1,348 research outputs found
Sampling and Inference for Beta Neutral-to-the-Left Models of Sparse Networks
Empirical evidence suggests that heavy-tailed degree distributions occurring
in many real networks are well-approximated by power laws with exponents
that may take values either less than and greater than two. Models based on
various forms of exchangeability are able to capture power laws with , and admit tractable inference algorithms; we draw on previous results to
show that cannot be generated by the forms of exchangeability used
in existing random graph models. Preferential attachment models generate power
law exponents greater than two, but have been of limited use as statistical
models due to the inherent difficulty of performing inference in
non-exchangeable models. Motivated by this gap, we design and implement
inference algorithms for a recently proposed class of models that generates
of all possible values. We show that although they are not exchangeable,
these models have probabilistic structure amenable to inference. Our methods
make a large class of previously intractable models useful for statistical
inference.Comment: Accepted for publication in the proceedings of Conference on
Uncertainty in Artificial Intelligence (UAI) 201
Class Proportion Estimation with Application to Multiclass Anomaly Rejection
This work addresses two classification problems that fall under the heading
of domain adaptation, wherein the distributions of training and testing
examples differ. The first problem studied is that of class proportion
estimation, which is the problem of estimating the class proportions in an
unlabeled testing data set given labeled examples of each class. Compared to
previous work on this problem, our approach has the novel feature that it does
not require labeled training data from one of the classes. This property allows
us to address the second domain adaptation problem, namely, multiclass anomaly
rejection. Here, the goal is to design a classifier that has the option of
assigning a "reject" label, indicating that the instance did not arise from a
class present in the training data. We establish consistent learning strategies
for both of these domain adaptation problems, which to our knowledge are the
first of their kind. We also implement the class proportion estimation
technique and demonstrate its performance on several benchmark data sets.Comment: Accepted to AISTATS 2014. 15 pages. 2 figure
Path integral Monte Carlo simulation of charged particles in traps
This chapter is devoted to the computation of equilibrium (thermodynamic)
properties of quantum systems. In particular, we will be interested in the
situation where the interaction between particles is so strong that it cannot
be treated as a small perturbation. For weakly coupled systems many efficient
theoretical and computational techniques do exist. However, for strongly
interacting systems such as nonideal gases or plasmas, strongly correlated
electrons and so on, perturbation methods fail and alternative approaches are
needed. Among them, an extremely successful one is the Monte Carlo (MC) method
which we are going to consider in this chapter.Comment: 18 pages, based on talks on Hareaus school on computational methods,
Greifswald, September 200
Shuffled Multi-Channel Sparse Signal Recovery
Mismatches between samples and their respective channel or target commonly
arise in several real-world applications. For instance, whole-brain calcium
imaging of freely moving organisms, multiple-target tracking or multi-person
contactless vital sign monitoring may be severely affected by mismatched
sample-channel assignments. To systematically address this fundamental problem,
we pose it as a signal reconstruction problem where we have lost
correspondences between the samples and their respective channels. Assuming
that we have a sensing matrix for the underlying signals, we show that the
problem is equivalent to a structured unlabeled sensing problem, and establish
sufficient conditions for unique recovery. To the best of our knowledge, a
sampling result for the reconstruction of shuffled multi-channel signals has
not been considered in the literature and existing methods for unlabeled
sensing cannot be directly applied. We extend our results to the case where the
signals admit a sparse representation in an overcomplete dictionary (i.e., the
sensing matrix is not precisely known), and derive sufficient conditions for
the reconstruction of shuffled sparse signals. We propose a robust
reconstruction method that combines sparse signal recovery with robust linear
regression for the two-channel case. The performance and robustness of the
proposed approach is illustrated in an application related to whole-brain
calcium imaging. The proposed methodology can be generalized to sparse signal
representations other than the ones considered in this work to be applied in a
variety of real-world problems with imprecise measurement or channel
assignment.Comment: Submitted to TS
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