Lifted Probabilistic Inference for Asymmetric Graphical Models

Abstract

Lifted probabilistic inference algorithms have been successfully applied to a large number of symmetric graphical models. Unfortunately, the majority of real-world graphical models is asymmetric. This is even the case for relational representations when evidence is given. Therefore, more recent work in the community moved to making the models symmetric and then applying existing lifted inference algorithms. However, this approach has two shortcomings. First, all existing over-symmetric approximations require a relational representation such as Markov logic networks. Second, the induced symmetries often change the distribution significantly, making the computed probabilities highly biased. We present a framework for probabilistic sampling-based inference that only uses the induced approximate symmetries to propose steps in a Metropolis-Hastings style Markov chain. The framework, therefore, leads to improved probability estimates while remaining unbiased. Experiments demonstrate that the approach outperforms existing MCMC algorithms.

Causal lifting and link prediction

“…We commence our discussion by presenting one of our key contributions: Causal lifting , a general concept of independent interest beyond link prediction. Causal lifting is a causal extension to the associational definition of lifting in probabilistic inference [26,46]. Here, instead of defining symmetries in the associational distribution, we define them in different layers of Pearl’s Causal Hierarchy (associational, interventional and counterfactual).…”

“…Definition 3.1 is used in probabilistic inference algorithms [26,46] to avoid unnecessary computations: one can replace the need to estimate false∣Gfalse∣ quantities in the marginal probability ∑g∈GPfalse(X=g⋅xfalse) by estimating a single quantity Pfalse(X=xfalse). While in probabilistic inference we are interested in efficiently computing associational distributions, in causal inference our main challenge is to identify a causal quantity : without causal lifting, our data may not be enough to answer the causal query.…”

“…Associational lifting[26,46]). Let X be our random variable of interest and G a group where • is the left action of G onto supp(X) (i.e.…”

Excursions in First-Order Logic and Probability: Infinitely Many Random Variables, Continuous Distributions, Recursive Programs and Beyond

“…Although decision-theoretic [30] and probabilistic-planning languages allow the modelling of actions and effects [59], they are neither logics (in allowing for arbitrary connectives and quantifiers) nor general models of actions in terms of being able to reason about past and future histories. Relational probabilistic models [57], including dynamic ones [17], offer some logical features (such as clausal reasoning), but are not usually embedded in a theory of action and so do not provide a framework to reason about unbounded sequences of actions. This is not to say that such a framework could not designed starting from one of the more practical options -and indeed, there are many that come close [48] -but just that the search for a general and restriction-free option is still ongoing.…”