Multivariate risk assessment via poisson shelves

A non-transitory computer readable medium comprising instructions that, when executed by a processor of a processing system, cause the processing system to perform a method for identifying outliers for risk assessment in multivariable count data having a first count variable xi and a second count variable yi, the method comprising:

• calculating a mixture of independent Poissons:
• ℙ
• MixedPoi
• (
• x
• )
• =
• ∫
• ℝ
• ++
• d
• g
• ⁡
• (
• λ
• )
• ⁢
• ∏
• i
• =
• 1
• d
• ℙ
• Poiss
• (
• x
• i
• |
• λ
• i
• )
• ⁢
• d
• ⁢
• λ
• where x=[x1, x2, . . . xd] is the dimension of data, λ=[λ1, λ2 . . . λd] is a vector where λi is a parameter of the Poisson distribution for xi, and g(λ) is the mixing distribution
• calculating a threshold value a for every combination of mixture component c and dimension i according to:
• ωic={circumflex over (λ)}ic+n√{square root over ({circumflex over (λ)}ic)}
• identifying at least one shelf in surviving data by identifying an abrupt variation in generative parameters of a sequence of data;
• defining outliers in component c:
• {r∈ Recordsc:
• ∃is.t. r[y1]>λic+n*ic√{square root over (λic)}}
• where yi is the ith dimension of count data, and n*ic is the final n value of a first detected shelf in the ith dimension for component c;
• and
• providing a visual representation of the outliers.

A method of identifying outliers for risk assessment in multivariable count data having a first count variable xi and a second count variable yi, the method comprising:

• calculating a mixture of independent Poissons:
• ℙ
• MixedPoi
• (
• x
• )
• =
• ∫
• ℝ
• ++
• d
• g
• ⁡
• (
• λ
• )
• ⁢
• ∏
• i
• =
• 1
• d
• ℙ
• Poiss
• (
• x
• i
• |
• λ
• i
• )
• ⁢
• d
• ⁢
• λ
• where x=[xi, x2, . . . xd] is the dimension of data, λ=[λ1, λ2, . . . λd] is a vector where λi is a parameter of the Poisson distribution for xi, and g(λ) is the mixing distribution
• calculating a threshold value a for every combination of mixture component c and dimension i according to:
• ωic={circumflex over (λ)}ic+n√{square root over ({circumflex over (λ)}ic)}
• identifying at least one shelf in surviving data by identifying an abrupt variation in generative parameters of a sequence of data;
• defining outliers in component c:
• {r∈ Recordsc:
• ∃is.t. r[y1]>λic+n*ic√{square root over (λic)}}
• where yi is the ith dimension of count data, and n*ic is the final n value of a first detected shelf in the ith dimension for component c;
• and
• identifying the outliers for further risk assessment.

A system for identifying outliers for risk assessment in multivariable count data having a first count variable xi and a second count variable yi, comprising:

• a memory comprising executable instructions;
• a processor configured to execute the executable instructions and cause the system to:
• calculate a mixture of independent Poissons:
• ℙ
• MixedPoi
• (
• x
• )
• =
• ∫
• ℝ
• ++
• d
• g
• ⁡
• (
• λ
• )
• ⁢
• ∏
• i
• =
• 1
• d
• ℙ
• Poiss
• (
• x
• i
• |
• λ
• i
• )
• ⁢
• d
• ⁢
• λ
• where x=[xi, x2, . . . xd] is the dimension of data, λ=[λ1, A2, . . . λd] is a vector where λi is a parameter of the Poisson distribution for xi, and g(λ) is the mixing distribution
• calculate a threshold value a for every combination of mixture component c and dimension i according to:
• ωic={circumflex over (λ)}ic+n√{square root over ({circumflex over (λ)}ic)}
• identify at least one shelf in surviving data by identifying an abrupt variation in generative parameters of a sequence of data;
• define outliers in component c:
• {r∈ Recordsc:
• ∃is.t. r[y1]>λic+n*ic√{square root over (λic)}}
• where yi is the ith dimension of count data, and n*ic is the final n value of a first detected shelf in the ith dimension for component c;
• and
• identify the outliers for further risk assessment.