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				|  | @ -17,7 +17,7 @@ | |||
|       "source": [ | ||||
|         "A `BayesNet` in GTSAM represents a directed graphical model, specifically the result of running sequential variable elimination (like Cholesky or QR factorization) on a `FactorGraph`.\n", | ||||
|         "\n", | ||||
|         "It is essentially a collection of `Conditional` objects, ordered according to the elimination order. Each conditional represents $P(\text{variable} | \text{parents})$, where the parents are variables that appear later in the elimination ordering.\n", | ||||
|         "It is essentially a collection of `Conditional` objects, ordered according to the elimination order. Each conditional represents $P(\\text{variable} | \\text{parents})$, where the parents are variables that appear later in the elimination ordering.\n", | ||||
|         "\n", | ||||
|         "A Bayes net represents the joint probability distribution as a product of conditional probabilities stored in the net:\n", | ||||
|         "\n", | ||||
|  |  | |||
|  | @ -15,7 +15,7 @@ | |||
|         "id": "bayestree_desc_md" | ||||
|       }, | ||||
|       "source": [ | ||||
|         "A `BayesTree` is a graphical model that represents the result of multifrontal variable elimination on a `FactorGraph`. It is a tree structure where each node is a 'clique' containing a set of conditional distributions $P(\text{Frontals} | \text{Separator})$.\n", | ||||
|         "A `BayesTree` is a graphical model that represents the result of multifrontal variable elimination on a `FactorGraph`. It is a tree structure where each node is a 'clique' containing a set of conditional distributions $P(\\text{Frontals} | \\text{Separator})$.\n", | ||||
|         "\n", | ||||
|         "Each clique k contains a conditional $P(F_k∣S_k)$, where $F_k$ are frontal variables and $S_k$ are separator variables. The joint probability distribution encoded by the Bayes tree is given by the product of all clique conditionals:\n", | ||||
|         "\n", | ||||
|  |  | |||
|  | @ -19,7 +19,7 @@ | |||
|         "\n", | ||||
|         "Key differences from related structures:\n", | ||||
|         "*   **vs. EliminationTree:** Junction tree nodes can represent the elimination of multiple variables simultaneously (a 'frontal' set), whereas elimination tree nodes typically represent single variable eliminations.\n", | ||||
|         "*   **vs. BayesTree:** A JunctionTree node contains the original factors associated with the variables being eliminated in that clique. A BayesTree node contains the *result* of eliminating those factors (i.e., a conditional density $P(\text{Frontals} | \text{Separator})$).\n", | ||||
|         "*   **vs. BayesTree:** A JunctionTree node contains the original factors associated with the variables being eliminated in that clique. A BayesTree node contains the *result* of eliminating those factors (i.e., a conditional density $P(\\text{Frontals} | \\text{Separator})$).\n", | ||||
|         "\n", | ||||
|         "Like `EliminationTree`, direct manipulation of `JunctionTree` objects in Python is uncommon. It's primarily an internal structure used by `eliminateMultifrontal` when producing a `BayesTree`." | ||||
|       ] | ||||
|  |  | |||
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