39,738 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
Discriminative Training of Deep Fully-connected Continuous CRF with Task-specific Loss
Recent works on deep conditional random fields (CRF) have set new records on
many vision tasks involving structured predictions. Here we propose a
fully-connected deep continuous CRF model for both discrete and continuous
labelling problems. We exemplify the usefulness of the proposed model on
multi-class semantic labelling (discrete) and the robust depth estimation
(continuous) problems.
In our framework, we model both the unary and the pairwise potential
functions as deep convolutional neural networks (CNN), which are jointly
learned in an end-to-end fashion. The proposed method possesses the main
advantage of continuously-valued CRF, which is a closed-form solution for the
Maximum a posteriori (MAP) inference.
To better adapt to different tasks, instead of using the commonly employed
maximum likelihood CRF parameter learning protocol, we propose task-specific
loss functions for learning the CRF parameters.
It enables direct optimization of the quality of the MAP estimates during the
course of learning.
Specifically, we optimize the multi-class classification loss for the
semantic labelling task and the Turkey's biweight loss for the robust depth
estimation problem.
Experimental results on the semantic labelling and robust depth estimation
tasks demonstrate that the proposed method compare favorably against both
baseline and state-of-the-art methods.
In particular, we show that although the proposed deep CRF model is
continuously valued, with the equipment of task-specific loss, it achieves
impressive results even on discrete labelling tasks
Exchangeable Variable Models
A sequence of random variables is exchangeable if its joint distribution is
invariant under variable permutations. We introduce exchangeable variable
models (EVMs) as a novel class of probabilistic models whose basic building
blocks are partially exchangeable sequences, a generalization of exchangeable
sequences. We prove that a family of tractable EVMs is optimal under zero-one
loss for a large class of functions, including parity and threshold functions,
and strictly subsumes existing tractable independence-based model families.
Extensive experiments show that EVMs outperform state of the art classifiers
such as SVMs and probabilistic models which are solely based on independence
assumptions.Comment: ICML 201
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