Related papers: Hilbert Space Embedding for Dirichlet Process Mixt…
Dirichlet process mixture model (DPMM) is a popular Bayesian nonparametric model. In this paper, we apply this model to weighted data and then estimate the un-weighted distribution from the corresponding weighted distribution using the…
Forecast combination integrates information from various sources by consolidating multiple forecast results from the target time series. Instead of the need to select a single optimal forecasting model, this paper introduces a deep learning…
In order to fully utilize "big data", it is often required to use "big models". Such models tend to grow with the complexity and size of the training data, and do not make strong parametric assumptions upfront on the nature of the…
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…
Predictive recursion is an accurate and computationally efficient algorithm for nonparametric estimation of mixing densities in mixture models. In semiparametric mixture models, however, the algorithm fails to account for any uncertainty in…
In this paper we consider the problem of dynamic clustering, where cluster memberships may change over time and clusters may split and merge over time, thus creating new clusters and destroying existing ones. We propose a Bayesian…
We present a mixed multinomial logit (MNL) model, which leverages the truncated stick-breaking process representation of the Dirichlet process as a flexible nonparametric mixing distribution. The proposed model is a Dirichlet process…
In real world machine learning applications, testing data may contain some meaningful new categories that have not been seen in labeled training data. To simultaneously recognize new data categories and assign most appropriate category…
Posterior computation in hierarchical Dirichlet process (HDP) mixture models is an active area of research in nonparametric Bayes inference of grouped data. Existing literature almost exclusively focuses on the Chinese restaurant franchise…
Using movement primitive libraries is an effective means to enable robots to solve more complex tasks. In order to build these movement libraries, current algorithms require a prior segmentation of the demonstration trajectories. A…
Many data are naturally modeled by an unobserved hierarchical structure. In this paper we propose a flexible nonparametric prior over unknown data hierarchies. The approach uses nested stick-breaking processes to allow for trees of…
The hierarchical Dirichlet process is the cornerstone of Bayesian nonparametric multilevel models. Its generative model can be described through a set of latent variables, commonly referred to as tables within the popular restaurant…
Image segmentation is a fundamental step for the interpretation of Remote Sensing Images. Clustering or segmentation methods usually precede the classification task and are used as support tools for manual labeling. The most common…
When constructing a Bayesian Machine Learning model, we might be faced with multiple different prior distributions and thus are required to properly consider them in a sensible manner in our model. While this situation is reasonably well…
The goal of this paper is to introduce a process that generates, given Hilbert space $H$ and symmetric operator $A$, an embedding of $H$ into an $L_2$-space through which $A$ is extended by a multiplication operator. This process will…
Kernel embeddings have emerged as a powerful tool for representing probability measures in a variety of statistical inference problems. By mapping probability measures into a reproducing kernel Hilbert space (RKHS), kernel embeddings enable…
We propose a vector-valued regression problem whose solution is equivalent to the reproducing kernel Hilbert space (RKHS) embedding of the Bayesian posterior distribution. This equivalence provides a new understanding of kernel Bayesian…
Inference in popular nonparametric Bayesian models typically relies on sampling or other approximations. This paper presents a general methodology for constructing novel tractable nonparametric Bayesian methods by applying the kernel trick…
We study reproducing kernels, and associated reproducing kernel Hilbert spaces (RKHSs) $\mathscr{H}$ over infinite, discrete and countable sets $V$. In this setting we analyze in detail the distributions of the corresponding Dirac…
A parallel splitting method is proposed for solving systems of coupled monotone inclusions in Hilbert spaces. Convergence is established for a wide class of coupling schemes. Unlike classical alternating algorithms, which are limited to two…