[R] Neural Network models

2019-07-28 Thread Agustín Alonso Rodriguez
I apologize for writing my question in Spanish. I thought that I was writing
my question to the Spanish list.



Agust�n Alonso







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[R] neural network, random forest with survey data

2015-02-09 Thread ying_chen wang
Hi, everyone:

Does anyone know if any statistical packages (such as R) can accommodate
neural network or random forest with survey data?

With survey data, we have to incorporate weight with sampling issue or even
with design effect.

Would appreciate if anyone can help.

Grace

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Re: [R] Neural Network

2015-01-26 Thread Charles Determan Jr
Javad,

You misunderstand what is meant be 'dependent' and 'independent'
variables.  What you are describing is with respect to statistical
independence.  Please review these basic statistical concepts
http://en.wikipedia.org/wiki/Dependent_and_independent_variables.  Perhaps,
the terms 'explanatory' (e.g. your phosphorus, nitrogen, etc.) and
'response' (e.g. eutrophication) variables are more approachable.

Now, as I was saying in my first response, you don't appear to have a
dependent/response variable (i.e. Eutrophication).  No where in your data
do you say that Eutrophication was measured or is represented in any way.
Now, I assume you have 'a priori' knowledge that those variables are
involved with eutrophication.  You are now asking if you can predict
eutrophication from these variables.  Well, without something for a
statistical model to evaluate against there is no means to do so, hence the
exploratory, unsupervised analysis I recommended.

With respect to your other question, "How can I predict these variables by
NN?", well you need something to test against.  For example, let's say I
want to predict how much ice cream will be sold today and I have a bunch of
data with amounts of ice cream sold but no other data.  No matter how you
approach this problem, you cannot get much out of a list of numbers with
nothing to test against.

Now, if my ice cream data has the amounts of ice cream and temperatures of
each day associated with the respective sold amount, now I can do
something.  I can do my basic linear regression so help predict how much
ice cream will be sold given today's temperature.

The same appears to be true of your data.  You have your variables, you
have all of your response variables (assuming you are trying to predict
Nitrogen, Chlorophyll, etc.) but nothing to test against.  The best you may
have is your time data which I can only assume is actual dates?  If so, you
could do some form of prediction based on the date.  If your data is just
every two weeks (no date, just repeated measures) you could analyze it
temporally to see if the various nutrients are changing over time and
potentially extrapolate (with caution) where the levels may ultimately
reach.  This may be of interest to you.

As a last point, seeing as this is environmental analysis you could also
try the R-sig-ecology mailing list.  I am admittedly not an ecologist and
there may be some other approaches or methods that could possibly be used.
Feel free to sign up on that list here
https://stat.ethz.ch/mailman/listinfo/r-sig-ecology

I hope this explanation helps you get a better grasp of what you are trying
to accomplish.
Regards,

On Sat, Jan 24, 2015 at 12:41 AM, javad bayat  wrote:

> Dear Charles;
> I think my variables are dependent. For e.g. the concentration of
> Phosphorus, Nitrogen, Silica and etc. have effect on the present of
> Chlorophyll a and the concentration of Chlorophyll a can make the
> Eutrophication in lake along with other algeas.
> So I think they are dependent variables.
> Regards.
>
>
>
> ------------
> On Thu, 1/22/15, Charles Determan Jr  wrote:
>
>  Subject: Re: [R] Neural Network
>  To: "javad bayat" , "r-help@r-project.org" <
> r-help@r-project.org>
>  Date: Thursday, January 22, 2015, 4:41 PM
>
>  Javad,
>  First,
>  please make sure to hit 'reply all' so that these
>  messages go to the R help list so others (many far more
>  skilled than I) may possibly chime in.
>  The problem here is that you appear
>  to have no dependent variable (i.e. no eutrophication
>  variable).  Without it, there is no way to a typical
>  'supervised' analysis.  Given that this is likely a
>  regression type problem (I assume eutrophication would be
>  continous) I'm not quite sure 'supervised' is
>  the correct description but it furthers my point that you
>  need a dependent variable for any neuralnet algorithm I am
>  aware of.  As such, if you don't have a dependent
>  variable then you will need to look at unsupervised methods
>  such as PCA.  Other users may have other
>  suggestions.
>  Regards,Charles
>  On Wed, Jan 21, 2015 at
>  11:36 PM, javad bayat 
>  wrote:
>  Dear
>  Charles;
>
>  Many thanks for your attention. what I want to know is: How
>  can I predict the Eutrophication by these parameters in the
>  future?
>
>  These variables are the most important variables that
>  control the Eutro. in lakes.
>
>  Let me break it to two parts.
>
>  1) How can I predict these variables by NN?
>
>  2) Is it possible to predict the Eutro. by these
>  variables?
>
>
>
>
>
>  Many thanks for your help.
>
>   Regards,
>
>
>
>
>
>
&g

Re: [R] Neural Network

2015-01-23 Thread javad bayat via R-help
Dear All;
Many thanks for your attention. what I want to know is: How can I predict the 
Eutrophication by these parameters in the future?
These variables are the most important variables that control the Eutro. in 
lakes.
Let me break it to two parts.
1) How can I predict these variables by NN?
2) Is it possible to predict the Eutro. by these variables?


Many thanks for your help.
Regards,

On Thu, 1/22/15, Charles Determan Jr  wrote:

 Subject: Re: [R] Neural Network

roject.org>
 Date: Thursday, January 22, 2015, 4:41 PM

 Javad,
 First,
 please make sure to hit 'reply all' so that these
 messages go to the R help list so others (many far more
 skilled than I) may possibly chime in.
 The problem here is that you appear
 to have no dependent variable (i.e. no eutrophication
 variable).  Without it, there is no way to a typical
 'supervised' analysis.  Given that this is likely a
 regression type problem (I assume eutrophication would be
 continous) I'm not quite sure 'supervised' is
 the correct description but it furthers my point that you
 need a dependent variable for any neuralnet algorithm I am
 aware of.  As such, if you don't have a dependent
 variable then you will need to look at unsupervised methods
 such as PCA.  Other users may have other
 suggestions.
 Regards,Charles
 On Wed, Jan 21, 2015 at

 wrote:
 Dear
 Charles;

 Many thanks for your attention. what I want to know is: How
 can I predict the Eutrophication by these parameters in the
 future?

 These variables are the most important variables that
 control the Eutro. in lakes.

 Let me break it to two parts.

 1) How can I predict these variables by NN?

 2) Is it possible to predict the Eutro. by these
 variables?





 Many thanks for your help.

  Regards,















 

 On Wed, 1/21/15, Charles Determan Jr 
 wrote:



  Subject: Re: [R] Neural Network



  Cc: "r-help@r-project.org"
 

  Date: Wednesday, January 21, 2015, 9:10 PM



  Javad,

  You

  question is a little too broad to be answered

  definitively.  Also, this is not a code writing
 service. 

  You should make a meaningful attempt and we are here to
 help

  when you get stuck.

  1.

  If you want to know if you can do neural nets, the answer
 is

  yes.  The three packages most commonly used (that I
 know

  of) are 'neuralnet', 'nnet' and

  'RSNNS'.  You should look in to these package

  documentation for how to use them.  There are also
 many

  examples online if you simply google them.

  2. You question is unclear, are you

  wanting to predict all the variables (e.g. phosphorus,
 Total

  N, etc.) or do you have some metric for
 eutrophication? 

  What exactly is the model supposed to predict?

  3. If you want to know if a

  neuralnet is appropriate, that is more of a statistical

  question.  It depends more on the question you want to

  answer.  Given your temporal data, you may want to look
 in

  to mixed effects models (e.g nlme, lme4) as another

  potential approach.

  Regards,

  On Tue, Jan 20, 2015 at

  11:35 PM, javad bayat via R-help 

  wrote:

  Dear

  all;



  I am the new user of R. I want to simulation or
 prediction

  the Eutrophication of a lake. I have weekly data(almost
 for

  two years) for Total phosphorus, Total N, pH, Chlorophyll
 a,

  Alkalinity, Silica.



  Can I predict the Eutrophication by Neural Network in
 R?



  How can I simulation the Eutrophication by these

  parameter?



  please help me to write the codes.



  many thanks.







  __



  R-help@r-project.org

  mailing list -- To UNSUBSCRIBE and more, see



  https://stat.ethz.ch/mailman/listinfo/r-help



  PLEASE do read the posting guide http://www.R-project.org/posting-guide.html



  and provide commented, minimal, self-contained,
 reproducible

  code.









  --

  Dr. Charles Determan, PhD

  Integrated Biosciences








 -- 
 Dr. Charles Determan, PhD
 Integrated Biosciences

__
R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see
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and provide commented, minimal, self-contained, reproducible code.


Re: [R] Neural Network

2015-01-23 Thread javad bayat via R-help
Dear Charles;
I think my variables are dependent. For e.g. the concentration of  Phosphorus, 
Nitrogen, Silica and etc. have effect on the present of Chlorophyll a and the 
concentration of Chlorophyll a can make the Eutrophication in lake along with 
other algeas. 
So I think they are dependent variables.
Regards. 




On Thu, 1/22/15, Charles Determan Jr  wrote:

 Subject: Re: [R] Neural Network

roject.org>
 Date: Thursday, January 22, 2015, 4:41 PM

 Javad,
 First,
 please make sure to hit 'reply all' so that these
 messages go to the R help list so others (many far more
 skilled than I) may possibly chime in.
 The problem here is that you appear
 to have no dependent variable (i.e. no eutrophication
 variable).  Without it, there is no way to a typical
 'supervised' analysis.  Given that this is likely a
 regression type problem (I assume eutrophication would be
 continous) I'm not quite sure 'supervised' is
 the correct description but it furthers my point that you
 need a dependent variable for any neuralnet algorithm I am
 aware of.  As such, if you don't have a dependent
 variable then you will need to look at unsupervised methods
 such as PCA.  Other users may have other
 suggestions.
 Regards,Charles
 On Wed, Jan 21, 2015 at

 wrote:
 Dear
 Charles;

 Many thanks for your attention. what I want to know is: How
 can I predict the Eutrophication by these parameters in the
 future?

 These variables are the most important variables that
 control the Eutro. in lakes.

 Let me break it to two parts.

 1) How can I predict these variables by NN?

 2) Is it possible to predict the Eutro. by these
 variables?





 Many thanks for your help.

  Regards,















 

 On Wed, 1/21/15, Charles Determan Jr 
 wrote:



  Subject: Re: [R] Neural Network



  Cc: "r-help@r-project.org"
 

  Date: Wednesday, January 21, 2015, 9:10 PM



  Javad,

  You

  question is a little too broad to be answered

  definitively.  Also, this is not a code writing
 service. 

  You should make a meaningful attempt and we are here to
 help

  when you get stuck.

  1.

  If you want to know if you can do neural nets, the answer
 is

  yes.  The three packages most commonly used (that I
 know

  of) are 'neuralnet', 'nnet' and

  'RSNNS'.  You should look in to these package

  documentation for how to use them.  There are also
 many

  examples online if you simply google them.

  2. You question is unclear, are you

  wanting to predict all the variables (e.g. phosphorus,
 Total

  N, etc.) or do you have some metric for
 eutrophication? 

  What exactly is the model supposed to predict?

  3. If you want to know if a

  neuralnet is appropriate, that is more of a statistical

  question.  It depends more on the question you want to

  answer.  Given your temporal data, you may want to look
 in

  to mixed effects models (e.g nlme, lme4) as another

  potential approach.

  Regards,

  On Tue, Jan 20, 2015 at

  11:35 PM, javad bayat via R-help 

  wrote:

  Dear

  all;



  I am the new user of R. I want to simulation or
 prediction

  the Eutrophication of a lake. I have weekly data(almost
 for

  two years) for Total phosphorus, Total N, pH, Chlorophyll
 a,

  Alkalinity, Silica.



  Can I predict the Eutrophication by Neural Network in
 R?



  How can I simulation the Eutrophication by these

  parameter?



  please help me to write the codes.



  many thanks.







  __



  R-help@r-project.org

  mailing list -- To UNSUBSCRIBE and more, see



  https://stat.ethz.ch/mailman/listinfo/r-help



  PLEASE do read the posting guide http://www.R-project.org/posting-guide.html



  and provide commented, minimal, self-contained,
 reproducible

  code.









  --

  Dr. Charles Determan, PhD

  Integrated Biosciences








 -- 
 Dr. Charles Determan, PhD
 Integrated Biosciences

__
R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.


Re: [R] Neural Network

2015-01-22 Thread Charles Determan Jr
Javad,

First, please make sure to hit 'reply all' so that these messages go to the
R help list so others (many far more skilled than I) may possibly chime in.

The problem here is that you appear to have no dependent variable (i.e. no
eutrophication variable).  Without it, there is no way to a typical
'supervised' analysis.  Given that this is likely a regression type problem
(I assume eutrophication would be continous) I'm not quite sure
'supervised' is the correct description but it furthers my point that you
need a dependent variable for any neuralnet algorithm I am aware of.  As
such, if you don't have a dependent variable then you will need to look at
unsupervised methods such as PCA.  Other users may have other suggestions.

Regards,
Charles

On Wed, Jan 21, 2015 at 11:36 PM, javad bayat  wrote:

> Dear Charles;
> Many thanks for your attention. what I want to know is: How can I predict
> the Eutrophication by these parameters in the future?
> These variables are the most important variables that control the Eutro.
> in lakes.
> Let me break it to two parts.
> 1) How can I predict these variables by NN?
> 2) Is it possible to predict the Eutro. by these variables?
>
>
> Many thanks for your help.
>  Regards,
>
>
>
>
>
>
>
> ------------
> On Wed, 1/21/15, Charles Determan Jr  wrote:
>
>  Subject: Re: [R] Neural Network
>  To: "javad bayat" 
>  Cc: "r-help@r-project.org" 
>  Date: Wednesday, January 21, 2015, 9:10 PM
>
>  Javad,
>  You
>  question is a little too broad to be answered
>  definitively.  Also, this is not a code writing service.
>  You should make a meaningful attempt and we are here to help
>  when you get stuck.
>  1.
>  If you want to know if you can do neural nets, the answer is
>  yes.  The three packages most commonly used (that I know
>  of) are 'neuralnet', 'nnet' and
>  'RSNNS'.  You should look in to these package
>  documentation for how to use them.  There are also many
>  examples online if you simply google them.
>  2. You question is unclear, are you
>  wanting to predict all the variables (e.g. phosphorus, Total
>  N, etc.) or do you have some metric for eutrophication?
>  What exactly is the model supposed to predict?
>  3. If you want to know if a
>  neuralnet is appropriate, that is more of a statistical
>  question.  It depends more on the question you want to
>  answer.  Given your temporal data, you may want to look in
>  to mixed effects models (e.g nlme, lme4) as another
>  potential approach.
>  Regards,
>  On Tue, Jan 20, 2015 at
>  11:35 PM, javad bayat via R-help 
>  wrote:
>  Dear
>  all;
>
>  I am the new user of R. I want to simulation or prediction
>  the Eutrophication of a lake. I have weekly data(almost for
>  two years) for Total phosphorus, Total N, pH, Chlorophyll a,
>  Alkalinity, Silica.
>
>  Can I predict the Eutrophication by Neural Network in R?
>
>  How can I simulation the Eutrophication by these
>  parameter?
>
>  please help me to write the codes.
>
>  many thanks.
>
>
>
>  __
>
>  R-help@r-project.org
>  mailing list -- To UNSUBSCRIBE and more, see
>
>  https://stat.ethz.ch/mailman/listinfo/r-help
>
>  PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html
>
>  and provide commented, minimal, self-contained, reproducible
>  code.
>
>
>
>
>  --
>  Dr. Charles Determan, PhD
>  Integrated Biosciences
>
>
>


-- 
Dr. Charles Determan, PhD
Integrated Biosciences

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and provide commented, minimal, self-contained, reproducible code.


Re: [R] Neural Network

2015-01-21 Thread Charles Determan Jr
Javad,

You question is a little too broad to be answered definitively.  Also, this
is not a code writing service.  You should make a meaningful attempt and we
are here to help when you get stuck.

1. If you want to know if you can do neural nets, the answer is yes.  The
three packages most commonly used (that I know of) are 'neuralnet', 'nnet'
and 'RSNNS'.  You should look in to these package documentation for how to
use them.  There are also many examples online if you simply google them.

2. You question is unclear, are you wanting to predict all the variables
(e.g. phosphorus, Total N, etc.) or do you have some metric for
eutrophication?  What exactly is the model supposed to predict?

3. If you want to know if a neuralnet is appropriate, that is more of a
statistical question.  It depends more on the question you want to answer.
Given your temporal data, you may want to look in to mixed effects models
(e.g nlme, lme4) as another potential approach.

Regards,

On Tue, Jan 20, 2015 at 11:35 PM, javad bayat via R-help <
r-help@r-project.org> wrote:

> Dear all;
> I am the new user of R. I want to simulation or prediction the
> Eutrophication of a lake. I have weekly data(almost for two years) for
> Total phosphorus, Total N, pH, Chlorophyll a, Alkalinity, Silica.
> Can I predict the Eutrophication by Neural Network in R?
> How can I simulation the Eutrophication by these parameter?
> please help me to write the codes.
> many thanks.
>
> __
> R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>



-- 
Dr. Charles Determan, PhD
Integrated Biosciences

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[R] Neural Network

2015-01-20 Thread javad bayat via R-help
Dear all;
I am the new user of R. I want to simulation or prediction the Eutrophication 
of a lake. I have weekly data(almost for two years) for Total phosphorus, Total 
N, pH, Chlorophyll a, Alkalinity, Silica.
Can I predict the Eutrophication by Neural Network in R?
How can I simulation the Eutrophication by these parameter? 
please help me to write the codes.
many thanks.

__
R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.


[R] neural network in R

2014-05-16 Thread azam jaafari
 Hello everybody
 
I try to fit a neural network on my data by using package 'neuralnet' or 
'nnet'. 
I did it several times but I got an unexpected answer, 
 
this is my code (num.obs=100): 
(
library('nnet')

y<-data.frame(data$CU) (y is cu concentration)
x<-data.frame(data$mrvbf,data$plcurvature,data$insol)
mod1<-nnet(x,y,size=3,linout=T)
 
)
when I write: mod1$fitted.values, it is same for all of 100 y.
e.g.
1  832.77
2  832.77
3  832.77
.
.
.
100 832.77
 
I don't know where is the problem?
Please help
 
Thanks alot
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and provide commented, minimal, self-contained, reproducible code.


[R] Neural Network Problem

2013-07-25 Thread nntx
Hello Professionals, 

I am new to R and am planning to use R for a Artificial Neural Network
regression. I have 10 different scenarios for each observation (Input). For
each scenario, there are 7 variables, which means 7 output.  I have 1000
observations in total and I do have 1000 expected output.I want to use 800
observations for training and the rest for testing. Could any one provide a
sample for my case? I don't quite understand the instructions from the
packages. Appreciated. 



--
View this message in context: 
http://r.789695.n4.nabble.com/Neural-Network-Problem-tp4672275.html
Sent from the R help mailing list archive at Nabble.com.

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PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.


[R] Neural network: Amore adaptative vs batch why the results are so different?

2013-05-20 Thread xiaoyan yu
I am using the iris example came with nnet package to test AMORE. I can see
the outcomes are similar to nnet with adaptative gradient descent. However,
when I changed the method in the newff to the batch gradient descent, even
by setting the epoch numbers very large, I still found all the iris
expected class=2 being classified as class=3. In addition, all those
records in the outcomes (y) are the three digits, 0, 0.4677313, and
0.5111955. The script is as below. Please help to understand this behavior.


library('AMORE')
ir <- rbind(iris3[,,1], iris3[,,2], iris3[,,3])
targets <- matrix(c(rep(c(1,0,0),50), rep(c(0,1,0),50), rep(c(0,0,1),50)),
150, 3, byrow=TRUE)
samp <- c(sample(1:50,25), sample(51:100,25), sample(101:150,25))
net <- newff(n.neurons=c(4, 2, 3), # number of units per layer
 learning.rate.global=1e-2,# learning rate at which
every neuron is trained
 momentum.global=5e-4,  # momentum for every
neuron
 error.criterium="LMS",# error criterium: least
mean squares
 hidden.layer="sigmoid",# activation function
of the hidden layer neurons
 output.layer="sigmoid",   # activation function of
the output layer neurons
 method="BATCHgdwm")   # training method:
adaptative or batch
nnfit <- train(net,   # network to train
ir[samp,],  # input training samples
targets[samp,],   # output training samples
error.criterium="LMS", # error criterium
report=TRUE,   # provide information
during training
n.show=10,  # number of times to
report
show.step=4)
y<-sim(nnfit$net,ir[samp,])

Thanks,
Xiaoyan

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Re: [R] Neural Network

2010-07-19 Thread Rainer Stuetz
2010/7/18 Arnaud Trébaol :
> Hi all,
>
> I am working for my master's thesis and I need to do a neural network to
> forecast stock market price, with also external inputs like technical
> indicators.
> I would like to know which function and package of R are more suitable for
> this study.
>
> Thanks a lot for your response,
> Arnaud TREBAOL.

See also the following article in the current issue of the R Journal:

neuralnet: Training of neural networks
http://journal.r-project.org/archive/2010-1/RJournal_2010-1_Guenther+Fritsch.pdf


-Rainer

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Re: [R] Neural Network

2010-07-18 Thread Corey Sparks

I'd start with the nnet library
type:
?nnet

CS

-
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Department of Demography and Organization Studies
University of Texas at San Antonio
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[R] Neural Network

2010-07-18 Thread Arnaud Trébaol
Hi all,


I am working for my master's thesis and I need to do a neural network to
forecast stock market price, with also external inputs like technical
indicators.
I would like to know which function and package of R are more suitable for
this study.


Thanks a lot for your response,


Arnaud TREBAOL.

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T.I.M.E. Student
Ecole Centrale de Lille (09)
Politecnico di Milano (10)

Mail : arnaud.treb...@centraliens-lille.org
Tel1 : +33 (0)6 76 46 42 92
Tel2 : +39 327 280 57 68

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[R] Neural Network package AMORE and a weight decay

2010-07-13 Thread Ron Shefi

Hi, 

I want to use the neural network package AMORE and I don't find in the 
documentation the weight decay option.
Could someone tell if it is possible to add a regularization parameter (also 
known as a weight decay) to the training method. 
Is it possible to alter the gradient descent rule for that?

Thanks,
   Ron
  
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[R] Neural Network

2010-03-05 Thread Francis_Statistics

Hi,


We are trying to implement a early stopping rule with validation set on a
neural network. We’re using the AMORE package
(http://rwiki.sciviews.org/doku.php?id=packages:cran:amore) of R and when
you train the network you have to specify following variables:
Pval
Tval

What do we have to put here, or how do we have to specify this values? We
are using simulated data from a sinc function. 

This is the code that we are using. 

#define a sinc function 
sinc <- function(x) sin(pi*x)/(pi*x)
size_data = 200

# Generate data from sin function
ticks = linspace(-1,1,size_data)
sin_data = sinc(ticks)

# Generate noise
std_dev = 0.5
noise_data <- runif(size_data, 0, std_dev)

# Impose noise on sin data
dat = sin_data + noise_data

#Normalise data
max_dat = max(dat)
norm_dat = dat/max(dat)

#Define a neural network
net.start <- newff(n.neurons=c(1,20, 1),  
 learning.rate.global=1e-3,
 momentum.global=0.5,
 error.criterium="LMS",   
 Stao=NA, hidden.layer="tansig",   
 output.layer="purelin", 
 method="ADAPTgd")

#Train the network
result <- train(net.start, ticks, norm_dat, Pval= NULL, Tval=NULL,
error.criterium="LMS", report=FALSE, show.step=8000, n.shows=0)


Are there any tips you can give for a better neural network or a better
training of this net? 

Thanks a lot,

A desperate team in search of help. 

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[R] neural network arguments

2009-10-07 Thread CJ Rubio

hi everyone!

my inquiry with neural network is rather basic. i am just learning neural
network, particularly the VR bundle. i read the documentations for the said
bundle but still is struggling on understanding some arguments

- x is the matrix or data frame of x values for example
   does this mean data frame for training?

- y is the matrix or data frame of target values for example
   does this mean data frame for testing?

- would fitting the single-hidden-layer NN train and test my data? what does
"fitting" really do?


i know these are very basic questions but i just started exploring NN
packages.
thanks in advance for your help!
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Re: [R] Neural Network resource

2009-06-02 Thread Indrajit Sengupta
Thanks to all those who have replied to my query. I have decided do a thorough 
reading on this subject and try to seek out a proper solution. I will stick to 
the nnet package as mentioned by Jude and try and compare results with other 
neural network software if possible.

Regards,
Indrajit
 





From: "jude.r...@ubs.com" 

Sent: Thursday, May 28, 2009 10:49:36 PM
Subject: Re: [R] Neural Network resource


The package AMORE appears to be more flexible, but I got very poor results 
using it when I tried to improve the predictive accuracy of a regression model. 
I don't understand all the options well enough to be able to fine tune it to 
get better predictions. However, using the nnet() function in package VR gave 
me decent results and is pretty easy to use (see the Venables and Ripley book, 
Modern Applied Statistics with S, pages 243 to 249, for more details). I tried 
using package neuralnet as well but the neural net failed to converge. I could 
not figure out how to set the threshold option (or other options) to get the 
neural net to converge. I explored package neural as well. Of all these 4 
packages, the nnet() function in package VR worked the best for me.
 
As another R user commented as well, you have too many hidden layers and too 
many neurons. In general you do not need more than 1 hidden layer. One hidden 
layer is sufficient for the "universal approximator" property of neural 
networks to hold true. As you keep adding neurons to the one hidden layer, the 
problem becomes more and more non-linear. If you add too many neurons you will 
overfit. In general, you do not need to add more than 10 neurons. The 
activation function in the hidden layer of Venables and Ripley's nnet() 
function is logistic, and you can specify the activation function in the output 
layer to be linear using linout = T in nnet(). Using one hidden layer, and 
starting with one hidden neuron and working up to 10 hidden neurons, I built 
several neural nets (4,000 records) and computed the training MSE. I also 
computed the validation MSE on a holdout sample of over 1,000 records. I also 
started with 2 variables and worked up to 15 variables in
 a "for" loop, so in all, I built 140 neural nets using 2 "for" loops, and 
stored the results in lists. I arranged my variables in the data frame based on 
correlations and partial correlations so that I could easily add variables in a 
"for" loop. This was my "crude" attempt to simulate variable selection since, 
from what I have seen, neural networks do not have variable selection methods. 
In my particular case, neural networks gave me marginally better results than 
regression. It all depends on the problem. If the data has non-linear patterns, 
neural networks will be better than linear regression.
 
My code is below. You can modify it to suit your needs if you find it useful. 
There are probably lines in the code that are redundant which can be deleted.
 
HTH.
 
Jude Ryan
 
My code:
 
# set order in data frame train2 based on correlations and partial correlations
train2 <- train[, c(5,27,19,20,25,26,4,9,3,10,16,6,2,14,21,28)]
dim(train2)
names(train2)
library(nnet)
# skip = T
# train 10 neural networks in a loop and find the one with the minimum test and 
validation error
# create various lists to store the results of the neural network running in 
two for loops
# The Column List is for the outer for loop, which loops over variables
# The Row List is for the inner for loop, which loops over number of neurons in 
the hidden layer
col_nn <- list()  # stores the results of nnet() over variables - outer loop
row_nn <- list()  # stores the results of nnet() over neurons - inner loop
col_mse <- list()
# row_mse <- list() # not needed because nn.mse is a data frame with rows
col_sum <- list()
row_sum <- list()
col_vars <- list()
row_vars <- list()
col_wts <- list()
row_wts <- list()
df_dim <- dim(train2)
df_dim[2]  # number of variables
df_dim[2] - 1
num_of_neurons <- 10
# build data frame to store results of neural net for each run
nn.mse <- data.frame(Train_MSE=seq(1:num_of_neurons), 
Valid_MSE=seq(1:num_of_neurons))
# open log file and redirect output to log file
sink("D:\\XXX\\YYY\\ Programs\\Neural_Network_v8_VR_log.txt")
# outer loop - loop over variables
for (i in 3:df_dim[2]) {  # df_dim[2]
  # inner loop - loop over number of hidden neurons
  for (j in 1:num_of_neurons) { # upto 10 neurons in the hidden layer
    # need to create a new data frame with just the predictor/input variables 
needed
    train3 <- train2[,c(1:i)]
    coreaff.nn <- nnet(dep_var ~ ., train3, size = j, decay = 1e-3, linout = T, 
skip = T, maxit = 1000, Hess = T)
    # row_vars[[j]] <- coreaff.nn$call # not what we want
    # row_vars[[j]] <- names(train3)[c(2:i)] # not needed in inner loop - same 
number of variables f

Re: [R] Neural Network resource

2009-05-28 Thread jude.ryan
The package AMORE appears to be more flexible, but I got very poor
results using it when I tried to improve the predictive accuracy of a
regression model. I don't understand all the options well enough to be
able to fine tune it to get better predictions. However, using the
nnet() function in package VR gave me decent results and is pretty easy
to use (see the Venables and Ripley book, Modern Applied Statistics with
S, pages 243 to 249, for more details). I tried using package neuralnet
as well but the neural net failed to converge. I could not figure out
how to set the threshold option (or other options) to get the neural net
to converge. I explored package neural as well. Of all these 4 packages,
the nnet() function in package VR worked the best for me.

 

As another R user commented as well, you have too many hidden layers and
too many neurons. In general you do not need more than 1 hidden layer.
One hidden layer is sufficient for the "universal approximator" property
of neural networks to hold true. As you keep adding neurons to the one
hidden layer, the problem becomes more and more non-linear. If you add
too many neurons you will overfit. In general, you do not need to add
more than 10 neurons. The activation function in the hidden layer of
Venables and Ripley's nnet() function is logistic, and you can specify
the activation function in the output layer to be linear using linout =
T in nnet(). Using one hidden layer, and starting with one hidden neuron
and working up to 10 hidden neurons, I built several neural nets (4,000
records) and computed the training MSE. I also computed the validation
MSE on a holdout sample of over 1,000 records. I also started with 2
variables and worked up to 15 variables in a "for" loop, so in all, I
built 140 neural nets using 2 "for" loops, and stored the results in
lists. I arranged my variables in the data frame based on correlations
and partial correlations so that I could easily add variables in a "for"
loop. This was my "crude" attempt to simulate variable selection since,
from what I have seen, neural networks do not have variable selection
methods. In my particular case, neural networks gave me marginally
better results than regression. It all depends on the problem. If the
data has non-linear patterns, neural networks will be better than linear
regression.

 

My code is below. You can modify it to suit your needs if you find it
useful. There are probably lines in the code that are redundant which
can be deleted.

 

HTH.

 

Jude Ryan

 

My code:

 

# set order in data frame train2 based on correlations and partial
correlations

train2 <- train[, c(5,27,19,20,25,26,4,9,3,10,16,6,2,14,21,28)]

dim(train2)

names(train2)

library(nnet)

# skip = T

# train 10 neural networks in a loop and find the one with the minimum
test and validation error

# create various lists to store the results of the neural network
running in two for loops

# The Column List is for the outer for loop, which loops over variables

# The Row List is for the inner for loop, which loops over number of
neurons in the hidden layer

col_nn <- list()  # stores the results of nnet() over variables - outer
loop

row_nn <- list()  # stores the results of nnet() over neurons - inner
loop

col_mse <- list()

# row_mse <- list() # not needed because nn.mse is a data frame with
rows

col_sum <- list()

row_sum <- list()

col_vars <- list()

row_vars <- list()

col_wts <- list()

row_wts <- list()

df_dim <- dim(train2)

df_dim[2]  # number of variables

df_dim[2] - 1

num_of_neurons <- 10

# build data frame to store results of neural net for each run

nn.mse <- data.frame(Train_MSE=seq(1:num_of_neurons),
Valid_MSE=seq(1:num_of_neurons))

# open log file and redirect output to log file

sink("D:\\XXX\\YYY\\ Programs\\Neural_Network_v8_VR_log.txt")

# outer loop - loop over variables

for (i in 3:df_dim[2]) {  # df_dim[2]

  # inner loop - loop over number of hidden neurons

  for (j in 1:num_of_neurons) { # upto 10 neurons in the hidden layer

# need to create a new data frame with just the predictor/input
variables needed

train3 <- train2[,c(1:i)]

coreaff.nn <- nnet(dep_var ~ ., train3, size = j, decay = 1e-3,
linout = T, skip = T, maxit = 1000, Hess = T)

# row_vars[[j]] <- coreaff.nn$call # not what we want

# row_vars[[j]] <- names(train3)[c(2:i)] # not needed in inner loop
- same number of variables for all neurons

row_sum[[j]] <- summary(coreaff.nn)

row_wts[[j]] <- coreaff.nn$wts

rownames(nn.mse)[j] <- paste("H", j, sep="")

nn.mse[j, "Train_MSE"] <- mean((train3$dep_var -
predict(coreaff.nn))^2)

nn.mse[j, "Valid_MSE"] <- mean((valid$dep_var - predict(coreaff.nn,
valid))^2)

  }

  col_vars[[i-2]] <- names(train3)[c(2:i)]

  col_sum[[i-2]] <- row_sum

  col_wts[[i-2]] <- row_wts

  col_mse[[i-2]] <- nn.mse

}

# cbind(col_vars[1],col_vars[2])

col_vars

col_sum

col_wts

sink()

cbind(col_mse[[1]],col_mse[[2]],col_mse[[3]],col_mse[[4]],col_mse[[5]

Re: [R] Neural Network resource

2009-05-27 Thread Tony Breyal
I haven't used the AMORE package before, but it sounds like you
haven't set linear output units or something. Here's an example using
the nnet package of what you're doing i think:

### R START###
> # set random seed to a cool number
> set.seed(42)
>
> # set up data
> x1<-rnorm(100); x2<-rnorm(100); x3<-rnorm(100)
> x4<-rnorm(100); x5<-rnorm(100); x6<-rnorm(100)
> b1<-1; b2<-2; b3<-3
> b4<-4; b5<-5; b6<-6
> y<-b1*x1 + b2*x2 + b3*x3 + b4*x4 + b5*x5 + b6*x6
> my.df <- data.frame(cbind(y, x1, x2, x3, x4, x5, x6))
>
> # 1. linear regression
> my.lm <- lm(y~., data=my.df)
>
> # look at correlation
> my.lm.predictions<-predict(my.lm)
> cor(my.df["y"], my.lm.predictions)
  [,1]
y1
>
> # 2. nnet
> library(nnet)
> my.nnet<-nnet(y~., data=my.df, size=3,
 linout=TRUE, skip=TRUE,
 trace=FALSE, maxit=1000)
>
> my.nnet.predictions<-predict(my.nnet, my.df)
> # look at correlation
> cor(my.df["y"], my.nnet.predictions)
  [,1]
y1
>
> # to look at the values side by side
> cbind(my.df["y"], my.nnet.predictions)
   y my.nnet.predictions
110.60102566 10.59958907
2 6.70939465  6.70956529
3 2.28934732  2.28928930
414.51012458 14.51043732
5   -12.85845371-12.85849345
[..etc]
### R END ###

Hope that helps a wee bit mate,

Tony Breyal


On 27 May, 15:36, Indrajit Sengupta  wrote:
> You are right there is a pdf file which describes the function. But let tell 
> you where I am coming from.
>
> Just to test if a neural network will work better than a ordinary least 
> square regression, I created a dataset with one dependent variable and 6 
> other independent variables. Now I had deliberately created the dataset in 
> such manner that we have an excellent regression model. Eg: Y = b0 + b1*x1 + 
> b2*x2 + b3*x3.. + b6*x6 + e
> where e is normal random variable. Naturally any statistical analysis system 
> running regression would easily predict the values of b1, b2, b3, ..., b6 
> with around 30-40 observations.
>
> I fed this data into a Neural network (3 hidden layers with 6 neurons in each 
> layer) and trained the network. When I passed the input dataset and tried to 
> get the predictions, all the predicted values were identical! This confused 
> me a bit and was wondering whether my understanding of the Neural Network was 
> wrong.
>
> Have you ever faced anything like it?
>
> Regards,
> Indrajit
>
> 
> From: "markle...@verizon.net" 
>
> Sent: Wednesday, May 27, 2009 7:54:59 PM
> Subject: Re: [R] Neural Network resource
>
> Hi: I've never used that package but most likely there is a  AMORE vignette 
> that shows examples and describes the functions.
> it should be on the same cran  web page where the package resides, in pdf 
> form.
>
> Hi All,
>
> I am trying to learn Neural Networks. I found that R has packages which can 
> help build Neural Nets - the popular one being AMORE package. Is there any 
> book / resource available which guides us in this subject using the AMORE 
> package?
>
> Any help will be much appreciated.
>
> Thanks,
> Indrajit
>
> __
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> PLEASE do read the posting guidehttp://www.R-project.org/posting-guide.html
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>
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Re: [R] Neural Network resource

2009-05-27 Thread Indrajit Sengupta

Here is the code that i had used:

#


## Read in the raw data
fitness <- c(44,89.47,44.609,11.37,62,178,182,
40,75.07,45.313,10.07,62,185,185,
44,85.84,54.297,8.65,45,156,168,
42,68.15,59.571,8.17,40,166,172,
38,89.02,49.874,9.22,55,178,180,
47,77.45,44.811,11.63,58,176,176,
40,75.98,45.681,11.95,70,176,180,
43,81.19,49.091,10.85,64,162,170,
44,81.42,39.442,13.08,63,174,176,
38,81.87,60.055,8.63,48,170,186,
44,73.03,50.541,10.13,45,168,168,
45,87.66,37.388,14.03,56,186,192,
45,66.45,44.754,11.12,51,176,176,
47,79.15,47.273,10.6,47,162,164,
54,83.12,51.855,10.33,50,166,170,
49,81.42,49.156,8.95,44,180,185,
51,69.63,40.836,10.95,57,168,172,
51,77.91,46.672,10,48,162,168,
48,91.63,46.774,10.25,48,162,164,
49,73.37,50.388,10.08,67,168,168,
57,73.37,39.407,12.63,58,174,176,
54,79.38,46.08,11.17,62,156,165,
52,76.32,45.441,9.63,48,164,166,
50,70.87,54.625,8.92,48,146,155,
51,67.25,45.118,11.08,48,172,172,
54,91.63,39.203,12.88,44,168,172,
51,73.71,45.79,10.47,59,186,188,
57,59.08,50.545,9.93,49,148,155,
49,76.32,48.673,9.4,56,186,188,
48,61.24,47.92,11.5,52,170,176,
52,82.78,47.467,10.5,53,170,172
)
fitness2 <- data.frame(matrix(fitness,nrow = 31, byrow = TRUE))
colnames(fitness2) <- 
c("Age","Weight","Oxygen","RunTime","RestPulse","RunPulse","MaxPulse")
attach(fitness2)
## Create the input dataset
indep <- fitness2[,-3]
## Create the neural network structure 
net.start <- newff(n.neurons=c(6,6,6,1),  
 learning.rate.global=1e-2,    
 momentum.global=0.5,  
 error.criterium="LMS",   
 Stao=NA, hidden.layer="tansig",   
 output.layer="purelin",   
 method="ADAPTgdwm")
## Train the net
result <- train(net.start, indep, Oxygen, error.criterium="LMS", report=TRUE, 
show.step=100, n.shows=5 ) 
## Predict
pred <- sim(result$net, indep)
pred 
### 

Here I am trying to predict Oxygen levels using the 6 independent 
variables. But whenever I am trying to run a prediction - I am getting constant 
values throughout (In the above example - the values of pred).

Thanks & Regards,
Indrajit

 


- Original Message 
From: Max Kuhn 
To: Indrajit Sengupta 
Cc: markle...@verizon.net; R Help 
Sent: Wednesday, May 27, 2009 9:19:47 PM
Subject: Re: [R] Neural Network resource

> I fed this data into a Neural network (3 hidden layers with 6 neurons in each 
> layer) and trained the network. When I passed the input dataset and tried to 
> get the predictions, all the predicted values were identical! This confused 
> me a bit and was wondering whether my understanding of the Neural Network was 
> wrong.
>
> Have you ever faced anything like it?

You should really provide code for us to help. I would initially
suspect that you didn't use a linear function between your hidden
units and the outcomes.

Also, using 3 hidden layers and 6 units per layer is a bit much for
your data set (30-40 samples). You will probably end up overfitting.

-- 

Max





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Re: [R] Neural Network resource

2009-05-27 Thread Max Kuhn
> I fed this data into a Neural network (3 hidden layers with 6 neurons in each 
> layer) and trained the network. When I passed the input dataset and tried to 
> get the predictions, all the predicted values were identical! This confused 
> me a bit and was wondering whether my understanding of the Neural Network was 
> wrong.
>
> Have you ever faced anything like it?

You should really provide code for us to help. I would initially
suspect that you didn't use a linear function between your hidden
units and the outcomes.

Also, using 3 hidden layers and 6 units per layer is a bit much for
your data set (30-40 samples). You will probably end up overfitting.

-- 

Max

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Re: [R] Neural Network resource

2009-05-27 Thread Indrajit Sengupta
You are right there is a pdf file which describes the function. But let tell 
you where I am coming from.

Just to test if a neural network will work better than a ordinary least square 
regression, I created a dataset with one dependent variable and 6 other 
independent variables. Now I had deliberately created the dataset in such 
manner that we have an excellent regression model. Eg: Y = b0 + b1*x1 + b2*x2 + 
b3*x3.. + b6*x6 + e
where e is normal random variable. Naturally any statistical analysis system 
running regression would easily predict the values of b1, b2, b3, ..., b6 with 
around 30-40 observations.

I fed this data into a Neural network (3 hidden layers with 6 neurons in each 
layer) and trained the network. When I passed the input dataset and tried to 
get the predictions, all the predicted values were identical! This confused me 
a bit and was wondering whether my understanding of the Neural Network was 
wrong.

Have you ever faced anything like it?

Regards,
Indrajit




From: "markle...@verizon.net" 

Sent: Wednesday, May 27, 2009 7:54:59 PM
Subject: Re: [R] Neural Network resource

Hi: I've never used that package but most likely there is a  AMORE vignette 
that shows examples and describes the functions.
it should be on the same cran  web page where the package resides, in pdf form.






Hi All,

I am trying to learn Neural Networks. I found that R has packages which can 
help build Neural Nets - the popular one being AMORE package. Is there any book 
/ resource available which guides us in this subject using the AMORE package?

Any help will be much appreciated.

Thanks,
Indrajit

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Re: [R] Neural Network resource

2009-05-27 Thread Tony Breyal
There's a link on the CRAN page for the AMORE package which apears to
have some cool information:

http://wiki.r-project.org/rwiki/doku.php?id=packages:cran:amore

Seems like an interesting package, I hadn't actually heard of it
before your post.

HTH,
Tony

On 27 May, 09:13, Indrajit Sengupta  wrote:
> Hi All,
>
> I am trying to learn Neural Networks. I found that R has packages which can 
> help build Neural Nets - the popular one being AMORE package. Is there any 
> book / resource available which guides us in this subject using the AMORE 
> package?
>
> Any help will be much appreciated.
>
> Thanks,
> Indrajit
>
> __
> r-h...@r-project.org mailing listhttps://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guidehttp://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.

__
R-help@r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.


[R] Neural Network resource

2009-05-27 Thread Indrajit Sengupta

Hi All,

I am trying to learn Neural Networks. I found that R has packages which can 
help build Neural Nets - the popular one being AMORE package. Is there any book 
/ resource available which guides us in this subject using the AMORE package?

Any help will be much appreciated.

Thanks,
Indrajit

__
R-help@r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.


[R] neural network not using all observations

2009-05-12 Thread jude.ryan
I am exploring neural networks (adding non-linearities) to see if I can
get more predictive power than a linear regression model I built. I am
using the function nnet and following the example of Venables and
Ripley, in Modern Applied Statistics with S, on pages 246 to 249. I have
standardized variables (z-scores) such as assets, age and tenure. I have
other variables that are binary (0 or 1). In max_acc_ownr_nwrth_n_med
for example, the variable has a value of 1 if the client's net worth is
above the median net worth and a value of 0 otherwise. These are derived
variable I created and variables that the regression algorithm has found
to be predictive. A regression on the same variables shown below gives
me an R-Square of about 0.12. I am trying to increase the predictive
power of this regression model with a neural network being careful to
avoid overfitting.

Similar to Venables and Ripley, I used the following code:

 

> library(nnet)

> dim(coreaff.trn.nn)

[1] 50888

> head(coreaff.trn.nn)

  hh.iast.y WC_Total_Assets all_assets_per_hh age  tenure
max_acc_ownr_liq_asts_n_med max_acc_ownr_nwrth_n_med
max_acc_ownr_ann_incm_n_med

1   3059448  -0.4692186-0.4173532 -0.06599001 -1.04747935
01   0

2   4899746   3.4854334 4.064 -0.06599001 -0.72540200
11   1

3727333  -0.2677357-0.4177944 -0.30136473 -0.40332465
11   1

4443138  -0.5295170-0.6999646 -0.1825 -1.04747935
00   0

5484253  -0.6112205-0.7306664  0.64013414  0.07979137
10   0

6799054   0.6580506 1.1763114  0.24784295  0.07979137
01   1

> coreaff.nn1 <- nnet(hh.iast.y ~ WC_Total_Assets + all_assets_per_hh +
age + tenure + max_acc_ownr_liq_asts_n_med +

+ max_acc_ownr_nwrth_n_med +
max_acc_ownr_ann_incm_n_med, coreaff.trn.nn, size = 2, decay = 1e-3,

+ linout = T, skip = T, maxit = 1000, Hess = T)

# weights:  26

initial  value 12893652845419998.00 

iter  10 value 6352515847944854.00

final  value 6287104424549762.00 

converged

> summary(coreaff.nn1)

a 7-2-1 network with 26 weights

options were - skip-layer connections  linear output units  decay=0.001

 b->h1 i1->h1 i2->h1 i3->h1 i4->h1 i5->h1
i6->h1 i7->h1 

 -21604.84   -2675.80   -5001.90   -1240.16-335.44  -12462.51
-13293.80   -9032.34 

 b->h2 i1->h2 i2->h2 i3->h2 i4->h2 i5->h2
i6->h2 i7->h2 

 210841.52   47296.92   58100.43  -13819.10   -9195.80  117088.99
131939.57  106994.47 

  b->o  h1->o  h2->o  i1->o  i2->o  i3->o
i4->o  i5->o  i6->o  i7->o 

1115190.67  894123.33 -417269.57   89621.84  170268.12   44833.63
59585.05  112405.30  437581.05  244201.69

> sum((hh.iast.y - predict(coreaff.nn1))^2)  

Error: object "hh.iast.y" not found

 

So I try:

 

> sum((coreaff.trn.nn$hh.iast.y - predict(coreaff.nn1))^2)

Error: dims [product 5053] do not match the length of object [5088]

In addition: Warning message:

In coreaff.trn.nn$hh.iast.y - predict(coreaff.nn1) :

  longer object length is not a multiple of shorter object length

 

Doing a little debugging:

 

> pred <- predict(coreaff.nn1)

> dim(pred)

[1] 50531

> dim(coreaff.trn.nn)

[1] 50888

 

So it looks like the dimensions (number of records/cases) of the vector
pred is 5,053 and the number of records of the input dataset is 5,088.

 

It looks like the neural network is dropping 35 records. Does anyone
have any idea of why it would do this? It is most probably because those
35 records are "bad" data, a pretty common occurrence in the real world.
Does anyone know how I can identify the dropped records? If I can do
this I can get the dimensions of the input dataset to be 5,053 and then:

 

> sum((coreaff.trn.nn$hh.iast.y - predict(coreaff.nn1))^2)

 

would work.

 

A summary of my dataset is:

 

> summary(coreaff.trn.nn)

   hh.iast.yWC_Total_Assets  all_assets_per_hh age
tenure   max_acc_ownr_liq_asts_n_med

 Min.   :   0   Min.   :-6.970e-01   Min.   :-8.918e-01   Min.
:-4.617e+00   Min.   :-1.209e+00   Min.   :0. 

 1st Qu.:  565520   1st Qu.:-5.387e-01   1st Qu.:-6.147e-01   1st
Qu.:-4.583e-01   1st Qu.:-7.254e-01   1st Qu.:0. 

 Median :  834164   Median :-3.160e-01   Median :-3.718e-01   Median :
9.093e-02   Median :-2.423e-01   Median :0. 

 Mean   : 1060244   Mean   : 2.948e-13   Mean   : 3.204e-12   Mean
:-1.884e-11   Mean   :-3.302e-12   Mean   :0.4951 

 3rd Qu.: 1207181   3rd Qu.: 1.127e-01   3rd Qu.: 1.891e-01   3rd Qu.:
5.617e-01   3rd Qu.: 5.629e-01   3rd Qu.:1.