ترغب بنشر مسار تعليمي؟ اضغط هنا

Dirichlet Process Mixture Models with Shrinkage Prior

104   0   0.0 ( 0 )
 نشر من قبل Dawei Ding
 تاريخ النشر 2020
  مجال البحث الاحصاء الرياضي
والبحث باللغة English




اسأل ChatGPT حول البحث

We propose Dirichlet Process Mixture (DPM) models for prediction and cluster-wise variable selection, based on two choices of shrinkage baseline prior distributions for the linear regression coefficients, namely the Horseshoe prior and Normal-Gamma prior. We show in a simulation study that each of the two proposed DPM models tend to outperform the standard DPM model based on the non-shrinkage normal prior, in terms of predictive, variable selection, and clustering accuracy. This is especially true for the Horseshoe model, and when the number of covariates exceeds the within-cluster sample size. A real data set is analyzed to illustrate the proposed modeling methodology, where both proposed DPM models again attained better predictive accuracy.


قيم البحث

اقرأ أيضاً

We study the problem of sparse signal detection on a spatial domain. We propose a novel approach to model continuous signals that are sparse and piecewise smooth as product of independent Gaussian processes (PING) with a smooth covariance kernel. The smoothness of the PING process is ensured by the smoothness of the covariance kernels of Gaussian components in the product, and sparsity is controlled by the number of components. The bivariate kurtosis of the PING process shows more components in the product results in thicker tail and sharper peak at zero. The simulation results demonstrate the improvement in estimation using the PING prior over Gaussian process (GP) prior for different image regressions. We apply our method to a longitudinal MRI dataset to detect the regions that are affected by multiple sclerosis (MS) in the greatest magnitude through an image-on-scalar regression model. Due to huge dimensionality of these images, we transform the data into the spectral domain and develop methods to conduct computation in this domain. In our MS imaging study, the estimates from the PING model are more informative than those from the GP model.
In this article, we consider a non-parametric Bayesian approach to multivariate quantile regression. The collection of related conditional distributions of a response vector Y given a univariate covariate X is modeled using a Dependent Dirichlet Proc ess (DDP) prior. The DDP is used to introduce dependence across x. As the realizations from a Dirichlet process prior are almost surely discrete, we need to convolve it with a kernel. To model the error distribution as flexibly as possible, we use a countable mixture of multidimensional normal distributions as our kernel. For posterior computations, we use a truncated stick-breaking representation of the DDP. This approximation enables us to deal with only a finitely number of parameters. We use a Block Gibbs sampler for estimating the model parameters. We illustrate our method with simulation studies and real data applications. Finally, we provide a theoretical justification for the proposed method through posterior consistency. Our proposed procedure is new even when the response is univariate.
Many panel studies collect refreshment samples---new, randomly sampled respondents who complete the questionnaire at the same time as a subsequent wave of the panel. With appropriate modeling, these samples can be leveraged to correct inferences for biases caused by non-ignorable attrition. We present such a model when the panel includes many categorical survey variables. The model relies on a Bayesian latent pattern mixture model, in which an indicator for attrition and the survey variables are modeled jointly via a latent class model. We allow the multinomial probabilities within classes to depend on the attrition indicator, which offers additional flexibility over standard applications of latent class models. We present results of simulation studies that illustrate the benefits of this flexibility. We apply the model to correct attrition bias in an analysis of data from the 2007-2008 Associated Press/Yahoo News election panel study.
We develop a sequential low-complexity inference procedure for Dirichlet process mixtures of Gaussians for online clustering and parameter estimation when the number of clusters are unknown a-priori. We present an easily computable, closed form param etric expression for the conditional likelihood, in which hyperparameters are recursively updated as a function of the streaming data assuming conjugate priors. Motivated by large-sample asymptotics, we propose a novel adaptive low-complexity design for the Dirichlet process concentration parameter and show that the number of classes grow at most at a logarithmic rate. We further prove that in the large-sample limit, the conditional likelihood and data predictive distribution become asymptotically Gaussian. We demonstrate through experiments on synthetic and real data sets that our approach is superior to other online state-of-the-art methods.
We consider the robust filtering problem for a nonlinear state-space model with outliers in measurements. To improve the robustness of the traditional Kalman filtering algorithm, we propose in this work two robust filters based on mixture correntropy , especially the double-Gaussian mixture correntropy and Laplace-Gaussian mixture correntropy. We have formulated the robust filtering problem by adopting the mixture correntropy induced cost to replace the quadratic one in the conventional Kalman filter for measurement fitting errors. In addition, a tradeoff weight coefficient is introduced to make sure the proposed approaches can provide reasonable state estimates in scenarios where measurement fitting errors are small. The formulated robust filtering problems are iteratively solved by utilizing the cubature Kalman filtering framework with a reweighted measurement covariance. Numerical results show that the proposed methods can achieve a performance improvement over existing robust solutions.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا