Analytics Ontology
type: Ontology
creator: Michael E. Cotterell
creator: Mustafa V. Nural
creator: John A. Miller
comment: This ontology aims to provide comphresensive yet practical representation of data analytics framework.
version info: 1.0

isIllConditioned
type: DatatypeProperty
type: FunctionalProperty
domain: Model
range: boolean
comment: Indicates whether the input matrix (predictors) of this model is ill-conditioned. If the log of condition number of the matrix is greater than or equal to 18, it is determined to be ill-conditioned.

ANCOVA
type: Class
equivalent class: Class
  intersection of: GLM
  intersection of: Restriction
    on property: hasPredictorVariable
    some values from: Restriction
      on property: hasVariableType
      all values from: Categorical
  intersection of: Restriction
    on property: hasResponseVariable
    all values from: Restriction
      on property: hasDistribution
      all values from: Normal Distribution
subclass of: GLM
alternative: Analysis of Covariance

Axiom
annotated source: ANCOVA
annotated property: equivalentClass
annotated target: Class
  intersection of: GLM
  intersection of: Restriction
    on property: hasPredictorVariable
    some values from: Restriction
      on property: hasVariableType
      all values from: Categorical
  intersection of: Restriction
    on property: hasResponseVariable
    all values from: Restriction
      on property: hasDistribution
      all values from: Normal Distribution
comment: A model may be considered as an ANCOVA model if in addition to conforming to GLM requirements it has some categorical variables (factors).

ANOVA
type: Class
equivalent class: Class
  intersection of: ANCOVA
  intersection of: Restriction
    on property: hasPredictorVariable
    all values from: Restriction
      on property: hasVariableType
      all values from: Categorical
subclass of: ANCOVA
alternative: Analysis of Variance

Axiom
annotated source: ANOVA
annotated property: equivalentClass
annotated target: Class
  intersection of: ANCOVA
  intersection of: Restriction
    on property: hasPredictorVariable
    all values from: Restriction
      on property: hasVariableType
      all values from: Categorical
comment: An ANCOVA model may be considered as an ANOVA model if it only has categorical variables (factors).

Bernoulli Distribution
type: Class
subclass of: Exponential Family
description: A Bernoulli distribution is a probability distribution that models the Bernoulli trials process. A sequence of Bernoulli trials satisfies the following assumptions: i) Each trial has two possible outcomes, in the language of reliability called success and failure; ii) The trials are independent; iii) On each trial, the probability of success is p and the probability of failure is 1−p where p is an element of [0,1].

Binary
type: Class
subclass of: Categorical
disjoint with: Ordinal
alternative: Dichotomous
description: A variable with a binary variable type generally denotes that the domain of discourse of the variable is dichotomous. This means that the variable can only take on one of two values.

Binomial Distribution
type: Class
subclass of: Exponential Family

Categorical
type: Class
subclass of: Discrete
disjoint with: Integer
alternative: Polychotomous
description: A variable with a categorical variable type generally denotes that the domain of discourse of the variable is polychotomous. This means that the variable can take on one of a finite number of values.

Continuous
type: Class
subclass of: Variable Type
disjoint with: Discrete
description: A variable with a continuous variable type generally denotes that the domain of discourse for the variable is the set of real numbers.

Dependent Model
type: Class
equivalent class: Class
  intersection of: Model
  intersection of: Restriction
    on property: hasRepeatedObservations
    has value: true
subclass of: Model

Discrete
type: Class
subclass of: Variable Type
description: A variable with a discrete variable type generally denotes that the domain of discourse of the variable includes only elements that are individually separate and distinct.

Distribution
type: Class
description: A probability distribution assigns a probability to each measurable subset of the possible outcomes of a random experiment, survey, or procedure of statistical inference.

Exponential Distribution
type: Class
subclass of: Exponential Family
description: An exponential distribution is a probability distribution that models the time between subsequent events based on a rate parameter.

Exponential Family
type: Class
subclass of: Distribution
description: The exponential family of distributions is the set of probability distributions whose probaility distribution functions (PDFs) and cumulative distribution functions (CDFs) can be written such that their terms are moved to the exponent (often called the canonical form.
source: FISHER, R. A. (1934). Two new properties of mathematical likelihood. Proceedings of the Royal Society A, 144, 285-307.

Exponential Regression
type: Class
equivalent class: Class
  intersection of: GZLM
  intersection of: Class
    union of: Restriction
      on property: hasResidualDistribution
      all values from: Exponential Distribution
    union of: Restriction
      on property: hasResidualDistribution
      cardinality: 0
  intersection of: Class
    union of: Restriction
      on property: hasResponseVariable
      all values from: Restriction
        on property: hasVariableType
        all values from: Non-Negative Continuous
    union of: Restriction
      on property: hasResponseVariable
      all values from: Restriction
        on property: hasVariableType
        all values from: Non-Negative Integer
subclass of: GZLM

Axiom
annotated source: Exponential Regression
annotated property: equivalentClass
annotated target: Class
  intersection of: GZLM
  intersection of: Class
    union of: Restriction
      on property: hasResidualDistribution
      all values from: Exponential Distribution
    union of: Restriction
      on property: hasResidualDistribution
      cardinality: 0
  intersection of: Class
    union of: Restriction
      on property: hasResponseVariable
      all values from: Restriction
        on property: hasVariableType
        all values from: Non-Negative Continuous
    union of: Restriction
      on property: hasResponseVariable
      all values from: Restriction
        on property: hasVariableType
        all values from: Non-Negative Integer
comment: A GZLM model may be considered as an Exponential Regression Model if the residual distribution of the model is Exponential Distribution and the response variable is a Non-Negative Continuous variable.

Function
type: Class
description: A function is a relation that uniquely associates members of one set with members of another set.

GEE
type: Class
equivalent class: Class
  intersection of: Dependent Model
  intersection of: Restriction
    on property: hasRepeatedObservations
    has value: true
subclass of: Dependent Model
alternative: Generalized Estimating Equations

GLM
type: Class
equivalent class: Class
  intersection of: GZLM
  intersection of: Class
    union of: Restriction
      on property: hasResidualDistribution
      all values from: Normal Distribution
    union of: Restriction
      on property: hasResidualDistribution
      cardinality: 0
  intersection of: Restriction
    on property: hasResponseVariable
    all values from: Restriction
      on property: hasVariableType
      all values from: Continuous
subclass of: GZLM
alternative: General Linear Model
comment: GLM model makes two major assumptions 1) The response variable is a Continuous variable. 2) The residuals are Normally distributed.
default model: Multiple Linear Regression

Axiom
annotated source: GLM
annotated property: equivalentClass
annotated target: Class
  intersection of: GZLM
  intersection of: Class
    union of: Restriction
      on property: hasResidualDistribution
      all values from: Normal Distribution
    union of: Restriction
      on property: hasResidualDistribution
      cardinality: 0
  intersection of: Restriction
    on property: hasResponseVariable
    all values from: Restriction
      on property: hasVariableType
      all values from: Continuous
comment: A GZLM model may be considered as a GLM model if its residuals are Normally Distributed and the response variable is a Continuous variable.

GLMM
type: Class
equivalent class: Class
  intersection of: Dependent Model
  intersection of: Restriction
    on property: hasRepeatedObservations
    has value: true
subclass of: Dependent Model
alternative: Generalized Linear Mixed Models

GMM
type: Class
subclass of: GLMM
alternative: Gaussian Mixture Models

GZLM
type: Class
equivalent class: Class
  intersection of: Independent Model
  intersection of: Restriction
    on property: hasConditionNumber
    some values from: Datatype
      on datatype: int
      with restrictions:
        max inclusive: 16
  intersection of: Restriction
    on property: hasNegativeDF
    has value: false
subclass of: Independent Model
alternative: Generalized Linear Model
default model: Multinomial Logistic Regression

Gamma Distribution
type: Class
subclass of: Exponential Family
description: The gamma distribution family is a subset of the exponential family of distributions that have a shape parameter and a rate parameter.

Gamma Regression
type: Class
subclass of: GZLM

Identity Function
type: Class
subclass of: Function
type: NamedIndividual
description: The identity function, given a number x, returns x (the identity).

Independent Model
type: Class
equivalent class: Class
  intersection of: Model
  intersection of: Class
    complement of: Restriction
      on property: hasTemporalVariable
      some values from: Variable
  intersection of: Restriction
    on property: hasRepeatedObservations
    has value: false
subclass of: Model
default model: GZLM

Axiom
annotated source: Independent Model
annotated property: equivalentClass
annotated target: Class
  intersection of: Model
  intersection of: Class
    complement of: Restriction
      on property: hasTemporalVariable
      some values from: Variable
  intersection of: Restriction
    on property: hasRepeatedObservations
    has value: false
comment: A model may be considered an independent model if the model does not have repeated observations (i.e., dependency within response).

Integer
type: Class
subclass of: Discrete
description: A variable with an integer variable type generally denotes that the domain of discourse for the variable is the set of integer numbers.

Inverse Function
type: Class
subclass of: Function
description: The inverse function is a function that reverses another function.

Inverse Gaussian Regression
type: Class
subclass of: GZLM

Lasso Regression
type: Class
equivalent class: Class
  union of: Class
    intersection of: Independent Model
    intersection of: Restriction
      on property: hasResponseVariable
      all values from: Restriction
        on property: hasVariableType
        all values from: Discrete
    intersection of: Restriction
      on property: hasNegativeDF
      has value: false
  union of: Class
    intersection of: Independent Model
    intersection of: Restriction
      on property: hasConditionNumber
      some values from: Datatype
        on datatype: int
subclass of: Independent Model

Log Linear Regression
type: Class
equivalent class: Class
  intersection of: GZLM
  intersection of: Class
    union of: Restriction
      on property: hasResidualDistribution
      all values from: Negative Binomial Distribution
    union of: Restriction
      on property: hasResidualDistribution
      all values from: Poisson Distribution
    union of: Restriction
      on property: hasResidualDistribution
      cardinality: 0
  intersection of: Restriction
    on property: hasPredictorVariable
    all values from: Restriction
      on property: hasVariableType
      all values from: Categorical
  intersection of: Restriction
    on property: hasResponseVariable
    all values from: Class
      intersection of: Restriction
        on property: hasDistribution
        all values from: Poisson Distribution
      intersection of: Restriction
        on property: hasVariableType
        all values from: Non-Negative Integer
subclass of: GZLM

Log Function
type: Class
subclass of: Function
type: NamedIndividual
alternative: Natural Log Function
description: The natural logarithm function, given a number x, produces a result y such that x = exp(y).

Logistic Regression
type: Class
equivalent class: Class
  intersection of: GZLM
  intersection of: Class
    union of: Restriction
      on property: hasResidualDistribution
      all values from: Bernoulli Distribution
    union of: Restriction
      on property: hasResidualDistribution
      cardinality: 0
  intersection of: Restriction
    on property: hasResponseVariable
    all values from: Restriction
      on property: hasVariableType
      all values from: Binary
subclass of: GZLM

Axiom
annotated source: Logistic Regression
annotated property: equivalentClass
annotated target: Class
  intersection of: GZLM
  intersection of: Class
    union of: Restriction
      on property: hasResidualDistribution
      all values from: Bernoulli Distribution
    union of: Restriction
      on property: hasResidualDistribution
      cardinality: 0
  intersection of: Restriction
    on property: hasResponseVariable
    all values from: Restriction
      on property: hasVariableType
      all values from: Binary
comment: A GZLM model may be considered as a Logistic Regression Model if the residual distribution of the model is Bernoulli Distribution and the response variable is a binary variable.

Logit Function
type: Class
subclass of: Function
type: NamedIndividual
description: The logit function is the inverse of the logistic transform.

Model
type: Class
comment: All individuals that have at least one variable are considered a Model. A model then could be inferred to have more specific model types depending on how it conforms to the equivalence axioms stated in the hierarchy.
comment: Model class and its subclasses define different model types that can be used for analyzing data. There are many ways of specifying the class hierarchy for a collection of model types, however, we have given priority to correspondence with implementations of these types (e.g., ScalaTion). This becomes important when running models generated from the abstract models represented in the ontology.

Multinomial Distribution
type: Class
subclass of: Exponential Family

Multinomial Logistic Regression
type: Class
equivalent class: Class
  intersection of: GZLM
  intersection of: Class
    union of: Restriction
      on property: hasResidualDistribution
      all values from: Multinomial Distribution
    union of: Restriction
      on property: hasResidualDistribution
      cardinality: 0
  intersection of: Restriction
    on property: hasResponseVariable
    all values from: Class
      intersection of: Restriction
        on property: hasDistribution
        all values from: Multinomial Distribution
      intersection of: Restriction
        on property: hasVariableType
        all values from: Multinomial
subclass of: GZLM

Multiple Linear Regression
type: Class
equivalent class: Class
  intersection of: GLM
  intersection of: Restriction
    on property: hasResponseVariable
    all values from: Restriction
      on property: hasDistribution
      all values from: Normal Distribution
subclass of: GLM
alternative: MLR
alternative: Multiple Regression

Axiom
annotated source: Multiple Linear Regression
annotated property: equivalentClass
annotated target: Class
  intersection of: GLM
  intersection of: Restriction
    on property: hasResponseVariable
    all values from: Restriction
      on property: hasDistribution
      all values from: Normal Distribution
comment: A GLM model may be considered a Multiple Linear Regression if at least some of its variables are Continuous variables.

Naive Bayes
type: Class
subclass of: Independent Model
alternative: Naïve Bayes

Negative Binomial Distribution
type: Class
subclass of: Exponential Family

Negative Binomial Regression
type: Class
equivalent class: Class
  intersection of: GZLM
  intersection of: Class
    intersection of: Restriction
      on property: hasResponseVariable
      all values from: Class
        intersection of: Restriction
    intersection of: Restriction
      on property: isOverDispersed
      has value: true
  intersection of: Class
    union of: Restriction
      on property: hasResidualDistribution
      all values from: Negative Binomial Distribution
    union of: Restriction
      on property: hasResidualDistribution
      all values from: Poisson Distribution
    union of: Restriction
      on property: hasResidualDistribution
      cardinality: 0
  intersection of: Restriction
    on property: hasPredictorVariable
    some values from: Restriction
      on property: hasVariableType
      all values from: Continuous
subclass of: GZLM

Non-Negative Continuous
type: Class
subclass of: Continuous
description: A variable with a continuous non-negative variable type generally denotes that the domain of discourse for the variable is the set of all non-negative real numbers.

Non-Negative Integer
type: Class
subclass of: Integer
alternative: Natural
description: A variable with an integer non-negative variable type generally denotes that the domain of discourse for the variable is the set of all non-negative integer numbers.

Normal Distribution
type: Class
subclass of: Exponential Family

Ordinal
type: Class
subclass of: Categorical
description: A variable with an ordinal variable type generally denotes that the domain of discourse of the variable is polychotomous and ordered. This means that the variable can take on one of a finite number of values and that the set has an ordering.

Ordinal Logistic Regression
type: Class
subclass of: GZLM

PartialLeastSquaresRegression
type: Class
equivalent class: Class
  intersection of: Independent Model
  intersection of: Restriction
    on property: hasNegativeDF
    has value: true
subclass of: Independent Model

Perceptron
type: Class
subclass of: Independent Model

Poisson Distribution
type: Class
subclass of: Exponential Family

Poisson Regression
type: Class
equivalent class: Class
  intersection of: GZLM
  intersection of: Class
    union of: Restriction
      on property: hasResidualDistribution
      all values from: Negative Binomial Distribution
    union of: Restriction
      on property: hasResidualDistribution
      all values from: Poisson Distribution
    union of: Restriction
      on property: hasResidualDistribution
      cardinality: 0
  intersection of: Restriction
    on property: hasPredictorVariable
    some values from: Restriction
      on property: hasVariableType
      all values from: Continuous
  intersection of: Restriction
    on property: hasResponseVariable
    all values from: Class
      intersection of: Restriction
        on property: hasDistribution
        all values from: Poisson Distribution
      intersection of: Restriction
        on property: hasVariableType
        all values from: Non-Negative Integer
subclass of: GZLM

Axiom
annotated source: Poisson Regression
annotated property: equivalentClass
annotated target: Class
  intersection of: GZLM
  intersection of: Class
    union of: Restriction
      on property: hasResidualDistribution
      all values from: Negative Binomial Distribution
    union of: Restriction
      on property: hasResidualDistribution
      all values from: Poisson Distribution
    union of: Restriction
      on property: hasResidualDistribution
      cardinality: 0
  intersection of: Restriction
    on property: hasPredictorVariable
    some values from: Restriction
      on property: hasVariableType
      all values from: Continuous
  intersection of: Restriction
    on property: hasResponseVariable
    all values from: Class
      intersection of: Restriction
        on property: hasDistribution
        all values from: Poisson Distribution
      intersection of: Restriction
        on property: hasVariableType
        all values from: Non-Negative Integer
comment: A GZLM model may be considered as a Poisson Regression model if the residual distribution of the model is Binomial Distribution and the response variable is a Non-Negative Integer.

Polynomial Regression
type: Class
subclass of: GLM

Reciprocal Function
type: Class
subclass of: Function
description: The reciprocal function, given a number x, returns 1/x (i.e., the reciprocal).

Response Surface Analysis
type: Class
subclass of: GLM

Simple Linear Regression
type: Class
equivalent class: Class
  intersection of: Multiple Linear Regression
  intersection of: Restriction
    on property: hasPredictorVariable
    qualified cardinality: 1
    on class: Variable
subclass of: Multiple Linear Regression
alternative: SLR

Axiom
annotated source: Simple Linear Regression
annotated property: equivalentClass
annotated target: Class
  intersection of: Multiple Linear Regression
  intersection of: Restriction
    on property: hasPredictorVariable
    qualified cardinality: 1
    on class: Variable
comment: A MLR model may be considered a Simple Linear Regression model if it has only one predictor variable.

Square Root Function
type: Class
subclass of: Function
description: The square root function, given a number x, returns a value y such that y * y = x. In most cases, this function produces a positive value. If the input to the function is a negative number, then the function produces a complex number.

Time Series Model
type: Class
equivalent class: Class
  intersection of: Dependent Model
  intersection of: Restriction
    on property: hasTemporalVariable
    some values from: Variable
subclass of: Dependent Model

Transformed Multiple Linear Regression
type: Class
equivalent class: Class
  intersection of: GLM
  intersection of: Class
    union of: Restriction
      on property: hasResidualDistribution
      all values from: Normal Distribution
    union of: Restriction
      on property: hasResidualDistribution
      cardinality: 0
  intersection of: Restriction
    on property: hasResponseVariable
    all values from: Class
      complement of: Restriction
        on property: hasDistribution
        all values from: Normal Distribution
subclass of: GLM
alternative: Transformed Multiple Regression

Trigonometric Regression
type: Class
subclass of: GLM

Variable
type: Class
description: A variable is an element, feature, or factor that is liable to vary or change.

Variable Type
type: Class
description: The type of a variable usually denotes or restricts its corresponding domain of discourse.

Weighted Least Squares Regression
type: Class
equivalent class: Class
  intersection of: Independent Model
  intersection of: Restriction
    on property: hasResponseVariable
    all values from: Restriction
      on property: hasKurtosis
      some values from: Datatype
        on datatype: double
subclass of: Independent Model

Zero-Inflated Negative Binomial Regression
type: Class
equivalent class: Class
  intersection of: Negative Binomial Regression
  intersection of: Restriction
    on property: hasResponseVariable
    all values from: Restriction
      on property: isZeroInflated
      has value: true
subclass of: Negative Binomial Regression

Zero-Inflated Poisson Regression
type: Class
equivalent class: Class
  intersection of: Poisson Regression
  intersection of: Restriction
    on property: hasResponseVariable
    all values from: Restriction
      on property: isZeroInflated
      has value: true
subclass of: Poisson Regression

GenericANCOVAModel
type: Thing
type: NamedIndividual
type: Restriction
  on property: hasResidualDistribution
  all values from: Class
    one of: Normal Distribution Instance
type: Restriction
  on property: hasVariable
  all values from: Class
    one of: cylinders
    one of: horsepower
    one of: mpg
has predictor variable: cylinders
has predictor variable: horsepower
has residual distribution: Normal Distribution Instance
has response variable: mpg
has repeated observations: false

GenericANOVAModel
type: Thing
type: NamedIndividual
type: Restriction
  on property: hasResidualDistribution
  all values from: Class
    one of: Normal Distribution Instance
type: Restriction
  on property: hasVariable
  all values from: Class
    one of: cylinders
    one of: mpg
has predictor variable: cylinders
has residual distribution: Normal Distribution Instance
has response variable: mpg
has repeated observations: false

GenericExponentialModel
type: Thing
type: NamedIndividual
type: Restriction
  on property: hasResidualDistribution
  all values from: Class
    one of: Exponential Distribution Instance
type: Restriction
  on property: hasVariable
  all values from: Class
    one of: horsepower
    one of: mpg
has predictor variable: horsepower
has residual distribution: Exponential Distribution Instance
has response variable: mpg
has repeated observations: false

GenericLogisticRegressionModel
type: Thing
type: NamedIndividual
type: Restriction
  on property: hasResidualDistribution
  all values from: Class
    one of: Bernoulli Distribution Instance
type: Restriction
  on property: hasVariable
  all values from: Class
    one of: cylinders
    one of: isDomestic
    one of: mpg
has predictor variable: cylinders
has predictor variable: mpg
has residual distribution: Bernoulli Distribution Instance
has response variable: isDomestic
has repeated observations: false

GenericMLRModel
type: Thing
type: NamedIndividual
type: Restriction
  on property: hasResidualDistribution
  all values from: Class
    one of: Normal Distribution Instance
type: Restriction
  on property: hasVariable
  all values from: Class
    one of: acceleration
    one of: horsepower
    one of: mpg
has predictor variable: acceleration
has predictor variable: horsepower
has residual distribution: Normal Distribution Instance
has response variable: mpg
has repeated observations: false

GenericModel
type: Thing
type: NamedIndividual
type: Restriction
  on property: hasVariable
  all values from: Class
    one of: acceleration
    one of: cylinders
    one of: displacement
    one of: horsepower
    one of: model year
    one of: mpg
    one of: origin
    one of: weight
has predictor variable: acceleration
has predictor variable: cylinders
has predictor variable: displacement
has predictor variable: horsepower
has predictor variable: model year
has predictor variable: origin
has predictor variable: weight
has response variable: mpg
has repeated observations: false

GenericSLRModel
type: Thing
type: NamedIndividual
type: Restriction
  on property: hasResidualDistribution
  all values from: Class
    one of: Normal Distribution Instance
type: Restriction
  on property: hasVariable
  all values from: Class
    one of: horsepower
    one of: mpg
has predictor variable: horsepower
has residual distribution: Normal Distribution Instance
has response variable: mpg
has repeated observations: false

min exclusive: 16

min exclusive: 100.0