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0

$begingroup$

Suppose that we have a set of candidate points $c_1<...<c_k$ and a set of variables $x_1<...<x_n$ where $k neq n$. Furthermore, we have the following distributions:
$p(x_1), p(x_2), ..., p(x_n).$

Our objective is to find the best assignment of candidate points $c_1<...<c_k$ to variables $x_1<...<x_n$. We are also allowed to assign ‘NaN’ to the variables. For example, in the figure below, we have 4 candidate points and 3 variables. Given the distributions, it seems that the best assignment is to assign ‘NaN’ to $x_1$, $c_1$ to $x_2$, and $c_2$ to $x_3$.

How can I formulate this problem as maximum likelihood? Should I use hypothesis testing to assign 'NaN' to some variables? For example, if $p(x_1 >= c_1) < alpha$ for some small $alpha$, then $x_1 = text'NaN'$.

Also, I have a dataset which contains the assignments (including 'NaN's). Is there a useful distribution to find? For example, $p(x_i = text'NaN')$?

probability probability-distributions hypothesis-testing maximum-likelihood

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asked Mar 25 at 18:31

KRLKRL

204

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I assume you have $n$ pdf $p_1, p_2, ldots, p_n$. Besides the NaN part, for each data point $c_i$, you may just try to find out the corresponding $p_i^*$ which maximize $p_j(c_i)$. I am not sure if some of the data point is out of the support of all the pdfs, or you simply have arbitrarily set a threshold $alpha$ such that when $p_i^*(c_i) < alpha$, you assign it to NaN.
  $endgroup$
  – BGM
  Mar 26 at 8:28
  

  
  
  
  

add a comment | 

0

$begingroup$

Suppose that we have a set of candidate points $c_1<...<c_k$ and a set of variables $x_1<...<x_n$ where $k neq n$. Furthermore, we have the following distributions:
$p(x_1), p(x_2), ..., p(x_n).$

Our objective is to find the best assignment of candidate points $c_1<...<c_k$ to variables $x_1<...<x_n$. We are also allowed to assign ‘NaN’ to the variables. For example, in the figure below, we have 4 candidate points and 3 variables. Given the distributions, it seems that the best assignment is to assign ‘NaN’ to $x_1$, $c_1$ to $x_2$, and $c_2$ to $x_3$.

How can I formulate this problem as maximum likelihood? Should I use hypothesis testing to assign 'NaN' to some variables? For example, if $p(x_1 >= c_1) < alpha$ for some small $alpha$, then $x_1 = text'NaN'$.

Also, I have a dataset which contains the assignments (including 'NaN's). Is there a useful distribution to find? For example, $p(x_i = text'NaN')$?

probability probability-distributions hypothesis-testing maximum-likelihood

share|cite|improve this question

asked Mar 25 at 18:31

KRLKRL

204

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I assume you have $n$ pdf $p_1, p_2, ldots, p_n$. Besides the NaN part, for each data point $c_i$, you may just try to find out the corresponding $p_i^*$ which maximize $p_j(c_i)$. I am not sure if some of the data point is out of the support of all the pdfs, or you simply have arbitrarily set a threshold $alpha$ such that when $p_i^*(c_i) < alpha$, you assign it to NaN.
  $endgroup$
  – BGM
  Mar 26 at 8:28
  

  
  
  
  

add a comment | 

$begingroup$

Suppose that we have a set of candidate points $c_1<...<c_k$ and a set of variables $x_1<...<x_n$ where $k neq n$. Furthermore, we have the following distributions:
$p(x_1), p(x_2), ..., p(x_n).$

Our objective is to find the best assignment of candidate points $c_1<...<c_k$ to variables $x_1<...<x_n$. We are also allowed to assign ‘NaN’ to the variables. For example, in the figure below, we have 4 candidate points and 3 variables. Given the distributions, it seems that the best assignment is to assign ‘NaN’ to $x_1$, $c_1$ to $x_2$, and $c_2$ to $x_3$.

How can I formulate this problem as maximum likelihood? Should I use hypothesis testing to assign 'NaN' to some variables? For example, if $p(x_1 >= c_1) < alpha$ for some small $alpha$, then $x_1 = text'NaN'$.

Also, I have a dataset which contains the assignments (including 'NaN's). Is there a useful distribution to find? For example, $p(x_i = text'NaN')$?

probability probability-distributions hypothesis-testing maximum-likelihood

share|cite|improve this question

asked Mar 25 at 18:31

KRLKRL

204

$endgroup$

share|cite|improve this question

asked Mar 25 at 18:31

KRLKRL

204

share|cite|improve this question

asked Mar 25 at 18:31

KRLKRL

204

asked Mar 25 at 18:31

KRLKRL

204

asked Mar 25 at 18:31

KRLKRL

204