Multivariate risk assessment via poisson shelves
AssigneeVerint Americas Inc.
InventorsJoseph Wayne Dumoulin, Cynthia Freeman, James DelloStritto
Life of this patent
Estimating the term…
Abstract
Detecting fraudulent activity can be a complex, manual process. In this paper, we adapt statistical properties of count data in a novel algorithm to uncover records exhibiting high risk for fraud. Our method identifies shelves, partitioning data under the counts using a Student's t-distribution. We apply this methodology on a univariate dataset including cumulative results from phone calls to a customer service center. Additionally, we extend this technique to multivariate data, illustrating that the same method is applicable to both univariate and multivariate data.
Claims15
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=[1, x2, . . . xd], d 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 co 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:∃i s.t.r[yi]>λic+nic*√{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=[x1, x2, . . . xd], d 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 co 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:
- ∃i s.t.r[yi]>λic+nic*√{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=[x1, x2, . . . xd], d 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
- calculate a threshold value ω 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:
- ∃i s.t.r[yi]>λic+nic*√{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.
Dependencies are inferred from the claim text.