Probabilistic soft logic: Difference between revisions

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Revision as of 15:24, 31 July 2021

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A PSL program defines a family of probabilistic [[graphical model]]s that are parameterized by data.

More specifically, the family of graphical models it defines belongs to a special class of [[Markov random field]] known as a Hinge-Loss Markov Field (HL-MRF).

An HL-MRF determines a density function over a set of continuous variables <math>\mathbf{y} = (y_1, \cdots , y_n)</math> with joint ___domain <math>[0, 1]^n</math> using set of evidence <math>\mathbf{x} = (x_1, \cdots , x_m)</math>, weights <math>\mathbf{w} = (w_1, \cdots , w_mw_k)</math>, and potential functions <math>\mathbf{\phi} = (\phi_1, \cdots , \phi_k)</math> of the form <math>\mathbf{\phi_i (\mathbf{x}, \mathbf{y})} = \max(\ell_i (\mathbf{x}, \mathbf{y}), 0)^{d_i}</math> where <math>\ell_i</math> is a linear function and <math>d_i \in \{1,2\}</math>.

The conditional distribution of <math>\mathbf{y}</math> given the observed data <math>\mathbf{x}</math> is defined as