1,330 research outputs found
Parsimonious Labeling
We propose a new family of discrete energy minimization problems, which we
call parsimonious labeling. Specifically, our energy functional consists of
unary potentials and high-order clique potentials. While the unary potentials
are arbitrary, the clique potentials are proportional to the {\em diversity} of
set of the unique labels assigned to the clique. Intuitively, our energy
functional encourages the labeling to be parsimonious, that is, use as few
labels as possible. This in turn allows us to capture useful cues for important
computer vision applications such as stereo correspondence and image denoising.
Furthermore, we propose an efficient graph-cuts based algorithm for the
parsimonious labeling problem that provides strong theoretical guarantees on
the quality of the solution. Our algorithm consists of three steps. First, we
approximate a given diversity using a mixture of a novel hierarchical
Potts model. Second, we use a divide-and-conquer approach for each mixture
component, where each subproblem is solved using an effficient
-expansion algorithm. This provides us with a small number of putative
labelings, one for each mixture component. Third, we choose the best putative
labeling in terms of the energy value. Using both sythetic and standard real
datasets, we show that our algorithm significantly outperforms other graph-cuts
based approaches
Worst-case Optimal Submodular Extensions for Marginal Estimation
Submodular extensions of an energy function can be used to efficiently
compute approximate marginals via variational inference. The accuracy of the
marginals depends crucially on the quality of the submodular extension. To
identify the best possible extension, we show an equivalence between the
submodular extensions of the energy and the objective functions of linear
programming (LP) relaxations for the corresponding MAP estimation problem. This
allows us to (i) establish the worst-case optimality of the submodular
extension for Potts model used in the literature; (ii) identify the worst-case
optimal submodular extension for the more general class of metric labeling; and
(iii) efficiently compute the marginals for the widely used dense CRF model
with the help of a recently proposed Gaussian filtering method. Using synthetic
and real data, we show that our approach provides comparable upper bounds on
the log-partition function to those obtained using tree-reweighted message
passing (TRW) in cases where the latter is computationally feasible.
Importantly, unlike TRW, our approach provides the first practical algorithm to
compute an upper bound on the dense CRF model.Comment: Accepted to AISTATS 201
Modeling Latent Variable Uncertainty for Loss-based Learning
We consider the problem of parameter estimation using weakly supervised
datasets, where a training sample consists of the input and a partially
specified annotation, which we refer to as the output. The missing information
in the annotation is modeled using latent variables. Previous methods
overburden a single distribution with two separate tasks: (i) modeling the
uncertainty in the latent variables during training; and (ii) making accurate
predictions for the output and the latent variables during testing. We propose
a novel framework that separates the demands of the two tasks using two
distributions: (i) a conditional distribution to model the uncertainty of the
latent variables for a given input-output pair; and (ii) a delta distribution
to predict the output and the latent variables for a given input. During
learning, we encourage agreement between the two distributions by minimizing a
loss-based dissimilarity coefficient. Our approach generalizes latent SVM in
two important ways: (i) it models the uncertainty over latent variables instead
of relying on a pointwise estimate; and (ii) it allows the use of loss
functions that depend on latent variables, which greatly increases its
applicability. We demonstrate the efficacy of our approach on two challenging
problems---object detection and action detection---using publicly available
datasets.Comment: ICML201
DISCO Nets: DISsimilarity COefficient Networks
We present a new type of probabilistic model which we call DISsimilarity
COefficient Networks (DISCO Nets). DISCO Nets allow us to efficiently sample
from a posterior distribution parametrised by a neural network. During
training, DISCO Nets are learned by minimising the dissimilarity coefficient
between the true distribution and the estimated distribution. This allows us to
tailor the training to the loss related to the task at hand. We empirically
show that (i) by modeling uncertainty on the output value, DISCO Nets
outperform equivalent non-probabilistic predictive networks and (ii) DISCO Nets
accurately model the uncertainty of the output, outperforming existing
probabilistic models based on deep neural networks
Coplanar Repeats by Energy Minimization
This paper proposes an automated method to detect, group and rectify
arbitrarily-arranged coplanar repeated elements via energy minimization. The
proposed energy functional combines several features that model how planes with
coplanar repeats are projected into images and captures global interactions
between different coplanar repeat groups and scene planes. An inference
framework based on a recent variant of -expansion is described and fast
convergence is demonstrated. We compare the proposed method to two widely-used
geometric multi-model fitting methods using a new dataset of annotated images
containing multiple scene planes with coplanar repeats in varied arrangements.
The evaluation shows a significant improvement in the accuracy of
rectifications computed from coplanar repeats detected with the proposed method
versus those detected with the baseline methods.Comment: 14 pages with supplemental materials attache
Efficient Optimization for Rank-based Loss Functions
The accuracy of information retrieval systems is often measured using complex
loss functions such as the average precision (AP) or the normalized discounted
cumulative gain (NDCG). Given a set of positive and negative samples, the
parameters of a retrieval system can be estimated by minimizing these loss
functions. However, the non-differentiability and non-decomposability of these
loss functions does not allow for simple gradient based optimization
algorithms. This issue is generally circumvented by either optimizing a
structured hinge-loss upper bound to the loss function or by using asymptotic
methods like the direct-loss minimization framework. Yet, the high
computational complexity of loss-augmented inference, which is necessary for
both the frameworks, prohibits its use in large training data sets. To
alleviate this deficiency, we present a novel quicksort flavored algorithm for
a large class of non-decomposable loss functions. We provide a complete
characterization of the loss functions that are amenable to our algorithm, and
show that it includes both AP and NDCG based loss functions. Furthermore, we
prove that no comparison based algorithm can improve upon the computational
complexity of our approach asymptotically. We demonstrate the effectiveness of
our approach in the context of optimizing the structured hinge loss upper bound
of AP and NDCG loss for learning models for a variety of vision tasks. We show
that our approach provides significantly better results than simpler
decomposable loss functions, while requiring a comparable training time.Comment: 15 pages, 2 figure
Adaptive Neural Compilation
This paper proposes an adaptive neural-compilation framework to address the
problem of efficient program learning. Traditional code optimisation strategies
used in compilers are based on applying pre-specified set of transformations
that make the code faster to execute without changing its semantics. In
contrast, our work involves adapting programs to make them more efficient while
considering correctness only on a target input distribution. Our approach is
inspired by the recent works on differentiable representations of programs. We
show that it is possible to compile programs written in a low-level language to
a differentiable representation. We also show how programs in this
representation can be optimised to make them efficient on a target distribution
of inputs. Experimental results demonstrate that our approach enables learning
specifically-tuned algorithms for given data distributions with a high success
rate.Comment: Submitted to NIPS 2016, code and supplementary materials will be
available on author's pag
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