Lower complexity bounds for lifted inference

Lower complexity bounds for lifted inference

One of the big challenges in the development of probabilistic relational (or probabilistic logical) modeling and learning frameworks is the design of inference techniques that operate on the level of the abstract model representation language, rather than on the level of ground, propositional instances of the model. Numerous approaches for such “lifted inference” techniques have been proposed. ...

Conditional Lower Bounds on the Complexity of Probabilistic Inference

The Inference problem in probabilistic networks (given a stochastic variable V , what is the posterior probability that V = v given evidence e?) has been proven to be intractable; in fact, has a PP-complete decision variant [17]. The currently most efficient algorithms for this problem are all exponential in the treewidth of the moralised graph of the network. We prove, using a recent result of...

Tight Lower Bounds for Homology Inference

The homology groups of a manifold are important topological invariants that provide an algebraic summary of the manifold. These groups contain rich topological information, for instance, about the connected components, holes, tunnels and sometimes the dimension of the manifold. In earlier work [1], we have considered the statistical problem of estimating the homology of a manifold from noiseles...

Some Lower Bounds for Estrada Index

Lower complexity bounds for interpolation algorithms

We introduce and discuss a new computational model for Hermite–Lagrange interpolation by nonlinear classes of polynomial interpolants. We distinguish between an interpolation problem and an algorithm that solves it. Our model includes also coalescence phenomena and captures a large variety of known Lagrange-Hermite interpolation problems and algorithms. Like in traditional Hermite–Lagrange inte...