Model reductions for inference: generality of pairwise, binary, and planar factor graphs.

We offer a solution to the problem of efficiently translating algorithms between different types of discrete statistical model. We investigate the expressive power of three classes of model-those with binary variables, with pairwise factors, and with planar topology-as well as their four intersections. We formalize a notion of "simple reduction" for the problem of inferring marginal probabilities and consider whether it is possible to "simply reduce" marginal inference from general discrete factor graphs to factor graphs in each of these seven subclasses. We characterize the reducibility of each class, showing in particular that the class of binary pairwise factor graphs is able to simply reduce only positive models. We also exhibit a continuous "spectral reduction" based on polynomial interpolation, which overcomes this limitation. Experiments assess the performance of standard approximate inference algorithms on the outputs of our reductions.

Mobilization distance for upheaval buckling of shallowly buried pipelines

Buried pipelines may be subject to upheaval buckling because of thermally induced compressive stresses. As the buckling load of a strut decreases with increasing out of straightness, not only the maximum available resistance from the soil cover, but also the movement of the pipeline required to mobilize this are important factors in design. This paper will describe the results of 15 full-scale laboratory tests that have been carried out on pipeline uplift in both sandy and rocky backfills. The cover to diameter ratio ranged from 0.1 to 6. The results show that mobilization distance exhibits a linear relationship with H=D ratio and that the postpeak uplift force-displacement response can be accurately modeled using existing models. A tentative design approach is suggested; the maximum available uplift resistance may be reliably predicted from the postpeak response, and the mobilization distance may be predicted using the relationships described in this paper. © 2012 American Society of Civil Engineers.

Low-rank optimization for distance matrix completion

This paper addresses the problem of low-rank distance matrix completion. This problem amounts to recover the missing entries of a distance matrix when the dimension of the data embedding space is possibly unknown but small compared to the number of considered data points. The focus is on high-dimensional problems. We recast the considered problem into an optimization problem over the set of low-rank positive semidefinite matrices and propose two efficient algorithms for low-rank distance matrix completion. In addition, we propose a strategy to determine the dimension of the embedding space. The resulting algorithms scale to high-dimensional problems and monotonically converge to a global solution of the problem. Finally, numerical experiments illustrate the good performance of the proposed algorithms on benchmarks. © 2011 IEEE.

From subspace learning to distance learning: A geometrical optimization approach

In this paper, we adopt a differential-geometry viewpoint to tackle the problem of learning a distance online. As this problem can be cast into the estimation of a fixed-rank positive semidefinite (PSD) matrix, we develop algorithms that exploits the rich geometry structure of the set of fixed-rank PSD matrices. We propose a method which separately updates the subspace of the matrix and its projection onto that subspace. A proper weighting of the two iterations enables to continuously interpolate between the problem of learning a subspace and learning a distance when the subspace is fixed. © 2009 IEEE.