NIPS Poster Testing Unfaithful Gaussian Graphical Models

Poster

Testing Unfaithful Gaussian Graphical Models

De Wen Soh · Sekhar C Tatikonda

Level 2, room 210D

[ Abstract ]

Abstract: The global Markov property for Gaussian graphical models ensures graph separation implies conditional independence. Specifically if a node set

S

$S$ graph separates nodes

u

$u$ and

v

$v$ then

X_{u}

$X_u$ is conditionally independent of

X_{v}

$X_v$ given

X_{S}

$X_S$ . The opposite direction need not be true, that is,

X_{u} ⊥ X_{v} ∣ X_{S}

$X_u \perp X_v \mid X_S$ need not imply

S

$S$ is a node separator of

u

$u$ and

v

$v$ . When it does, the relation

X_{u} ⊥ X_{v} ∣ X_{S}

$X_u \perp X_v \mid X_S$ is called faithful. In this paper we provide a characterization of faithful relations and then provide an algorithm to test faithfulness based only on knowledge of other conditional relations of the form

X_{i} ⊥ X_{j} ∣ X_{S}

$X_i \perp X_j \mid X_S$ .

Live content is unavailable. Log in and register to view live content