In spite of the recent surge of interest in quantile regression, joint estimation of linear quantile planes remains a great challenge in statistics and econometrics. We propose a novel parameterization that characteri...
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In spite of the recent surge of interest in quantile regression, joint estimation of linear quantile planes remains a great challenge in statistics and econometrics. We propose a novel parameterization that characterizes any collection of noncrossing quantile planes over arbitrarily shaped convex predictor domains in any dimension by means of unconstrained scalar, vector and function valued parameters. Statistical models based on this parameterization inherit a fast computation of the likelihood function, enabling penalized likelihood or bayesian approaches to model fitting. We introduce a complete bayesian methodology by using Gaussian process prior distributions on the function valued parameters and develop a robust and efficient Markov chain Monte Carlo parameter estimation. The resulting method is shown to offer posterior consistency under mild tail and regularity conditions. We present several illustrative examples where the new method is compared against existing approaches and is found to offer better accuracy, coverage and model fit. Supplementary materials for this article are available online.
Forming an accurate representation of a task environment often takes place incrementally as the information relevant to learning the representation only unfolds over time. This incremental nature of learning poses an ...
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Forming an accurate representation of a task environment often takes place incrementally as the information relevant to learning the representation only unfolds over time. This incremental nature of learning poses an important problem: it is usually unclear whether a sequence of stimuli consists of only a single pattern, or multiple patterns that are spliced together. In the former case, the learner can directly use each observed stimulus to continuously revise its representation of the task environment. In the latter case, however, the learner must first parse the sequence of stimuli into different bundles, so as to not conflate the multiple patterns. We created a video-game statistical learning paradigm and investigated (1) whether learners without prior knowledge of the existence of multiple "stimulus bundles" - subsequences of stimuli that define locally coherent statistical patterns could detect their presence in the input and (2) whether learners are capable of constructing a rich representation that encodes the various statistical patterns associated with bundles. By comparing human learning behavior to the predictions of three computational models, we find evidence that learners can handle both tasks successfully. In addition we discuss the underlying reasons for why the learning of stimulus bundles occurs even when such behavior may seem irrational. (C) 2016 Elsevier B.V. All rights reserved.
Topical communities have shown useful tools for characterizing social networks. However data in social networks often come as streams , i.e., both text content (e.g., emails, user postings) and network structure (e.g....
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Topical communities have shown useful tools for characterizing social networks. However data in social networks often come as streams , i.e., both text content (e.g., emails, user postings) and network structure (e.g., user friendship) evolve over time. We propose two nonparametric statistic models where infinite latent community variables coupled with infinite latent topic variables. The temporal dependencies between variables across epochs are modeled via a rich-gets-richer scheme. We focus on characterizing three dynamic aspects in social streams: the number of communities or topics changes (e.g., new communities or topics are born and old ones die out); the popularity of communities or topics evolves; the semantics such as community topic distribution, community participant distribution and topic word distribution drift. Furthermore, we develop an effective online posterior inference algorithm for the models, which is concordant with the online nature of social streams. Experiments using real-world data show the effectiveness of our model at discovering the dynamic topical communities in social streams.
Most current model reference adaptive control (MRAC) methods rely on parametric adaptive elements, in which the number of parameters of the adaptive element are fixed a priori, often through expert judgment. An exampl...
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Most current model reference adaptive control (MRAC) methods rely on parametric adaptive elements, in which the number of parameters of the adaptive element are fixed a priori, often through expert judgment. An example of such an adaptive element is radial basis function networks (RBFNs), with RBF centers preallocated based on the expected operating domain. If the system operates outside of the expected operating domain, this adaptive element can become noneffective in capturing and canceling the uncertainty, thus rendering the adaptive controller only semiglobal in nature. This paper investigates a Gaussian process-based bayesian MRAC architecture (GP-MRAC), which leverages the power and flexibility of GP bayesian nonparametric models of uncertainty. The GP-MRAC does not require the centers to be preallocated, can inherently handle measurement noise, and enables MRAC to handle a broader set of uncertainties, including those that are defined as distributions over functions. We use stochastic stability arguments to show that GP-MRAC guarantees good closed-loop performance with no prior domain knowledge of the uncertainty. Online implementable GP inference methods are compared in numerical simulations against RBFN-MRAC with preallocated centers and are shown to provide better tracking and improved long-term learning.
Spatially constrained Dirichlet process mixture models are springing up in image processing in recent years. However, inference for the model is NP-hard. Gibbs sampling which is a generic Markov chain Monte Carlo tech...
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Spatially constrained Dirichlet process mixture models are springing up in image processing in recent years. However, inference for the model is NP-hard. Gibbs sampling which is a generic Markov chain Monte Carlo technique is commonly employed for the model inference. It needs to traverse all the nodes of the constructed graph in each iteration. The sampling process hardly crosses over the intermediate low probabilistic state. In addition, it is not well informed by the spatial relationship in the sampling process. In this paper, a spatially dependent split-merge algorithm for sampling the MRF/DPMM model based on Swendsen-Wang Cuts is proposed. It is a state of the art algorithm which combines the spatial relationship to direct the sampling, and lessen the mixing time drastically. In this algorithm, a set of nodes are being frozen together according to the discriminative probability of the edges between neighboring nodes. The frozen nodes update their states simultaneously in contrast to the single node update in a Gibbs sampling. The final step of the algorithm is to accept the proposed new state according to the Metropolis Hasting scheme, in which only the ratio of posterior distribution needs to be calculated in each iteration. Experimental results demonstrated that the proposed sampling algorithm is able to reduce the mixing time considerably. At the same time, it can obtain comparably stable results with a random initial state. (C) 2014 Elsevier Inc. All rights reserved.
作者：
Qin, LijingZhu, XiaoyanTsinghua Univ
Dept Comp Sci & Technol Tsinghua Natl Lab Informat Sci & Technol State Key Lab Intelligent Technol & Syst Beijing Peoples R China
Dirichlet process mixture (DPM) model is one of the most important bayesian nonparametric models owing to its efficiency of inference and flexibility for various applications. A fundamental assumption made by DPM mode...
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ISBN:
(纸本)9781450322638
Dirichlet process mixture (DPM) model is one of the most important bayesian nonparametric models owing to its efficiency of inference and flexibility for various applications. A fundamental assumption made by DPM model is that all data items are generated from a single, shared DP. This assumption, however, is restrictive in many practical settings where samples are generated from a collection of dependent DPs, each associated with a point in some covariate space. For example, documents in the proceedings of a conference are organized by year, or photos may be tagged and recorded with GPS locations. We present a general method for constructing dependent Dirichlet processes (DP) on arbitrary covariate space. The approach is based on restricting and projecting a DP defined on a space of continuous functions with different domains, which results in a collection of dependent random measures, each associated with a point in covariate space and is marginally DP distributed. The constructed collection of dependent DPs can be used as a nonparametric prior of infinite dynamic mixture models, which allow each mixture component to appear/disappear and vary in a subspace of covariate space. Furthermore, we discuss choices of base distributions of functions in a variety of settings as a flexible method to control dependencies. In addition, we develop an efficient Gibbs sampler for model inference where all underlying random measures are integrated out. Finally, experiment results on temporal modeling and spatial modeling datasets demonstrate the effectiveness of the method in modeling dynamic mixture models on different types of covariates.
We introduce a semi-parametric bayesian framework for a simultaneous analysis of linear quantile regression models. A simultaneous analysis is essential to attain the true potential of the quantile regression framewor...
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We introduce a semi-parametric bayesian framework for a simultaneous analysis of linear quantile regression models. A simultaneous analysis is essential to attain the true potential of the quantile regression framework, but is computationally challenging due to the associated monotonicity constraint on the quantile curves. For a univariate covariate, we present a simpler equivalent characterization of the monotonicity constraint through an interpolation of two monotone curves. The resulting formulation leads to a tractable likelihood function and is embedded within a bayesian framework where the two monotone curves are modeled via logistic transformations of a smooth Gaussian process. A multivariate extension is suggested by combining the full support univariate model with a linear projection of the predictors. The resulting single-index model remains easy to fit and provides substantial and measurable improvement over the first order linear heteroscedastic model. Two illustrative applications of the proposed method are provided.
We consider inference for data from a clinical trial of treatments for metastatic prostate cancer. Pot tents joined the trial with diverse prior treatment histories. The resulting heterogeneous patient population give...
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We consider inference for data from a clinical trial of treatments for metastatic prostate cancer. Pot tents joined the trial with diverse prior treatment histories. The resulting heterogeneous patient population gives rise to challenging statistical inference problems when trying to predict time to progression on different treatment. arms. Inference is further complicated by the need to include a longitudinal marker as a covariate. To address these challenges, we develop a semiparametric model for joint inference of longitudinal data and an event time. The proposed approach includes the possibility of cure for some patients. The event time distribution is based on a nonparametric Polya tree prior. For the longitudinal data we assume a mixed effects model. Incorporating a regression on covariates in it nonparametric event time model in general. and for a Polya tree model in particular, is a challenging problem. We exploit the fact that. the covariate itself is a random variable. We achieve an implementation of the desired regression by factoring the joint model for the event time and the longitudinal outcome into a marginal rnodel for the event;time and a regression of the longitudinal outcomes on the event time, i.e.. we implicitly model the desired regression by modeling die reverse conditional distribution
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