2,430 research outputs found
Relaxations for inference in restricted Boltzmann machines
We propose a relaxation-based approximate inference algorithm that samples
near-MAP configurations of a binary pairwise Markov random field. We experiment
on MAP inference tasks in several restricted Boltzmann machines. We also use
our underlying sampler to estimate the log-partition function of restricted
Boltzmann machines and compare against other sampling-based methods.Comment: ICLR 2014 workshop track submissio
Uniform sampling of steady states in metabolic networks: heterogeneous scales and rounding
The uniform sampling of convex polytopes is an interesting computational
problem with many applications in inference from linear constraints, but the
performances of sampling algorithms can be affected by ill-conditioning. This
is the case of inferring the feasible steady states in models of metabolic
networks, since they can show heterogeneous time scales . In this work we focus
on rounding procedures based on building an ellipsoid that closely matches the
sampling space, that can be used to define an efficient hit-and-run (HR) Markov
Chain Monte Carlo. In this way the uniformity of the sampling of the convex
space of interest is rigorously guaranteed, at odds with non markovian methods.
We analyze and compare three rounding methods in order to sample the feasible
steady states of metabolic networks of three models of growing size up to
genomic scale. The first is based on principal component analysis (PCA), the
second on linear programming (LP) and finally we employ the lovasz ellipsoid
method (LEM). Our results show that a rounding procedure is mandatory for the
application of the HR in these inference problem and suggest that a combination
of LEM or LP with a subsequent PCA perform the best. We finally compare the
distributions of the HR with that of two heuristics based on the Artificially
Centered hit-and-run (ACHR), gpSampler and optGpSampler. They show a good
agreement with the results of the HR for the small network, while on genome
scale models present inconsistencies.Comment: Replacement with major revision
A discriminative view of MRF pre-processing algorithms
While Markov Random Fields (MRFs) are widely used in computer vision, they
present a quite challenging inference problem. MRF inference can be accelerated
by pre-processing techniques like Dead End Elimination (DEE) or QPBO-based
approaches which compute the optimal labeling of a subset of variables. These
techniques are guaranteed to never wrongly label a variable but they often
leave a large number of variables unlabeled. We address this shortcoming by
interpreting pre-processing as a classification problem, which allows us to
trade off false positives (i.e., giving a variable an incorrect label) versus
false negatives (i.e., failing to label a variable). We describe an efficient
discriminative rule that finds optimal solutions for a subset of variables. Our
technique provides both per-instance and worst-case guarantees concerning the
quality of the solution. Empirical studies were conducted over several
benchmark datasets. We obtain a speedup factor of 2 to 12 over expansion moves
without preprocessing, and on difficult non-submodular energy functions produce
slightly lower energy.Comment: ICCV 201
Combinatorial persistency criteria for multicut and max-cut
In combinatorial optimization, partial variable assignments are called
persistent if they agree with some optimal solution. We propose persistency
criteria for the multicut and max-cut problem as well as fast combinatorial
routines to verify them. The criteria that we derive are based on mappings that
improve feasible multicuts, respectively cuts. Our elementary criteria can be
checked enumeratively. The more advanced ones rely on fast algorithms for upper
and lower bounds for the respective cut problems and max-flow techniques for
auxiliary min-cut problems. Our methods can be used as a preprocessing
technique for reducing problem sizes or for computing partial optimality
guarantees for solutions output by heuristic solvers. We show the efficacy of
our methods on instances of both problems from computer vision, biomedical
image analysis and statistical physics
Modeling Perceptual Aliasing in SLAM via Discrete-Continuous Graphical Models
Perceptual aliasing is one of the main causes of failure for Simultaneous
Localization and Mapping (SLAM) systems operating in the wild. Perceptual
aliasing is the phenomenon where different places generate a similar visual
(or, in general, perceptual) footprint. This causes spurious measurements to be
fed to the SLAM estimator, which typically results in incorrect localization
and mapping results. The problem is exacerbated by the fact that those outliers
are highly correlated, in the sense that perceptual aliasing creates a large
number of mutually-consistent outliers. Another issue stems from the fact that
most state-of-the-art techniques rely on a given trajectory guess (e.g., from
odometry) to discern between inliers and outliers and this makes the resulting
pipeline brittle, since the accumulation of error may result in incorrect
choices and recovery from failures is far from trivial. This work provides a
unified framework to model perceptual aliasing in SLAM and provides practical
algorithms that can cope with outliers without relying on any initial guess. We
present two main contributions. The first is a Discrete-Continuous Graphical
Model (DC-GM) for SLAM: the continuous portion of the DC-GM captures the
standard SLAM problem, while the discrete portion describes the selection of
the outliers and models their correlation. The second contribution is a
semidefinite relaxation to perform inference in the DC-GM that returns
estimates with provable sub-optimality guarantees. Experimental results on
standard benchmarking datasets show that the proposed technique compares
favorably with state-of-the-art methods while not relying on an initial guess
for optimization.Comment: 13 pages, 14 figures, 1 tabl
Efficient Decomposed Learning for Structured Prediction
Structured prediction is the cornerstone of several machine learning
applications. Unfortunately, in structured prediction settings with expressive
inter-variable interactions, exact inference-based learning algorithms, e.g.
Structural SVM, are often intractable. We present a new way, Decomposed
Learning (DecL), which performs efficient learning by restricting the inference
step to a limited part of the structured spaces. We provide characterizations
based on the structure, target parameters, and gold labels, under which DecL is
equivalent to exact learning. We then show that in real world settings, where
our theoretical assumptions may not completely hold, DecL-based algorithms are
significantly more efficient and as accurate as exact learning.Comment: ICML201
Bayesian inference on compact binary inspiral gravitational radiation signals in interferometric data
Presented is a description of a Markov chain Monte Carlo (MCMC) parameter
estimation routine for use with interferometric gravitational radiational data
in searches for binary neutron star inspiral signals. Five parameters
associated with the inspiral can be estimated, and summary statistics are
produced. Advanced MCMC methods were implemented, including importance
resampling and prior distributions based on detection probability, in order to
increase the efficiency of the code. An example is presented from an
application using realistic, albeit fictitious, data.Comment: submitted to Classical and Quantum Gravity. 14 pages, 5 figure
Detection and classification of neurodegenerative diseases: a spatially informed bayesian deep learning approach
Dissertation submitted in partial fulfilment of the requirements for the Degree of Master of Science in Geospatial TechnologiesNeurodegenerative diseases comprise a group of chronic and irreversible conditions
characterized by the progressive degeneration of the structure and function
of the central nervous system. The detection and classification of patients according
to the underlying disease are crucial for developing oriented treatments and
enriching prognosis. In this context, Magnetic resonance imaging (MRI) data can
provide meaningful insights into neurodegeneration by detecting the physiological
manifestations in the brain caused by the disease processes. One field of extensive
clinical use of MRI is the accurate and automated classification of neurodegenerative
disorders. Most studies distinguish patients from healthy subjects or stages
within the same disease. Such distinction does not mirror clinical practice, as a
patient may not show all symptoms, especially if the disease is in an early stage,
or show, due to comorbidities, other symptoms as well. Likewise, automated
classifiers are partly suited for medical diagnosis since they cannot produce probabilistic
predictions nor account for uncertainty. Also, existent studies ignore the
spatial heterogeneity of the brain alterations caused by neurodegenerative processes.
The spatial configuration of the neuronal loss is a characteristic hallmark
for each disorder. To fill these gaps, this thesis aims to develop a classification
technique that incorporates uncertainty and spatial information for distinguishing
four neurodegenerative diseases, Alzheimer’s disease, Mild cognitive impairment,
Parkinson’s disease and Multiple Sclerosis, and healthy subjects. This technique
will produce automated, contingent, and accurate predictions to support clinical
diagnosis.
To quantify prediction uncertainty and improve classification accuracy, this study
introduces a Bayesian neural network with a spatially informed input. A convolutional
neural network (CNN) is developed to identify a neurodegenerative
condition based on T1weighted MRI scans from patients and healthy controls.
Bayesian inference is incorporated into the CNN to measure uncertainty and produce
probabilistic predictions. Also, a spatially informed MRI scan is added to
the CNN to improve feature detection and classification accuracy.
The Spatially informed Bayesian Neural Network (SBNN) proposed in this work
demonstrates that classification accuracy can be increased up to 25% by including
the spatially informed MRI scan. Furthermore, the SBNN provides robust
probabilistic diagnosis that resembles clinical decision-making and accounts for
atypical, numerous, and early presentations of neurodegenerative disorders
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