How to calculate the most likely output based in input values and their probabilities?
0
I have a set of values with their appropriate truthiness probabilities.
I need to find the most likely value based on all the available input values.
Note: Probabilities are subjective and can conflict - but they represent the truthiness of the final output.
E.g a data set like this.
data = [
{value: 1, probability: 1},
{value: 1, probability: 0.5}
];
// i would expect to output 1, because all input agree on the value and 1 is certain in its value.
data = [
{value: 1, probability: 1},
{value: 0.5, probability: 1}
];
// Id expect the value to be half way between 1 and 0.5. Both values are equally likely - so final output is in between the 2.
data = [
{value: 1, probability: 1},
{value: 0.5, probability: 0.1}
];
// Id expect the value to be almost 1 but not quite.
data = [
{value: 1, probability: 1},
{value: 1, probability: 0.1},
{value: 0.1, probability: 1},
{value: 0, probability: 0.5},
{value: 0, probability: 0.9},
... thousands of more values here ...
quickly gets complicated and cpu intensive
];
javascript algorithm math
asked Nov 10 at 20:04
Rainer Plumer
2,36311024
|
show 1 more comment
0
I have a set of values with their appropriate truthiness probabilities.
I need to find the most likely value based on all the available input values.
Note: Probabilities are subjective and can conflict - but they represent the truthiness of the final output.
E.g a data set like this.
data = [
{value: 1, probability: 1},
{value: 1, probability: 0.5}
];
// i would expect to output 1, because all input agree on the value and 1 is certain in its value.
data = [
{value: 1, probability: 1},
{value: 0.5, probability: 1}
];
// Id expect the value to be half way between 1 and 0.5. Both values are equally likely - so final output is in between the 2.
data = [
{value: 1, probability: 1},
{value: 0.5, probability: 0.1}
];
// Id expect the value to be almost 1 but not quite.
data = [
{value: 1, probability: 1},
{value: 1, probability: 0.1},
{value: 0.1, probability: 1},
{value: 0, probability: 0.5},
{value: 0, probability: 0.9},
... thousands of more values here ...
quickly gets complicated and cpu intensive
];
javascript algorithm math
asked Nov 10 at 20:04
Rainer Plumer
2,36311024
The most likely output in the third example is "1". The data does not say anything about other values, just 1 and 0.5. If you want to somehow interpolate between all the possible values and output that as a result, you need to reword the question.
– kfx
Nov 10 at 20:07
What is the actual question here?
– charlietfl
Nov 10 at 20:07
@kfx The most likely output is close to 1, but not 1 because there is a conflict between values. Each item in the array gives its "opinion" of what the value is. First entry says it is certainly 1. The other entry says it might be 0.5. So which is it ? Most likely 1, but not quite. In my real data set i have thousands of value/probability pairs.
– Rainer Plumer
Nov 10 at 20:15
Could you try being more precise in defining what the outcome should be? Do you have an interpolation formula in mind? As you say, So which is it ? Most likely 1 - so this is your answer unless you reword the question and make it more precise.
– kfx
Nov 10 at 20:17
@kfx The outcome should be a number(a value) that combines all the proposed values with their probabilities and returns a value that is the best at satisfying all the probability claims. I don't have any formulas/algorithms in mind(that's kind of what I'm looking for)
– Rainer Plumer
Nov 10 at 20:25
|
show 1 more comment
0
0
0
I have a set of values with their appropriate truthiness probabilities.
I need to find the most likely value based on all the available input values.
Note: Probabilities are subjective and can conflict - but they represent the truthiness of the final output.
E.g a data set like this.
data = [
{value: 1, probability: 1},
{value: 1, probability: 0.5}
];
// i would expect to output 1, because all input agree on the value and 1 is certain in its value.
data = [
{value: 1, probability: 1},
{value: 0.5, probability: 1}
];
// Id expect the value to be half way between 1 and 0.5. Both values are equally likely - so final output is in between the 2.
data = [
{value: 1, probability: 1},
{value: 0.5, probability: 0.1}
];
// Id expect the value to be almost 1 but not quite.
data = [
{value: 1, probability: 1},
{value: 1, probability: 0.1},
{value: 0.1, probability: 1},
{value: 0, probability: 0.5},
{value: 0, probability: 0.9},
... thousands of more values here ...
quickly gets complicated and cpu intensive
];
javascript algorithm math
asked Nov 10 at 20:04
Rainer Plumer
2,36311024
I have a set of values with their appropriate truthiness probabilities.
I need to find the most likely value based on all the available input values.
Note: Probabilities are subjective and can conflict - but they represent the truthiness of the final output.
E.g a data set like this.
data = [
{value: 1, probability: 1},
{value: 1, probability: 0.5}
];
// i would expect to output 1, because all input agree on the value and 1 is certain in its value.
data = [
{value: 1, probability: 1},
{value: 0.5, probability: 1}
];
// Id expect the value to be half way between 1 and 0.5. Both values are equally likely - so final output is in between the 2.
data = [
{value: 1, probability: 1},
{value: 0.5, probability: 0.1}
];
// Id expect the value to be almost 1 but not quite.
data = [
{value: 1, probability: 1},
{value: 1, probability: 0.1},
{value: 0.1, probability: 1},
{value: 0, probability: 0.5},
{value: 0, probability: 0.9},
... thousands of more values here ...
quickly gets complicated and cpu intensive
];
javascript algorithm math
javascript algorithm math
asked Nov 10 at 20:04
Rainer Plumer
2,36311024
asked Nov 10 at 20:04
Rainer Plumer
2,36311024
asked Nov 10 at 20:04
Rainer Plumer
2,36311024
asked Nov 10 at 20:04
Rainer Plumer
2,36311024
asked Nov 10 at 20:04
Rainer Plumer
2,36311024
2,36311024
The most likely output in the third example is "1". The data does not say anything about other values, just 1 and 0.5. If you want to somehow interpolate between all the possible values and output that as a result, you need to reword the question.
– kfx
Nov 10 at 20:07
What is the actual question here?
– charlietfl
Nov 10 at 20:07
@kfx The most likely output is close to 1, but not 1 because there is a conflict between values. Each item in the array gives its "opinion" of what the value is. First entry says it is certainly 1. The other entry says it might be 0.5. So which is it ? Most likely 1, but not quite. In my real data set i have thousands of value/probability pairs.
– Rainer Plumer
Nov 10 at 20:15
Could you try being more precise in defining what the outcome should be? Do you have an interpolation formula in mind? As you say, So which is it ? Most likely 1 - so this is your answer unless you reword the question and make it more precise.
– kfx
Nov 10 at 20:17
@kfx The outcome should be a number(a value) that combines all the proposed values with their probabilities and returns a value that is the best at satisfying all the probability claims. I don't have any formulas/algorithms in mind(that's kind of what I'm looking for)
– Rainer Plumer
Nov 10 at 20:25
|
show 1 more comment
The most likely output in the third example is "1". The data does not say anything about other values, just 1 and 0.5. If you want to somehow interpolate between all the possible values and output that as a result, you need to reword the question.
– kfx
Nov 10 at 20:07
What is the actual question here?
– charlietfl
Nov 10 at 20:07
@kfx The most likely output is close to 1, but not 1 because there is a conflict between values. Each item in the array gives its "opinion" of what the value is. First entry says it is certainly 1. The other entry says it might be 0.5. So which is it ? Most likely 1, but not quite. In my real data set i have thousands of value/probability pairs.
– Rainer Plumer
Nov 10 at 20:15
Could you try being more precise in defining what the outcome should be? Do you have an interpolation formula in mind? As you say, So which is it ? Most likely 1 - so this is your answer unless you reword the question and make it more precise.
– kfx
Nov 10 at 20:17
@kfx The outcome should be a number(a value) that combines all the proposed values with their probabilities and returns a value that is the best at satisfying all the probability claims. I don't have any formulas/algorithms in mind(that's kind of what I'm looking for)
– Rainer Plumer
Nov 10 at 20:25
The most likely output in the third example is "1". The data does not say anything about other values, just 1 and 0.5. If you want to somehow interpolate between all the possible values and output that as a result, you need to reword the question.
– kfx
Nov 10 at 20:07
The most likely output in the third example is "1". The data does not say anything about other values, just 1 and 0.5. If you want to somehow interpolate between all the possible values and output that as a result, you need to reword the question.
– kfx
Nov 10 at 20:07
What is the actual question here?
– charlietfl
Nov 10 at 20:07
What is the actual question here?
– charlietfl
Nov 10 at 20:07
@kfx The most likely output is close to 1, but not 1 because there is a conflict between values. Each item in the array gives its "opinion" of what the value is. First entry says it is certainly 1. The other entry says it might be 0.5. So which is it ? Most likely 1, but not quite. In my real data set i have thousands of value/probability pairs.
– Rainer Plumer
Nov 10 at 20:15
@kfx The most likely output is close to 1, but not 1 because there is a conflict between values. Each item in the array gives its "opinion" of what the value is. First entry says it is certainly 1. The other entry says it might be 0.5. So which is it ? Most likely 1, but not quite. In my real data set i have thousands of value/probability pairs.
– Rainer Plumer
Nov 10 at 20:15
Could you try being more precise in defining what the outcome should be? Do you have an interpolation formula in mind? As you say, So which is it ? Most likely 1 - so this is your answer unless you reword the question and make it more precise.
– kfx
Nov 10 at 20:17
Could you try being more precise in defining what the outcome should be? Do you have an interpolation formula in mind? As you say, So which is it ? Most likely 1 - so this is your answer unless you reword the question and make it more precise.
– kfx
Nov 10 at 20:17
@kfx The outcome should be a number(a value) that combines all the proposed values with their probabilities and returns a value that is the best at satisfying all the probability claims. I don't have any formulas/algorithms in mind(that's kind of what I'm looking for)
– Rainer Plumer
Nov 10 at 20:25
@kfx The outcome should be a number(a value) that combines all the proposed values with their probabilities and returns a value that is the best at satisfying all the probability claims. I don't have any formulas/algorithms in mind(that's kind of what I'm looking for)
– Rainer Plumer
Nov 10 at 20:25
|
show 1 more comment
1 Answer
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Seems like you're looking for a weighted average. Multiply each value by its probability, compute the sum of the products, and divide by the sum of the probabilities.
First example: (1.0*1.0 + 1.0*0.5) / (1.0+0.5) = 1.5/1.5 = 1.00
Second example: (1.0*1.0 + 0.5*1.0) / (1.0+1.0) = 1.5/2.0 = 0.75
Third example: (1.0*1.0 + 0.5*0.1) / (1.0+0.1) = 1.05/1.1 = 0.95
answered Nov 10 at 22:15
user3386109
27.9k53247
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Seems like you're looking for a weighted average. Multiply each value by its probability, compute the sum of the products, and divide by the sum of the probabilities.
First example: (1.0*1.0 + 1.0*0.5) / (1.0+0.5) = 1.5/1.5 = 1.00
Second example: (1.0*1.0 + 0.5*1.0) / (1.0+1.0) = 1.5/2.0 = 0.75
Third example: (1.0*1.0 + 0.5*0.1) / (1.0+0.1) = 1.05/1.1 = 0.95
answered Nov 10 at 22:15
user3386109
27.9k53247
add a comment |
0
Seems like you're looking for a weighted average. Multiply each value by its probability, compute the sum of the products, and divide by the sum of the probabilities.
First example: (1.0*1.0 + 1.0*0.5) / (1.0+0.5) = 1.5/1.5 = 1.00
Second example: (1.0*1.0 + 0.5*1.0) / (1.0+1.0) = 1.5/2.0 = 0.75
Third example: (1.0*1.0 + 0.5*0.1) / (1.0+0.1) = 1.05/1.1 = 0.95
answered Nov 10 at 22:15
user3386109
27.9k53247
add a comment |
0
0
0
Seems like you're looking for a weighted average. Multiply each value by its probability, compute the sum of the products, and divide by the sum of the probabilities.
First example: (1.0*1.0 + 1.0*0.5) / (1.0+0.5) = 1.5/1.5 = 1.00
Second example: (1.0*1.0 + 0.5*1.0) / (1.0+1.0) = 1.5/2.0 = 0.75
Third example: (1.0*1.0 + 0.5*0.1) / (1.0+0.1) = 1.05/1.1 = 0.95
answered Nov 10 at 22:15
user3386109
27.9k53247
Seems like you're looking for a weighted average. Multiply each value by its probability, compute the sum of the products, and divide by the sum of the probabilities.
First example: (1.0*1.0 + 1.0*0.5) / (1.0+0.5) = 1.5/1.5 = 1.00
Second example: (1.0*1.0 + 0.5*1.0) / (1.0+1.0) = 1.5/2.0 = 0.75
Third example: (1.0*1.0 + 0.5*0.1) / (1.0+0.1) = 1.05/1.1 = 0.95
answered Nov 10 at 22:15
user3386109
27.9k53247
answered Nov 10 at 22:15
user3386109
27.9k53247
answered Nov 10 at 22:15
user3386109
27.9k53247
answered Nov 10 at 22:15
user3386109
27.9k53247
27.9k53247
add a comment |
add a comment |
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The most likely output in the third example is "1". The data does not say anything about other values, just 1 and 0.5. If you want to somehow interpolate between all the possible values and output that as a result, you need to reword the question.
– kfx
Nov 10 at 20:07
What is the actual question here?
– charlietfl
Nov 10 at 20:07
@kfx The most likely output is close to 1, but not 1 because there is a conflict between values. Each item in the array gives its "opinion" of what the value is. First entry says it is certainly 1. The other entry says it might be 0.5. So which is it ? Most likely 1, but not quite. In my real data set i have thousands of value/probability pairs.
– Rainer Plumer
Nov 10 at 20:15
Could you try being more precise in defining what the outcome should be? Do you have an interpolation formula in mind? As you say, So which is it ? Most likely 1 - so this is your answer unless you reword the question and make it more precise.
– kfx
Nov 10 at 20:17
@kfx The outcome should be a number(a value) that combines all the proposed values with their probabilities and returns a value that is the best at satisfying all the probability claims. I don't have any formulas/algorithms in mind(that's kind of what I'm looking for)
– Rainer Plumer
Nov 10 at 20:25