Inductive Process Modeling (IPM)

An Inductive Process Modeling (IPM) is machine learning task that learns quantitative process models from time series data.

• AKA: Process-Based Modeling.
• Context:
  • Input:
    • Observations dataset of a continuous variable X over time: [math]\displaystyle{ \{x_1(t_1),x_2(t_2),\cdots,x_n(t_n)\} }[/math].
    • A dataset of observed, unobserved and exogenous variable(s) Y: [math]\displaystyle{ \{y_1,y_2,\cdots,y_m\} }[/math]
  • output: Process Model parameters predicted values, Errors.
  • Task Requirements: Process Model [math]\displaystyle{ \mathcal M (X, Y, f(X, \theta)) }[/math], Parameter Constraints.
• Example(s):
  • Hierarchical Inductive Process Modeling (HIPM).
  • …
• Counter-Example(s):
  • Explanation-Based Learning (EBL) Task,
  • Abductive Concept Learning (ACL) Task,
  • A/B Testing.
• See: Inductive Logic Programming, Inductive Transfer, Equation Discovery, Inductive Inference, Induction, Scientific Discovery, Process Model, Compositional Modeling, System Identification, Ecosystem Modeling.

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References

2017a

• (Todorovski, 2017) ⇒ Ljupco Todorovski. (2017). "Inductive Process Modeling". In: Sammut & Webb, 2017.
  • QUOTE: Inductive process modeling is a machine learning task that deals with the problem of learning quantitative process models from time series data about the behavior of an observed dynamic system. Process models are models based on ordinary differential equations that add an explanatory layer to the equations. Namely, scientists and engineers use models to both predict and explain the behavior of an observed system. In many domains, models commonly refer to processes that govern system dynamics and entities altered by those processes. Ordinary differential equations, often used to cast models of dynamic systems, offer one way to represent these mechanisms and can be used to simulate and predict the system behavior, but fail to make the processes and entities explicit. In response, process models tie the explanatory information about processes and entities to the mathematical formulation, based on equations, that enables simulation.

2017b

• (Sammut & Webb, 2017) ⇒ (2017). "Process-Based Modeling". In: Sammut & Webb, 2017.

2008

• (Bridewell et al., 2008) ⇒ Will Bridewell, Pat Langley, Ljupco Todorovski, & Saso Dzerosk (2008). "Inductive process modeling" (PDF). Machine learning, 71(1), 1-32. DOI: 10.1007/s10994-007-5042-6.
  • QUOTE: We can state the task of inductive process modeling as:
    • Given: Observations for a set of continuous variables as they change over time;
    • Given: A set of observed, unobserved, and exogenous (i.e., unpredicted or forcing) variables that the model may include;
    • Given: Generic processes that specify causal relations among variables using generalized functional forms;
    • Given: Constraints, such as variable type information, that determine which processes may relate particular variables;
    • Find: A specific process model that, when given initial values for the modeled variables and values for any exogenous variables, explains the observed data and predicts unseen data accurately.

2005

• (Todorovski et al., 2005) ⇒ Ljupco Todorovski, Will Bridewell, Oren Shiran, & Pat Langley (2005, July). "Inducing hierarchical process models in dynamic domains"(PDF). In: Proceedings of The National Conference on Artificial Intelligence (Vol. 20, No. 2, p. 892). Menlo Park, CA; Cambridge, MA; London; AAAI Press; MIT Press; 1999.
  • QUOTE: Although the previous approach to inducing process models has proven successful on a variety of modeling tasks, two assumptions about how to combine processes into a model limit its usefulness. The first suggests that one can combine any set of generic processes to produce a valid model structure. This assumption leads to an underconstrained model space containing many candidates that violate domain experts’ expectations. The second portrays all process influences as additive, which is unrealistic in some domains. We can illustrate the problems raised by these assumptions with an example from population dynamics.

    Consider an aquatic ecosystem in which a single plankton species depends on two inorganic nutrients — nitrate and phosphorus. A human expert would expect a well-formed model to include a process for plankton growth, whereas IPM would consider models that omit it.

    (...) To overcome these limitations, we designed an extended formalism that supports hierarchical process models …

2003

• (Langley et al., 2003) ⇒ Pat Langley, Dileep George, Stephen D. Bay, & Kazumi Saito. (2003). "Robust induction of process models from time-series data" (PDF). In: Proceedings of the 20th International Conference on Machine Learning (ICML-03) (pp. 432-439).
  • QUOTE: … we defined the task of inductive process modeling. This paradigm revolves around a novel class of quantitative process models and their construction from time-series data. Process models are explanatory in that they account for observations in terms of interactions among unobserved processes, which in turn make contact with generic background knowledge. Inductive process modeling constitutes a new paradigm for computational scientific discovery that seems especially appropriate for integrative fields like Earth science, but it is relevant to any discipline that utilizes quantitative models of dynamic systems.

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