no longer have the pleasure of doing this as an occupation, but money was =
never what motivated me.<br><br>My perception is that the solution is strai=
ght forward, but tedious to implement because of size. The obvious solutio=
n to me is, write a program to generate a GMPL file. I *think* it is a mix=
ed integer problem, but not yet convinced that's the best formulation.<=
br><br>I am very grateful for the assistance provided by this list 8-10 yea=
rs ago and should very much enjoy contributing something useful. GLPK is a=
true "tour de force". Many thanks to Andrew et al.<br><br>Have =
Fun!<br>Reg<br> </div> <div class=3D"yahoo_quoted" st=
yle=3D"margin:10px 0px 0px 0.8ex;border-left:1px solid #ccc;padding-left:1e=
x;"> <div style=3D"font-family:'Helvetica Neue', Hel=
vetica, Arial, sans-serif;font-size:13px;color:#26282a;"> <d=
iv>----- Forwarded Message -----</div> <div><b>From:</b> Reg=
inald Beardsley <[email protected]></div><div><b>To:</b> Federico M=
iyara <[email protected]></div><div><b>Sent:</b> Monday, May 1=
9, 2025 at 12:10:37 PM CDT</div><div><b>Subject:</b> Re: Question</div><div=
><br></div> <div><div id=3D"=
yiv6790832716"><div><div> Federico,<br clear=3D"none"><br cl=
ear=3D"none">Is this a correct statement of your problem?<br clear=3D"none"=
><br clear=3D"none">You have a dictionary of N words composed of various el=
ements from a set of M symbols each of which has a certain number of occurr=
ences in the N words. The number of symbols from M which form an word in th=
e set N varies but is small.<br clear=3D"none"><br clear=3D"none">You wish =
to determine the number of recurrences of a smaller subset of P words whic=
h have the same proportion of the M symbols as the entire set of N words, b=
ut with P << N. Further, you wish to be able to select different sub=
sets of P words that all have the best matched frequency of occurrence of t=
he M symbols in P as in N with Q selections from P. The particular sets of=
P words in each case being chosen independently based on other criteria un=
related to the frequency of occurrence of the M symbols in N.<br clear=3D"n=
one"><br clear=3D"none">The desired output is a list of the number of occur=
rences of each word in the set P which best approximates the number of occu=
rrences of the M symbols in the set N for Q selections from the list M for =
the case Q >=3D P. <br clear=3D"none"><br clear=3D"none">The fundamental=
problem is then constructing Ax=3Dy where y is the vector of probabilities=
of each element in M in N. The vector x is a integer valued number of rep=
etitions of words in P. The hard part is creating the correct A matrix.<br=
clear=3D"none"><br clear=3D"none">Have Fun!<br clear=3D"none">Reg<br clear=
=3D"none"> </div> <div id=3D"yiv6790832716yqt35542" c=
lass=3D"yiv6790832716yqt9332962494"><div style=3D"margin:10px 0px 0px 0.8ex=
;border-left:1px solid #ccc;padding-left:1ex;" class=3D"yiv6790832716yahoo_=
quoted"> <div style=3D"font-family:'Helvetica Neue',=
Helvetica, Arial, sans-serif;font-size:13px;color:#26282a;"> =
<div> On Friday, May 16, 2025 at 0=
4:55:34 PM CDT, Federico Miyara <[email protected]> wrote: =
</div> <div><br clear=3D"none"></div> =
<div><br clear=3D"none"></div> =
<div><div dir=3D"ltr"><br clear=3D"none"></div><div dir=
=3D"ltr">I need to solve the following problem:<br clear=3D"none"></div><di=
v dir=3D"ltr"><br clear=3D"none"></div><div dir=3D"ltr">I have an alphabet =
of n symbols and a dictionary with N words of m<br clear=3D"none"></div><di=
v dir=3D"ltr">symbols (n in the order of tens, N in the order of tens of th=
ousands, m<br clear=3D"none"></div><div dir=3D"ltr">=3D 4, say)<br clear=3D=
"none"></div><div dir=3D"ltr"><br clear=3D"none"></div><div dir=3D"ltr">Ass=
uming each symbol has a definite probability, I need to generate a<br clear=
=3D"none"></div><div dir=3D"ltr">list of M words (M in the order of 100) ta=
ken from the dictionary in<br clear=3D"none"></div><div dir=3D"ltr">which t=
he proportion of each symbol matches as best as possible the<br clear=3D"no=
ne"></div><div dir=3D"ltr">required probability.<br clear=3D"none"></div><d=
iv dir=3D"ltr"><br clear=3D"none"></div><div dir=3D"ltr">Is this a problem =
that can be solved using GLPK?<br clear=3D"none"></div><div dir=3D"ltr"><br=
clear=3D"none"></div><div dir=3D"ltr">Thanks.<br clear=3D"none"></div><div=
dir=3D"ltr"><br clear=3D"none"></div><div dir=3D"ltr">Bes regards,<br clea=
r=3D"none"></div><div dir=3D"ltr"><br clear=3D"none"></div><div dir=3D"ltr"=
>Federico Miyara<br clear=3D"none"></div><div dir=3D"ltr"><br clear=3D"none=
"></div><div dir=3D"ltr">--<br clear=3D"none"></div><div dir=3D"ltr">Este c=
orreo electr=C3=B3nico ha sido analizado en busca de virus por el software =
antivirus de Avast.<br clear=3D"none"></div><div dir=3D"ltr">www.avast.com<=
br clear=3D"none"></div><div dir=3D"ltr"><br clear=3D"none"></div></div> =
</div> </div></div></div></div></div> </=
div> </div>
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