Probabilistic logic programming for hybrid relational domains

Abstract

We introduce a probabilistic language and an efficient inference algorithm based on distributional clauses for static and dynamic inference in hybrid relational domains. Static inference is based on sampling, where the samples represent (partial) worlds (with discrete and continuous variables). Furthermore, we use backward reasoning to determine which facts should be included in the partial worlds. For filtering in dynamic models we combine the static inference algorithm with particle filters and guarantee that the previous partial samples can be safely forgotten, a condition that does not hold in most logical filtering frameworks. Experiments show that the proposed framework can outperform classic sampling methods for static and dynamic inference and that it is promising for robotics and vision applications. In addition, it provides the correct results in domains in which most probabilistic programming languages fail.

Exact and Approximate Weighted Model Integration with Probability Density Functions Using Knowledge Compilation

“…For Q2, we compare Sampo to the inference algorithms of Distributional Clauses (DC) (Nitti, De Laet, andDe Raedt 2016) 3 , BLOG (Milch et al 2007) 4 and to Hybrid Probabilistic Model Counting (IHPMC) (Michels, Hommersom, and Lucas 2016) 5 . These are state-of-the-art probabilistic programming systems that all support first order logic as well as hybrid representations.…”

“…In order to evaluate Sampo, we chose benchmarks from (Nitti, De Laet, and De Raedt 2016) and (Michels, Hommersom, and Lucas 2016), which were stated to be hardest in terms of query complexity. We show our results in Figures 2 and 3.…”

“…Secondly, for what concerns approximate inference, we have the sampling approaches in Distributional Clauses by Nitti, De Laet, and De Raedt 2016) and BLOG by (Milch et al 2007), which we have already discussed in section 6 and which both deploy importance sampling in order to sample from probability distributions and densities alike, combined with likelihood weighting.…”

cplint on SWISH: Probabilistic Logical Inference with a Web Browser

“…A semantics to such programs was given independently in [GTK + 11] and [IRR12]. In [NDLDR16] the semantics of these programs, called Hybrid Probabilistic Logic Programs (HPLP), is defined by means of a stochastic generalization ST p of the T p operator that applies to continuous variables the sampling interpretation of the distribution seman-tics: ST p is applied to interpretations that contain ground atoms (as in standard logic programming) and terms of the form t = v where t is a term indicating a continuous random variable and v is a real number. If the body of a clause is true in an interpretation I, ST p(I) will contain a sample from the head.…”

“…If the evidence is on an atom defining another continuous random variable, the definition of conditional probability cannot be applied, as the probability of the evidence would be 0 and so the fraction would be undefined. This problem is resolved in [NDLDR16] by providing a definition using limits.…”