Probabilistic soft logic

PSL
Developer(s)	LINQS Lab
Initial release	September 23, 2011 (2011-09-23)
Stable release	2.2.2 / May 20, 2020 (2020-05-20)
Repository	github.com/linqs/psl
Written in	Java
Platform	Linux, macOS, Windows
Type	Machine Learning Statistical relational learning
License	Apache License 2.0
Website	psl.linqs.org

Probabilistic Soft Logic (PSL) is a SRL framework for modeling probabilistic and relational domains . It is applicable to a variety of machine learning problems, such as collective classification, entity resolution, link prediction, and ontology alignment. PSL combines the strengths of two powerful theories – first-order logic, with its ability to succinctly represent complex phenomena, and probabilistic graphical models, which capture the uncertainty and incompleteness inherent in real-world knowledge. More specifically, PSL uses "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 MAP state). The "softening" of the logical formulas allows us to cast the inference problem as a polynomial-time optimization, rather than a (much more difficult NP-hard) combinatorial one.

Description

In recent years there has been a rise in the approaches that combine graphical models and first-order logic to allow the development of complex probabilistic models with relational structures. A notable example of such approaches is Markov logic networks (MLNs). Like MLNs PSL is a modelling language (with an accompanying implementation) for learning and predicting in relational domains. Unlike MLNs, PSL uses soft truth values for predicates in an interval between [0,1]. This allows for the underlying inference to be solved quickly as a convex optimization problem. This is useful in problems such as collective classification, link prediction, social network modelling, and object identification/entity resolution/record linkage.

Semantics

HL-MRF

A PSL program defines a family of probabilistic probabilistic graphical models 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). A HL-MRF determines a density function over a set of continuous variables $\mathbf {y} =(y_{1},\cdots ,y_{n})$ with joint domain $[0,1]^{n}$ using set of evidence $\mathbf {x} =(x_{1},\cdots ,x_{m})$, weights $\mathbf {w} =(w_{1},\cdots ,w_{m})$, and potential functions $\mathbf {\phi } =(\phi _{1},\cdots ,\phi _{k})$ of the form $\mathbf {\phi _{i}(\mathbf {x} ,\mathbf {y} )} =\max(\ell _{i}(\mathbf {x} ,\mathbf {y} ),0)^{d_{i}}$ where $\ell _{i}$ is a linear function and $d_{i}\in \{1,2\}$. The conditional distribution of $\mathbf {y}$ given the observed data $\mathbf {x}$ is defined as:
$P(\mathbf {y} |\mathbf {x} )={\frac {1}{Z(\mathbf {y} )}}\exp(\sum _{i=1}^{k}w_{i}\phi _{i}(\mathbf {x} ,\mathbf {y} ))$

This density is a Logarithmically convex function, and thus finding a Maximum a posteriori estimation of the joint state of $\mathbf {y}$ is a convex problem. This useful property allows inference in PSL to be solvable in polynomial-time.

See also

• Statistical relational learning
• Probabilistic logic network
• Markov logic network
• Fuzzy logic

External links

• Probabilistic soft logic main web page
• Official PSL implementation
• A list of publications about PSL
• Video lectures about PSL on Youtube