380 research outputs found
Hierarchical subspace models for contingency tables
For statistical analysis of multiway contingency tables we propose modeling
interaction terms in each maximal compact component of a hierarchical model. By
this approach we can search for parsimonious models with smaller degrees of
freedom than the usual hierarchical model, while preserving conditional
independence structures in the hierarchical model. We discuss estimation and
exacts tests of the proposed model and illustrate the advantage of the proposed
modeling with some data sets.Comment: 26 page
Efficient and Scalable 4-th order Match Propagation
International audienceWe propose a robust method to match image feature points taking into account geometric consistency. It is a careful adaptation of the match propagation principle to 4th-order geometric constraints (match quadruple consistency). With our method, a set of matches is explained by a network of locally-similar affinities. This approach is useful when simple descriptor-based matching strategies fail, in particular for highly ambiguous data, e.g., with repetitive patterns or where texture is lacking. As it scales easily to hundreds of thousands of matches, it is also useful when denser point distributions are sought, e.g., for high-precision rigid model estimation. Experiments show that our method is competitive (efficient, scalable, accurate, robust) against state-of-the-art methods in deformable object matching, camera calibration and pattern detection
Recurrently Predicting Hypergraphs
This work considers predicting the relational structure of a hypergraph for a
given set of vertices, as common for applications in particle physics,
biological systems and other complex combinatorial problems. A problem arises
from the number of possible multi-way relationships, or hyperedges, scaling in
for a set of elements. Simply storing an indicator
tensor for all relationships is already intractable for moderately sized ,
prompting previous approaches to restrict the number of vertices a hyperedge
connects. Instead, we propose a recurrent hypergraph neural network that
predicts the incidence matrix by iteratively refining an initial guess of the
solution. We leverage the property that most hypergraphs of interest are
sparsely connected and reduce the memory requirement to ,
where is the maximum number of positive edges, i.e., edges that actually
exist. In order to counteract the linearly growing memory cost from training a
lengthening sequence of refinement steps, we further propose an algorithm that
applies backpropagation through time on randomly sampled subsequences. We
empirically show that our method can match an increase in the intrinsic
complexity without a performance decrease and demonstrate superior performance
compared to state-of-the-art models
Labeling the Features Not the Samples: Efficient Video Classification with Minimal Supervision
Feature selection is essential for effective visual recognition. We propose
an efficient joint classifier learning and feature selection method that
discovers sparse, compact representations of input features from a vast sea of
candidates, with an almost unsupervised formulation. Our method requires only
the following knowledge, which we call the \emph{feature sign}---whether or not
a particular feature has on average stronger values over positive samples than
over negatives. We show how this can be estimated using as few as a single
labeled training sample per class. Then, using these feature signs, we extend
an initial supervised learning problem into an (almost) unsupervised clustering
formulation that can incorporate new data without requiring ground truth
labels. Our method works both as a feature selection mechanism and as a fully
competitive classifier. It has important properties, low computational cost and
excellent accuracy, especially in difficult cases of very limited training
data. We experiment on large-scale recognition in video and show superior speed
and performance to established feature selection approaches such as AdaBoost,
Lasso, greedy forward-backward selection, and powerful classifiers such as SVM.Comment: arXiv admin note: text overlap with arXiv:1411.771
Differential equation approximations for Markov chains
We formulate some simple conditions under which a Markov chain may be
approximated by the solution to a differential equation, with quantifiable
error probabilities. The role of a choice of coordinate functions for the
Markov chain is emphasised. The general theory is illustrated in three
examples: the classical stochastic epidemic, a population process model with
fast and slow variables, and core-finding algorithms for large random
hypergraphs.Comment: Published in at http://dx.doi.org/10.1214/07-PS121 the Probability
Surveys (http://www.i-journals.org/ps/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Software Engineering and Complexity in Effective Algebraic Geometry
We introduce the notion of a robust parameterized arithmetic circuit for the
evaluation of algebraic families of multivariate polynomials. Based on this
notion, we present a computation model, adapted to Scientific Computing, which
captures all known branching parsimonious symbolic algorithms in effective
Algebraic Geometry. We justify this model by arguments from Software
Engineering. Finally we exhibit a class of simple elimination problems of
effective Algebraic Geometry which require exponential time to be solved by
branching parsimonious algorithms of our computation model.Comment: 70 pages. arXiv admin note: substantial text overlap with
arXiv:1201.434
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