m******t
发帖数: 273 | 1 【 以下文字转载自 Statistics 讨论区 】
发信人: myregmit (myregmit), 信区: Statistics
标 题: data prediction by regression or better ways
发信站: BBS 未名空间站 (Fri Mar 7 17:24:34 2014, 美东)
I am working on data prediction.
Given data of a random variable X and Y, find out how to predict Y by X.
I know how to do it by linear regression, y = k x + b .
But, here, x is always non-negative and y is required to be non-negative.
Sometimes, b is not non-negative so that y < 0.
How to assure that b > 0 and also minimize the prediction error ?
Are there other better ways (not regression) to do the prediction ?
Any help would be appreciated. |
f******y
发帖数: 2971 | 2 做个transform可以不？
比如说ln（y）= k ln(x) + b
【在 m******t 的大作中提到】
: 【 以下文字转载自 Statistics 讨论区 】
: 发信人: myregmit (myregmit), 信区: Statistics
: 标 题: data prediction by regression or better ways
: 发信站: BBS 未名空间站 (Fri Mar 7 17:24:34 2014, 美东)
: I am working on data prediction.
: Given data of a random variable X and Y, find out how to predict Y by X.
: I know how to do it by linear regression, y = k x + b .
: But, here, x is always non-negative and y is required to be non-negative.
: Sometimes, b is not non-negative so that y < 0.
: How to assure that b > 0 and also minimize the prediction error ?
|
m******t
发帖数: 273 | 3 【 以下文字转载自 Statistics 讨论区 】
发信人: myregmit (myregmit), 信区: Statistics
标 题: data prediction by regression or better ways
发信站: BBS 未名空间站 (Fri Mar 7 17:24:34 2014, 美东)
I am working on data prediction.
Given data of a random variable X and Y, find out how to predict Y by X.
I know how to do it by linear regression, y = k x + b .
But, here, x is always non-negative and y is required to be non-negative.
Sometimes, b is not non-negative so that y < 0.
How to assure that b > 0 and also minimize the prediction error ?
Are there other better ways (not regression) to do the prediction ?
Any help would be appreciated. |
f******y
发帖数: 2971 | 4 做个transform可以不？
比如说ln（y）= k ln(x) + b
【在 m******t 的大作中提到】
: 【 以下文字转载自 Statistics 讨论区 】
: 发信人: myregmit (myregmit), 信区: Statistics
: 标 题: data prediction by regression or better ways
: 发信站: BBS 未名空间站 (Fri Mar 7 17:24:34 2014, 美东)
: I am working on data prediction.
: Given data of a random variable X and Y, find out how to predict Y by X.
: I know how to do it by linear regression, y = k x + b .
: But, here, x is always non-negative and y is required to be non-negative.
: Sometimes, b is not non-negative so that y < 0.
: How to assure that b > 0 and also minimize the prediction error ?
|
m******t
发帖数: 273 | 5 what if x = 0 ? also, in some cases, y is also 0.
thanks!
【在 f******y 的大作中提到】
: 做个transform可以不？
: 比如说ln（y）= k ln(x) + b
|
m******t
发帖数: 273 | 6 x and y are discrete and between 0 and 100,000.
Any help would be appreciated.
【在 f******y 的大作中提到】
: 做个transform可以不？
: 比如说ln（y）= k ln(x) + b
|
m******t
发帖数: 273 | 7 This y and x scatter plot.
Any help would be appreciated.
【在 m******t 的大作中提到】
: x and y are discrete and between 0 and 100,000.
: Any help would be appreciated.
|
m******t
发帖数: 273 | 8 The data are not counts and not number of success either.
They are numerical values calculated by black box functions.
Any help would be appreciated.
【在 m******t 的大作中提到】
: This y and x scatter plot.
: Any help would be appreciated.
|
m******t
发帖数: 273 | 9 This is the log-norm scatter plot.
log with base as 10.
For the x =0 and y =0, we change it to be 1.
Any help would be appreciated.
【在 m******t 的大作中提到】
: The data are not counts and not number of success either.
: They are numerical values calculated by black box functions.
: Any help would be appreciated.
|
k***g
发帖数: 7244 | 10 如果有现成的 non-linear least-square 的library，let m = ln(k), 把你的formula
变成 y = exp(m)x+b 来做回归，estimate m 之后，用 k = exp(m)来得到 k, k 肯定
是大于零的；
如果没有现成的 nls library，直接用optimizer来 minimize sum of squared
residuals subject to b>0 就行了，也很简单。
【在 m******t 的大作中提到】
: This is the log-norm scatter plot.
: log with base as 10.
: For the x =0 and y =0, we change it to be 1.
: Any help would be appreciated.
|
m******t
发帖数: 273 | 11 for y = exp(m)x + b , what if k > 0 but b < 0 ?
In this way, y is still possible to be < 0.
Thanks
formula
【在 k***g 的大作中提到】
: 如果有现成的 non-linear least-square 的library，let m = ln(k), 把你的formula
: 变成 y = exp(m)x+b 来做回归，estimate m 之后，用 k = exp(m)来得到 k, k 肯定
: 是大于零的；
: 如果没有现成的 nls library，直接用optimizer来 minimize sum of squared
: residuals subject to b>0 就行了，也很简单。
|
k***g
发帖数: 7244 | 12 哦，我把你的k 和 b 看串了，一样的，你可以把 b 作同样的形变，这是一个
constrained linear regression 里常用的trick
【在 m******t 的大作中提到】
: for y = exp(m)x + b , what if k > 0 but b < 0 ?
: In this way, y is still possible to be < 0.
: Thanks
:
: formula
|
