Post Reopened by Raphael
3 deleted 1204 characters in body
source | link

I'm studying Bayesian networks and want to clarify a couple of things with people who are more knowledgable in the area than me.

As far as I understand it, a Bayesian network (BN) is a directed acyclic graph (DAG) that encodes conditional dependencies between random variables. The graph is drawn in such a way that the the distribution (dictated by a conditional probability table (CPT)) of a random variable conditioned on its parents is independent of all other random variables. I'm assuming that, by definition, both the structure (nodes and edges of the DAG) and the entries of the CPT in a BN assumed to be fixed in time.

Now, I'm wondering about the distinction between BNs and Dynamic BNs (DBNs)., specifically, where the dynamic term in a DBN arises from:

  1. Is both the structure (nodes and edges of the DAG) and the entries of the CPT in a BN assumed to be fixed?

  2. (i). What is dynamic about a DBN? Does this mean that the conditional dependencies between variables are time-varying?

    (ii). A related question to 2(i): If both the structure of the DAG and the CPT probabilities are assumed to be time-varying in a DBN, is a BN with a fixed structure (DAG) but time-varying probabilities also considered a DBN? Does this type of 'DBN' have a name?

  3. Finally, there is a notion of what is known about a BN. I'm attempting to classify problem types and list them in increasing computational difficulty (that is, performing statistical inference on the problem). I'm wondering if this is a correct classification.

    (i) For BNs, problems of increasing difficulty are:

    • BN with a known static (not time-varying) structure and static probabilities
    • BN with a static structure and static probabilities -- known structure, unknown probabilities
    • BN with a static structure and static probabilities -- unknown structure, unknown probabilities

    (ii) For DBNs:

    • DBN with a known static structure and dynamic probabilities
    • DBN with a static structure and dynamic probabilities -- known structure, unknown probabilities
    • DBN with a static structure and dynamic probabilities -- unknown structure, unknown probabilities
    • DBN with a dynamic structure and dynamic probabilities -- known structure, unknown probabilities
    • DBN with a dynamic structure and dynamic probabilities -- unknown structure, unknown probabilities

Does this mean that the structure AND conditional dependencies between variables are time-varying? If so, is a BN with a fixed structure (DAG) but time-varying probabilities also considered a DBN (does this type of 'DBN' have a name)?

I'm not sure if what I've said is correct. Please let me know if I went wrong anywhere or if there is a better way of thinking about this.

I'm studying Bayesian networks and want to clarify a couple of things with people who are more knowledgable in the area than me.

As far as I understand it, a Bayesian network (BN) is a directed acyclic graph (DAG) that encodes conditional dependencies between random variables. The graph is drawn in such a way that the the distribution (dictated by a conditional probability table (CPT)) of a random variable conditioned on its parents is independent of all other random variables.

Now, I'm wondering about the distinction between BNs and Dynamic BNs (DBNs).

  1. Is both the structure (nodes and edges of the DAG) and the entries of the CPT in a BN assumed to be fixed?

  2. (i). What is dynamic about a DBN? Does this mean that the conditional dependencies between variables are time-varying?

    (ii). A related question to 2(i): If both the structure of the DAG and the CPT probabilities are assumed to be time-varying in a DBN, is a BN with a fixed structure (DAG) but time-varying probabilities also considered a DBN? Does this type of 'DBN' have a name?

  3. Finally, there is a notion of what is known about a BN. I'm attempting to classify problem types and list them in increasing computational difficulty (that is, performing statistical inference on the problem). I'm wondering if this is a correct classification.

    (i) For BNs, problems of increasing difficulty are:

    • BN with a known static (not time-varying) structure and static probabilities
    • BN with a static structure and static probabilities -- known structure, unknown probabilities
    • BN with a static structure and static probabilities -- unknown structure, unknown probabilities

    (ii) For DBNs:

    • DBN with a known static structure and dynamic probabilities
    • DBN with a static structure and dynamic probabilities -- known structure, unknown probabilities
    • DBN with a static structure and dynamic probabilities -- unknown structure, unknown probabilities
    • DBN with a dynamic structure and dynamic probabilities -- known structure, unknown probabilities
    • DBN with a dynamic structure and dynamic probabilities -- unknown structure, unknown probabilities

I'm not sure if what I've said is correct. Please let me know if I went wrong anywhere or if there is a better way of thinking about this.

I'm studying Bayesian networks and want to clarify a couple of things with people who are more knowledgable in the area than me.

As far as I understand it, a Bayesian network (BN) is a directed acyclic graph (DAG) that encodes conditional dependencies between random variables. The graph is drawn in such a way that the the distribution (dictated by a conditional probability table (CPT)) of a random variable conditioned on its parents is independent of all other random variables. I'm assuming that, by definition, both the structure (nodes and edges of the DAG) and the entries of the CPT in a BN assumed to be fixed in time.

Now, I'm wondering about the distinction between BNs and Dynamic BNs (DBNs), specifically, where the dynamic term in a DBN arises from:

Does this mean that the structure AND conditional dependencies between variables are time-varying? If so, is a BN with a fixed structure (DAG) but time-varying probabilities also considered a DBN (does this type of 'DBN' have a name)?

I'm not sure if what I've said is correct. Please let me know if I went wrong anywhere or if there is a better way of thinking about this.

    Post Closed as "unclear what you're asking" by Raphael
2 edited tags
| link
1
source | link

Difference between Bayesian Networks and Dynamic Bayesian Networks

I'm studying Bayesian networks and want to clarify a couple of things with people who are more knowledgable in the area than me.

As far as I understand it, a Bayesian network (BN) is a directed acyclic graph (DAG) that encodes conditional dependencies between random variables. The graph is drawn in such a way that the the distribution (dictated by a conditional probability table (CPT)) of a random variable conditioned on its parents is independent of all other random variables.

Now, I'm wondering about the distinction between BNs and Dynamic BNs (DBNs).

  1. Is both the structure (nodes and edges of the DAG) and the entries of the CPT in a BN assumed to be fixed?

  2. (i). What is dynamic about a DBN? Does this mean that the conditional dependencies between variables are time-varying?

    (ii). A related question to 2(i): If both the structure of the DAG and the CPT probabilities are assumed to be time-varying in a DBN, is a BN with a fixed structure (DAG) but time-varying probabilities also considered a DBN? Does this type of 'DBN' have a name?

  3. Finally, there is a notion of what is known about a BN. I'm attempting to classify problem types and list them in increasing computational difficulty (that is, performing statistical inference on the problem). I'm wondering if this is a correct classification.

    (i) For BNs, problems of increasing difficulty are:

    • BN with a known static (not time-varying) structure and static probabilities
    • BN with a static structure and static probabilities -- known structure, unknown probabilities
    • BN with a static structure and static probabilities -- unknown structure, unknown probabilities

    (ii) For DBNs:

    • DBN with a known static structure and dynamic probabilities
    • DBN with a static structure and dynamic probabilities -- known structure, unknown probabilities
    • DBN with a static structure and dynamic probabilities -- unknown structure, unknown probabilities
    • DBN with a dynamic structure and dynamic probabilities -- known structure, unknown probabilities
    • DBN with a dynamic structure and dynamic probabilities -- unknown structure, unknown probabilities

I'm not sure if what I've said is correct. Please let me know if I went wrong anywhere or if there is a better way of thinking about this.