495.txt

This complete matlab for neural network

发信人: GzLi (笑梨), 信区: DataMining
标  题: [转载] Re: 什么叫validation set(转寄)
发信站: 南京大学小百合站 (Tue Dec 24 23:13:58 2002)

【 以下文字转载自 GzLi 的信箱 】
【 原文由 <[e-mail]> 所发表 】

来  源: 211.68.16.32

发信人: IKM (IKM), 信区: AI       
标  题: Re: 什么叫validation set
发信站: BBS 水木清华站 (Tue Dec 24 13:06:24 2002)

来自ANN的FAQ

Subject: What are the population, sample, training set, design set, validation

 set, and test set?
It is rarely useful to have a NN simply memorize a set of data, since memoriza

tion can be done much more efficiently by numerous algorithms for table look-u

p. Typically, you want the NN to be able to perform accurately on new data, th

at is, to generalize. 
There seems to be no term in the NN literature for the set of all cases that y

ou want to be able to generalize to. Statisticians call this set the "populati

on". Tsypkin (1971) called it the "grand truth distribution," but this term ha

s never caught on. 

Neither is there a consistent term in the NN literature for the set of cases t

hat are available for training and evaluating an NN. Statisticians call this s

et the "sample". The sample is usually a subset of the population. 

(Neurobiologists mean something entirely different by "population," apparently

 some collection of neurons, but I have never found out the exact meaning.. I a

m going to continue to use "population" in the statistical sense until NN rese

archers reach a consensus on some other terms for "population" and "sample"; I

 suspect this will never happen.) 

In NN methodology, the sample is often subdivided into "training", "validation

", and "test" sets. The distinctions among these subsets are crucial, but the 

terms "validation" and "test" sets are often confused. Bishop (1995), an indis

pensable reference on neural networks, provides the following explanation (p. 

372): 

Since our goal is to find the network having the best performance on new data,

 the simplest approach to the comparison of different networks is to evaluate 

the error function using data which is independent of that used for training. 

Various networks are trained by minimization of an appropriate error function 

defined with respect to a training data set. The performance of the networks i

s then compared by evaluating the error function using an independent validati

on set, and the network having the smallest error with respect to the validati

on set is selected. This approach is called the hold out method. Since this pr

ocedure can itself lead to some overfitting to the validation set, the perform

ance of the selected network should be confirmed by measuring its performance 

on a third independent set of data called a test set. 
And there is no book in the NN literature more authoritative than Ripley (1996

), from which the following definitions are taken (p.354): 
Training set: 
A set of examples used for learning, that is to fit the parameters [i.e., weig

hts] of the classifier. 
Validation set: 
A set of examples used to tune the parameters [i.e., architecture, not weights

] of a classifier, for example to choose the number of hidden units in a neura

l network. 
Test set: 
A set of examples used only to assess the performance [generalization] of a fu

lly-specified classifier. 
The literature on machine learning often reverses the meaning of "validation" 

and "test" sets. This is the most blatant example of the terminological confus

ion that pervades artificial intelligence research. 
The crucial point is that a test set, by the standard definition in the NN lit

erature, is never used to choose among two or more networks, so that the error

 on the test set provides an unbiased estimate of the generalization error (as

suming that the test set is representative of the population, etc.). Any data 

set that is used to choose the best of two or more networks is, by definition,

 a validation set, and the error of the chosen network on the validation set i

s optimistically biased. 

There is a problem with the usual distinction between training and validation 

sets. Some training approaches, such as early stopping, require a validation s

et, so in a sense, the validation set is used for training. Other approaches, 

such as maximum likelihood, do not inherently require a validation set. So the

 "training" set for maximum likelihood might encompass both the "training" and

 "validation" sets for early stopping. Greg Heath has suggested the term "desi

gn" set be used for cases that are used solely to adjust the weights in a netw

ork, while "training" set be used to encompass both design and validation sets

.. There is considerable merit to this suggestion, but it has not yet been wide

ly adopted. 

But things can get more complicated. Suppose you want to train nets with 5 ,10

, and 20 hidden units using maximum likelihood, and you want to train nets wit

h 20 and 50 hidden units using early stopping. You also want to use a validati

on set to choose the best of these various networks. Should you use the same v

alidation set for early stopping that you use for the final network choice, or

 should you use two separate validation sets? That is, you could divide the sa

mple into 3 subsets, say A, B, C and proceed as follows: 

Do maximum likelihood using A. 
Do early stopping with A to adjust the weights and B to decide when to stop (t

his makes B a validation set). 
Choose among all 3 nets trained by maximum likelihood and the 2 nets trained b

y early stopping based on the error computed on B (the validation set). 
Estimate the generalization error of the chosen network using C (the test set)

.. 
Or you could divide the sample into 4 subsets, say A, B, C, and D and proceed 

as follows: 
Do maximum likelihood using A and B combined. 
Do early stopping with A to adjust the weights and B to decide when to stop (t

his makes B a validation set with respect to early stopping). 
Choose among all 3 nets trained by maximum likelihood and the 2 nets trained b

y early stopping based on the error computed on C (this makes C a second valid

ation set). 
Estimate the generalization error of the chosen network using D (the test set)

.. 
Or, with the same 4 subsets, you could take a third approach: 
Do maximum likelihood using A. 
Choose among the 3 nets trained by maximum likelihood based on the error compu

ted on B (the first validation set) 
Do early stopping with A to adjust the weights and B (the first validation set

) to decide when to stop. 
Choose among the best net trained by maximum likelihood and the 2 nets trained

 by early stopping based on the error computed on C (the second validation set

). 
Estimate the generalization error of the chosen network using D (the test set)

.. 
You could argue that the first approach is biased towards choosing a net train

ed by early stopping. Early stopping involves a choice among a potentially lar

ge number of networks, and therefore provides more opportunity for overfitting

 the validation set than does the choice among only 3 networks trained by maxi

mum likelihood. Hence if you make the final choice of networks using the same 

validation set (B) that was used for early stopping, you give an unfair advant

age to early stopping. If you are writing an article to compare various traini

ng methods, this bias could be a serious flaw. But if you are using NNs for so

me practical application, this bias might not matter at all, since you obtain 

an honest estimate of generalization error using C. 
You could also argue that the second and third approaches are too wasteful in 

their use of data. This objection could be important if your sample contains 1

00 cases, but will probably be of little concern if your sample contains 100,0

00,000 cases. For small samples, there are other methods that make more effici

ent use of data; see "What are cross-validation and bootstrapping?" 

References: 

Bishop, C.M. (1995), Neural Networks for Pattern Recognition, Oxford: Oxford U

niversity Press. 

Ripley, B.D. (1996) Pattern Recognition and Neural Networks, Cambridge: Cambri

dge University Press. 

Tsypkin, Y. (1971), Adaptation and Learning in Automatic Systems, NY: Academic

 Press. 

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【 在 xinjian 的大作中提到: 】
: 不是一回事
: 我看到有的系统需要三个数据集，训练集，校验集，测试集
: 我也分得不清楚
: 感觉训练集是训练学习过程的参数的
: 而校验集，我觉得是一个简单的测试，但它到底起挑选作用呢（从多个学习算法中挑..

:   还是起二次训练作用呢，我就不清楚了，也许由人自己定的吧
: 而测试集那就是最后的评判了
: 【 在 Karpov (卡尔波夫) 的大作中提到: 】
: : 是不是校验集，它和测试集是一回事吗？

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