Probability graph model (PGM) learning notes (5)-template Model

Template models mainly includes templatevariables and language ).

 

The template model can be applied to an infinitely large Bayesian Network;

The template variable is a variable that has been reused multiple times:

Such as location (time), genotype (characters), tags (pixels), difficulty (course), and so on.

 

Language is used to describe how template variables inherit Dependencies from templates.

There are many languages, and various languages have various application conditions to construct a large number of very useful languages.

 

The template model can be described in a compact manner.

1. Repetition in time series (such as dynamic Bayesian Network Dynamic Bayesian Networks ).

2. Repetition of Object Relationships (directed or undirected)

 

 

Time series model (temporal models)

The chain rule can be used to describe a time series model:

 

To simplify the model, we make the following two assumptions:

 

Markov hypothesis (Markov assumption-forgetting hypothesis)

Once you know the current status, do not care about the previous status:

This assumption is often not reasonable and can be corrected by two means:

1. Add a variable describing the status.

2. Increase the correlation with the previous state (semi-Markov Model ).

 

Time invariance hypothesis

Changes Between system states do not depend on time:

This assumption is often unreasonable, such as the transportation system.

 

Template transition model)

Take the transportation system as an example.

The left side shows the t time status, and the right side shows the t + 1 time status. This model shows how the traffic system changes dynamically over time, with variables such as weather, vehicle speed, vehicle location, and sensor failure. The OBS in the lower-right corner is the sensor observation volume.

The entire model is represented by the chain rule:

Observe the image and find that there is a dependency between different statuses (such as failure-obs) or between different statuses (such as failure-failure) at the same time. Why? Because failure '-obs' is instantaneous and does not need to be converted by time.

In addition, why is there no obs on the left? Because OBS in the previous state does not affect any variables in the next state.

The figure shows several typical edges:

Persistenceedges: location-location'

Intra-timeslice edges: Failure '-obs'

Inter-timeslice edges: location-location'

 

With the above foundation, we can expand the ground Bayesian Network (also a dynamic Bayesian Network ):

 

Characteristics of Dynamic Bayesian Network

1. The network structure is the same in each timeslice.

2. The T-piece network is only related to the t + 1-piece network of the T-1.

3. DBN is a compact representation of any length of time series structure distribution.

 

Hidden Markov Model (Hidden Markov models, hmm)

For more details, see my previous blog

Hidden Markov Model (HMM) and Its Implementation

The hmm-based robot positioning system is shown as follows:

 

The core component is the middle part of the Red Circle.

 

-Hmm is a subclass of DBN.

-From the conditional probability of random variables, the structure of HMM is very sparse (compared with general DBN)

-Hmm is widely used in the speech recognition field.

 

Plate Models)

The reason is that it is mainly used to model repeated variables: "like a stack of the same Board (And the reason for calling it a plate is because the intuition ofthis is a stack of identical plates, that's kind of where the idea comes from, fora plate model.)"

 

The Board draws a small box around the output variable and writes the index of the output variable in the lower right corner of the box. For example, the duplicate score model is indexed by student s:

 

 

Nested Plates)

Nested panels think that the inner layer must be indexed by the outer layer.

 

 

Overlapping plates)

For a board model, the index of its parent node must be a subset of the template variable index.

That is, the structure of grades (S, C) ---> honor (s) cannot be expressed.

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Probability graph model (PGM) learning notes (5)-template Model