| 12 | | * '''First-order Markov Model (FOMM)''': In FOMMs the probability of the next event only depends on the last observed events. Using a GUI application as example, this means that the next click of a user only depends on the last click. All previous click do not impact the probability. The advantage of FOMMs is their low complexity. The drawback is that such models are not well suited to even model rather simple preconditions. As an example, consider a form where you need to check two boxes: that you accept a privacy agreement and that you accept the terms and conditions of a product. If only one click is remembered, it is impossible to know if both fields have been checked. |
| 13 | | * '''Higher-order Markov Model (HOMM)''': In HOMMs the probability of the next event only depends on the ''k'' observed events, where ''k'' is a positive integer known as the ''Markov order'' of the HOMM. Using a GUI application as example, this means that the next click of a user only depends on the last ''k'' clicks. All clicks that are at least ''k+1'' clicks ago do not impact the probability. The advantages and drawbacks of the HOMMs are the opposite of the FOMMs. The complexity is exponential in ''k'' and can easily get out of hand |
| 14 | | * '''Prediction by Partial Match Models (PPMM)''': '''''TODO''''' |
| 15 | | * '''Random Deterministic Finite Automata (RDFA)''': '''''TODO''''' |
| | 12 | * '''First-order Markov Model (FOMM)''': In FOMMs the probability of the next event only depends on the last observed events. Using a GUI application as example, this means that the next click of a user only depends on the last click. All previous click do not impact the probability. The advantages of FOMMs are their low complexity and high flexibility. With flexibility, we mean that a lot of scenarios have a positive probability in the FOMM, because only the last event impacts the probability. The drawback is that such models are not well suited to even model rather simple preconditions. As an example, consider a form where you need to check two boxes: that you accept a privacy agreement and that you accept the terms and conditions of a product. If only one click is remembered, it is impossible to know if both fields have been checked. |
| | 13 | * '''Higher-order Markov Model (HOMM)''': In HOMMs the probability of the next event only depends on the ''k'' observed events, where ''k'' is a positive integer known as the ''Markov order'' of the HOMM. Using a GUI application as example, this means that the next click of a user only depends on the last ''k'' clicks. All clicks that are at least ''k+1'' clicks ago do not impact the probability. The advantages and drawbacks of the HOMMs are the opposite of the FOMMs. The complexity is exponential in ''k'' and can easily get out of hand and the HOMMs are less flexible because they remember ''k'' events. On the other hand, if ''k'' clicks are remembered, it is possible to model pre-conditions that require up to ''k'' events to model. |
| | 14 | * '''Prediction by Partial Match Model (PPMM)''': PPMMs are a combination of Markov models with different Markov orders. In principle, a ''k_max'' order PPMM is a HOMM with Markov order ''k_max''. However, the PPMMs have an opt-out probability ''escape'', with which a lower Markov order is used. This is bounded by a minimal Markov order ''k_min'' for which we set the opt-out probability to zero. The PPMMs, therefore, combine the advantages and drawbacks of the FOMMs and HOMMs in terms of modelling of pre-conditions and flexibility. |
| | 15 | * '''Random Deterministic Finite Automata (RDFA)''': The RDFAs are a subtype of the FOMMs. They structure is the same as a FOMM, the difference lies in the calculation of the probabilities. In an RDFA, all possibly following symbols have the same probability. |
