259 research outputs found
Markov Network Structure Learning via Ensemble-of-Forests Models
Real world systems typically feature a variety of different dependency types
and topologies that complicate model selection for probabilistic graphical
models. We introduce the ensemble-of-forests model, a generalization of the
ensemble-of-trees model. Our model enables structure learning of Markov random
fields (MRF) with multiple connected components and arbitrary potentials. We
present two approximate inference techniques for this model and demonstrate
their performance on synthetic data. Our results suggest that the
ensemble-of-forests approach can accurately recover sparse, possibly
disconnected MRF topologies, even in presence of non-Gaussian dependencies
and/or low sample size. We applied the ensemble-of-forests model to learn the
structure of perturbed signaling networks of immune cells and found that these
frequently exhibit non-Gaussian dependencies with disconnected MRF topologies.
In summary, we expect that the ensemble-of-forests model will enable MRF
structure learning in other high dimensional real world settings that are
governed by non-trivial dependencies.Comment: 13 pages, 6 figure
Efficient Regularization of Squared Curvature
Curvature has received increased attention as an important alternative to
length based regularization in computer vision. In contrast to length, it
preserves elongated structures and fine details. Existing approaches are either
inefficient, or have low angular resolution and yield results with strong block
artifacts. We derive a new model for computing squared curvature based on
integral geometry. The model counts responses of straight line triple cliques.
The corresponding energy decomposes into submodular and supermodular pairwise
potentials. We show that this energy can be efficiently minimized even for high
angular resolutions using the trust region framework. Our results confirm that
we obtain accurate and visually pleasing solutions without strong artifacts at
reasonable run times.Comment: 8 pages, 12 figures, to appear at IEEE conference on Computer Vision
and Pattern Recognition (CVPR), June 201
Hierarchical Object Parsing from Structured Noisy Point Clouds
Object parsing and segmentation from point clouds are challenging tasks
because the relevant data is available only as thin structures along object
boundaries or other features, and is corrupted by large amounts of noise. To
handle this kind of data, flexible shape models are desired that can accurately
follow the object boundaries. Popular models such as Active Shape and Active
Appearance models lack the necessary flexibility for this task, while recent
approaches such as the Recursive Compositional Models make model
simplifications in order to obtain computational guarantees. This paper
investigates a hierarchical Bayesian model of shape and appearance in a
generative setting. The input data is explained by an object parsing layer,
which is a deformation of a hidden PCA shape model with Gaussian prior. The
paper also introduces a novel efficient inference algorithm that uses informed
data-driven proposals to initialize local searches for the hidden variables.
Applied to the problem of object parsing from structured point clouds such as
edge detection images, the proposed approach obtains state of the art parsing
errors on two standard datasets without using any intensity information.Comment: 13 pages, 16 figure
DPP-PMRF: Rethinking Optimization for a Probabilistic Graphical Model Using Data-Parallel Primitives
We present a new parallel algorithm for probabilistic graphical model
optimization. The algorithm relies on data-parallel primitives (DPPs), which
provide portable performance over hardware architecture. We evaluate results on
CPUs and GPUs for an image segmentation problem. Compared to a serial baseline,
we observe runtime speedups of up to 13X (CPU) and 44X (GPU). We also compare
our performance to a reference, OpenMP-based algorithm, and find speedups of up
to 7X (CPU).Comment: LDAV 2018, October 201
Lagrangian Relaxation for MAP Estimation in Graphical Models
We develop a general framework for MAP estimation in discrete and Gaussian
graphical models using Lagrangian relaxation techniques. The key idea is to
reformulate an intractable estimation problem as one defined on a more
tractable graph, but subject to additional constraints. Relaxing these
constraints gives a tractable dual problem, one defined by a thin graph, which
is then optimized by an iterative procedure. When this iterative optimization
leads to a consistent estimate, one which also satisfies the constraints, then
it corresponds to an optimal MAP estimate of the original model. Otherwise
there is a ``duality gap'', and we obtain a bound on the optimal solution.
Thus, our approach combines convex optimization with dynamic programming
techniques applicable for thin graphs. The popular tree-reweighted max-product
(TRMP) method may be seen as solving a particular class of such relaxations,
where the intractable graph is relaxed to a set of spanning trees. We also
consider relaxations to a set of small induced subgraphs, thin subgraphs (e.g.
loops), and a connected tree obtained by ``unwinding'' cycles. In addition, we
propose a new class of multiscale relaxations that introduce ``summary''
variables. The potential benefits of such generalizations include: reducing or
eliminating the ``duality gap'' in hard problems, reducing the number or
Lagrange multipliers in the dual problem, and accelerating convergence of the
iterative optimization procedure.Comment: 10 pages, presented at 45th Allerton conference on communication,
control and computing, to appear in proceeding
Complexity of Discrete Energy Minimization Problems
Discrete energy minimization is widely-used in computer vision and machine
learning for problems such as MAP inference in graphical models. The problem,
in general, is notoriously intractable, and finding the global optimal solution
is known to be NP-hard. However, is it possible to approximate this problem
with a reasonable ratio bound on the solution quality in polynomial time? We
show in this paper that the answer is no. Specifically, we show that general
energy minimization, even in the 2-label pairwise case, and planar energy
minimization with three or more labels are exp-APX-complete. This finding rules
out the existence of any approximation algorithm with a sub-exponential
approximation ratio in the input size for these two problems, including
constant factor approximations. Moreover, we collect and review the
computational complexity of several subclass problems and arrange them on a
complexity scale consisting of three major complexity classes -- PO, APX, and
exp-APX, corresponding to problems that are solvable, approximable, and
inapproximable in polynomial time. Problems in the first two complexity classes
can serve as alternative tractable formulations to the inapproximable ones.
This paper can help vision researchers to select an appropriate model for an
application or guide them in designing new algorithms.Comment: ECCV'16 accepte
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