Probabilistic soft logic: Difference between revisions

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'''Probabilistic Soft Logic (PSL)''' is a [[Statistical relational learning | statistical relational learning (SRL)]] framework for modeling probabilistic and relational domains.

<ref name=bach:jmlr17 />

It is applicable to a variety of [[machine learning]] problems, such as [[collective classification]], [[Record linkage | entity resolution]], [[link prediction]], and [[ontology alignment]].

PSL combines two tools: [[first-order logic]], with its ability to succinctly represent complex phenomena, and [[graphical model | probabilistic graphical models]], which capture the uncertainty and incompleteness inherent in real-world knowledge.

More specifically, PSL uses [[Fuzzy logic | "soft" logic]] as its logical component and [[Markov random fields]] as its statistical model.

PSL provides sophisticated inference techniques for finding the most likely answer (i.e. the [[Maximum_a_posteriori_estimation|maximum a posteriori (MAP)]] state).

The "softening" of the logical formulas makes inference a [[polynomial time]] operation rather than an [[NP-hardness | NP-hard]] operation.

== Description ==

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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

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<ref name=psl:repo>

{{cite web|url=https://github.com/linqs/psl|title=GitHub repository|website=[[GitHub]] |accessdate=26 March 2018}}

</ref>