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Bayesian Compressive Sensing
, 2007
"... The data of interest are assumed to be represented as Ndimensional real vectors, and these vectors are compressible in some linear basis B, implying that the signal can be reconstructed accurately using only a small number M ≪ N of basisfunction coefficients associated with B. Compressive sensing ..."
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Cited by 132 (15 self)
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The data of interest are assumed to be represented as Ndimensional real vectors, and these vectors are compressible in some linear basis B, implying that the signal can be reconstructed accurately using only a small number M ≪ N of basisfunction coefficients associated with B. Compressive sensing is a framework whereby one does not measure one of the aforementioned Ndimensional signals directly, but rather a set of related measurements, with the new measurements a linear combination of the original underlying Ndimensional signal. The number of required compressivesensing measurements is typically much smaller than N, offering the potential to simplify the sensing system. Let f denote the unknown underlying Ndimensional signal, and g a vector of compressivesensing measurements, then one may approximate f accurately by utilizing knowledge of the (underdetermined) linear relationship between f and g, in addition to knowledge of the fact that f is compressible in B. In this paper we employ a Bayesian formalism for estimating the underlying signal f based on compressivesensing measurements g. The proposed framework has the following properties: (i) in addition to estimating the underlying signal f, “error bars ” are also estimated, these giving a measure of confidence in the inverted signal; (ii) using knowledge of the error bars, a principled means is provided for determining when a sufficient
Multitask learning for classification with dirichlet process priors
 Journal of Machine Learning Research
, 2007
"... Multitask learning (MTL) is considered for logisticregression classifiers, based on a Dirichlet process (DP) formulation. A symmetric MTL (SMTL) formulation is considered in which classifiers for multiple tasks are learned jointly, with a variational Bayesian (VB) solution. We also consider an asy ..."
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Cited by 98 (9 self)
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Multitask learning (MTL) is considered for logisticregression classifiers, based on a Dirichlet process (DP) formulation. A symmetric MTL (SMTL) formulation is considered in which classifiers for multiple tasks are learned jointly, with a variational Bayesian (VB) solution. We also consider an asymmetric MTL (AMTL) formulation in which the posterior density function from the SMTL model parameters, from previous tasks, is used as a prior for a new task; this approach has the significant advantage of not requiring storage and use of all previous data from prior tasks. The AMTL formulation is solved with a simple Markov Chain Monte Carlo (MCMC) construction. Comparisons are also made to simpler approaches, such as singletask learning, pooling of data across tasks, and simplified approximations to DP. A comprehensive analysis of algorithm performance is addressed through consideration of two data sets that are matched to the MTL problem.
SemiSupervised Multitask Learning
"... A semisupervised multitask learning (MTL) framework is presented, in which M parameterized semisupervised classifiers, each associated with one of M partially labeled data manifolds, are learned jointly under the constraint of a softsharing prior imposed over the parameters of the classifiers. The ..."
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Cited by 23 (5 self)
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A semisupervised multitask learning (MTL) framework is presented, in which M parameterized semisupervised classifiers, each associated with one of M partially labeled data manifolds, are learned jointly under the constraint of a softsharing prior imposed over the parameters of the classifiers. The unlabeled data are utilized by basing classifier learning on neighborhoods, induced by a Markov random walk over a graph representation of each manifold. Experimental results on real data sets demonstrate that semisupervised MTL yields significant improvements in generalization performance over either semisupervised singletask learning (STL) or supervised MTL. 1
Timeline: A Dynamic Hierarchical Dirichlet Process Model for Recovering Birth/Death and Evolution of Topics in Text Stream
"... Topic models have proven to be a useful tool for discovering latent structures in document collections. However, most document collections often come as temporal streams and thus several aspects of the latent structure such as the number of topics, the topics ’ distribution and popularity are timee ..."
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Cited by 13 (6 self)
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Topic models have proven to be a useful tool for discovering latent structures in document collections. However, most document collections often come as temporal streams and thus several aspects of the latent structure such as the number of topics, the topics ’ distribution and popularity are timeevolving. Several models exist that model the evolution of some but not all of the above aspects. In this paper we introduce infinite dynamic topic models, iDTM, that can accommodate the evolution of all the aforementioned aspects. Our model assumes that documents are organized into epochs, where the documents within each epoch are exchangeable but the order between the documents is maintained across epochs. iDTM allows for unbounded number of topics: topics can die or be born at any epoch, and the representation of each topic can evolve according to a Markovian dynamics. We use iDTM to analyze the birth and evolution of topics in the NIPS community and evaluated the efficacy of our model on both simulated and real datasets with favorable outcome. 1
Learning to Extract International Relations from Political Context
"... We describe a new probabilistic model for extracting events between major political actors from news corpora. Our unsupervised model brings together familiar components in natural language processing (like parsers and topic models) with contextual political information— temporal and dyad dependence— ..."
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Cited by 1 (1 self)
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We describe a new probabilistic model for extracting events between major political actors from news corpora. Our unsupervised model brings together familiar components in natural language processing (like parsers and topic models) with contextual political information— temporal and dyad dependence—to infer latent event classes. We quantitatively evaluate the model’s performance on political science benchmarks: recovering expertassigned event class valences, and detecting realworld conflict. We also conduct a small case study based on our model’s inferences. A supplementary appendix, and replication software/data are available online, at:
unknown title
, 2013
"... 1 Lexical scale impurity at the typelevel As noted in the paper the measure we want is a posterior expectation defined for instance pairs, which we can reformulate at the type level as follows. Let i and j index over instances, and w and v index over types. Consider an expectation using a single sa ..."
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1 Lexical scale impurity at the typelevel As noted in the paper the measure we want is a posterior expectation defined for instance pairs, which we can reformulate at the type level as follows. Let i and j index over instances, and w and v index over types. Consider an expectation using a single sample to represent the posterior, E [ g(wi) − g(wj)   zi = zj & wi = wj & wi, wj ∈ M] = Q N where N is the number of instance pair comparisons satisfying the conditional, and Q is,