12,690 research outputs found
Maximum Persistency via Iterative Relaxed Inference with Graphical Models
We consider the NP-hard problem of MAP-inference for undirected discrete
graphical models. We propose a polynomial time and practically efficient
algorithm for finding a part of its optimal solution. Specifically, our
algorithm marks some labels of the considered graphical model either as (i)
optimal, meaning that they belong to all optimal solutions of the inference
problem; (ii) non-optimal if they provably do not belong to any solution. With
access to an exact solver of a linear programming relaxation to the
MAP-inference problem, our algorithm marks the maximal possible (in a specified
sense) number of labels. We also present a version of the algorithm, which has
access to a suboptimal dual solver only and still can ensure the
(non-)optimality for the marked labels, although the overall number of the
marked labels may decrease. We propose an efficient implementation, which runs
in time comparable to a single run of a suboptimal dual solver. Our method is
well-scalable and shows state-of-the-art results on computational benchmarks
from machine learning and computer vision.Comment: Reworked version, submitted to PAM
Practical Bayesian Modeling and Inference for Massive Spatial Datasets On Modest Computing Environments
With continued advances in Geographic Information Systems and related
computational technologies, statisticians are often required to analyze very
large spatial datasets. This has generated substantial interest over the last
decade, already too vast to be summarized here, in scalable methodologies for
analyzing large spatial datasets. Scalable spatial process models have been
found especially attractive due to their richness and flexibility and,
particularly so in the Bayesian paradigm, due to their presence in hierarchical
model settings. However, the vast majority of research articles present in this
domain have been geared toward innovative theory or more complex model
development. Very limited attention has been accorded to approaches for easily
implementable scalable hierarchical models for the practicing scientist or
spatial analyst. This article is submitted to the Practice section of the
journal with the aim of developing massively scalable Bayesian approaches that
can rapidly deliver Bayesian inference on spatial process that are practically
indistinguishable from inference obtained using more expensive alternatives. A
key emphasis is on implementation within very standard (modest) computing
environments (e.g., a standard desktop or laptop) using easily available
statistical software packages without requiring message-parsing interfaces or
parallel programming paradigms. Key insights are offered regarding assumptions
and approximations concerning practical efficiency.Comment: 20 pages, 4 figures, 2 table
Efficient Semidefinite Branch-and-Cut for MAP-MRF Inference
We propose a Branch-and-Cut (B&C) method for solving general MAP-MRF
inference problems. The core of our method is a very efficient bounding
procedure, which combines scalable semidefinite programming (SDP) and a
cutting-plane method for seeking violated constraints. In order to further
speed up the computation, several strategies have been exploited, including
model reduction, warm start and removal of inactive constraints.
We analyze the performance of the proposed method under different settings,
and demonstrate that our method either outperforms or performs on par with
state-of-the-art approaches. Especially when the connectivities are dense or
when the relative magnitudes of the unary costs are low, we achieve the best
reported results. Experiments show that the proposed algorithm achieves better
approximation than the state-of-the-art methods within a variety of time
budgets on challenging non-submodular MAP-MRF inference problems.Comment: 21 page
Patterns of Scalable Bayesian Inference
Datasets are growing not just in size but in complexity, creating a demand
for rich models and quantification of uncertainty. Bayesian methods are an
excellent fit for this demand, but scaling Bayesian inference is a challenge.
In response to this challenge, there has been considerable recent work based on
varying assumptions about model structure, underlying computational resources,
and the importance of asymptotic correctness. As a result, there is a zoo of
ideas with few clear overarching principles.
In this paper, we seek to identify unifying principles, patterns, and
intuitions for scaling Bayesian inference. We review existing work on utilizing
modern computing resources with both MCMC and variational approximation
techniques. From this taxonomy of ideas, we characterize the general principles
that have proven successful for designing scalable inference procedures and
comment on the path forward
Scalable Semidefinite Relaxation for Maximum A Posterior Estimation
Maximum a posteriori (MAP) inference over discrete Markov random fields is a
fundamental task spanning a wide spectrum of real-world applications, which is
known to be NP-hard for general graphs. In this paper, we propose a novel
semidefinite relaxation formulation (referred to as SDR) to estimate the MAP
assignment. Algorithmically, we develop an accelerated variant of the
alternating direction method of multipliers (referred to as SDPAD-LR) that can
effectively exploit the special structure of the new relaxation. Encouragingly,
the proposed procedure allows solving SDR for large-scale problems, e.g.,
problems on a grid graph comprising hundreds of thousands of variables with
multiple states per node. Compared with prior SDP solvers, SDPAD-LR is capable
of attaining comparable accuracy while exhibiting remarkably improved
scalability, in contrast to the commonly held belief that semidefinite
relaxation can only been applied on small-scale MRF problems. We have evaluated
the performance of SDR on various benchmark datasets including OPENGM2 and PIC
in terms of both the quality of the solutions and computation time.
Experimental results demonstrate that for a broad class of problems, SDPAD-LR
outperforms state-of-the-art algorithms in producing better MAP assignment in
an efficient manner.Comment: accepted to International Conference on Machine Learning (ICML 2014
Arriving on time: estimating travel time distributions on large-scale road networks
Most optimal routing problems focus on minimizing travel time or distance
traveled. Oftentimes, a more useful objective is to maximize the probability of
on-time arrival, which requires statistical distributions of travel times,
rather than just mean values. We propose a method to estimate travel time
distributions on large-scale road networks, using probe vehicle data collected
from GPS. We present a framework that works with large input of data, and
scales linearly with the size of the network. Leveraging the planar topology of
the graph, the method computes efficiently the time correlations between
neighboring streets. First, raw probe vehicle traces are compressed into pairs
of travel times and number of stops for each traversed road segment using a
`stop-and-go' algorithm developed for this work. The compressed data is then
used as input for training a path travel time model, which couples a Markov
model along with a Gaussian Markov random field. Finally, scalable inference
algorithms are developed for obtaining path travel time distributions from the
composite MM-GMRF model. We illustrate the accuracy and scalability of our
model on a 505,000 road link network spanning the San Francisco Bay Area
Graphical model-based approaches to target tracking in sensor networks: an overview of some recent work and challenges
Sensor Networks have provided a technology base for distributed target tracking applications among others. Conventional centralized approaches to the problem lack scalability in such a scenario where a large number of sensors provide measurements simultaneously under a possibly non-collaborating environment. Therefore research efforts have focused on scalable, robust, and distributed algorithms for the inference tasks related to target tracking, i.e. localization, data association, and track maintenance. Graphical models provide a rigorous tool for development of such algorithms by modeling the information structure of a given task and providing distributed solutions through message passing algorithms. However, the limited communication capabilities and energy resources of sensor networks pose the additional difculty of considering the tradeoff between the communication cost and the accuracy of the result. Also the network structure and the information structure are different aspects of the problem and a mapping between the physical entities and the information structure is needed. In this paper we discuss available formalisms based on graphical models for target tracking in sensor networks with a focus on the aforementioned issues. We point out additional constraints that must be asserted in order to achieve further insight and more effective solutions
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