Robust tracking of a target in a clutter environment is an important and challenging task. In recent years, the nearest neighbor methods and probabilistic data association filters were proposed. However, the performance of these methods diminishes as the number of measurements increases. In this paper, we propose a robust generative approach to effectively model multiple sensor measurements for tracking a moving target in an environment with high clutter. We assume a time-dependent number of measurements that include sensor observations with unknown origin, some of which may only contain clutter with no additional information. We robustly and accurately estimate the trajectory of the moving target in a high clutter environment with an unknown number of clutters by employing Bayesian nonparametric modeling. In particular, we employ a class of joint Bayesian nonparametric models to construct the joint prior distribution of target and clutter measurements such that the conditional distributions follow a Dirichlet process. The marginalized Dirichlet process prior of the target measurements is then used in a Bayesian tracker to estimate the dynamically-varying target state. We show through experiments that the tracking performance and effectiveness of our proposed framework are increased by suppressing high clutter measurements. In addition, we show that our proposed method outperforms existing methods such as nearest neighbor and probability data association filters.
This work considers an estimation task in compressive sensing, where the goal is to estimate an unknown signal from compressive measurements that are corrupted by additive pre-measurement noise (interference, or clutter) as well as post-measurement noise, in the specific setting where some (perhaps limited) prior knowledge on the signal, interference, and noise is available. The specific aim here is to devise a strategy for incorporating this prior information into the design of an appropriate compressive measurement strategy. Here, the prior information is interpreted as statistics of a prior…
We study the problem of estimating the continuous response over time to interventions using observational time series---a retrospective dataset where the policy by which the data are generated is unknown to the learner. We are motivated by applications where response varies by individuals and therefore, estimating responses at the individual-level is valuable for personalizing decision-making. We refer to this as the problem of estimating individualized treatment response (ITR) curves. In statistics, G-computation formula (Robins, 1986) has been commonly used for estimating treatment responses…
Memorial Sloan Kettering Cancer Center（纪念斯隆凯特琳癌症中心）
We present a Bayesian hierarchical multi-view mixture model termed Symphony that simultaneously learns clusters of cells representing cell types and their underlying gene regulatory networks by integrating data from two views: single-cell gene expression data and paired epigenetic data, which is informative of gene-gene interactions. This model improves interpretation of clusters as cell types with similar expression patterns as well as regulatory networks driving expression, by explaining gene-gene covariances with the biological machinery regulating gene expression. We show the theoretical a…
This paper describes a method to estimate a production frontier that satisfies the axioms of monotonicity and concavity in a non-parametric Bayesian setting. An inefficiency term that allows for significant departure from prior distributional assumptions is jointly estimated in a single stage with parametric prior assumptions. We introduce heteroscedasticity into the inefficiency terms by local hyperplane-specific shrinkage hyperparameters and impose monotonicity using bound-constrained local nonlinear regression. Our minimum-of-hyperplanes estimator imposes concavity. Our Monte Carlo simulati…
Some challenging problems in tracking multiple objects include the time-dependent cardinality, unordered measurements and object parameter labeling. In this paper, we employ Bayesian Bayesian nonparametric methods to address these challenges. In particular, we propose modeling the multiple object parameter state prior using the dependent Dirichlet and Pitman-Yor processes. These nonparametric models have been shown to be more flexible and robust, when compared to existing methods, for estimating the time-varying number of objects, providing object labeling and identifying measurement to object…
Recently, there has been a surge of interest in using spectral methods for estimating latent variable models. However, it is usually assumed that the distribution of the observations conditioned on the latent variables is either discrete or belongs to a parametric family. In this paper, we study the estimation of an $m$-state hidden Markov model (HMM) with only smoothness assumptions, such as Hölderian conditions, on the emission densities. By leveraging some recent advances in continuous linear algebra and numerical analysis, we develop a computationally efficient spectral algorithm for learn…
The problem of estimating discovery probabilities originated in the context of statistical ecology, and in recent years it has become popular due to its frequent appearance in challenging applications arising in genetics, bioinformatics, linguistics, designs of experiments, machine learning, etc. A full range of statistical approaches, parametric and nonparametric as well as frequentist and Bayesian, has been proposed for estimating discovery probabilities. In this paper we investigate the relationships between the celebrated Good-Turing approach, which is a frequentist nonparametric approach …
The vast majority of models for the spread of communicable diseases are parametric in nature and involve underlying assumptions about how the disease spreads through a population. In this article we consider the use of Bayesian nonparametric approaches to analysing data from disease outbreaks. Specifically we focus on methods for estimating the infection process in simple models under the assumption that this process has an explicit time-dependence.
The number of species can be estimated by sampling individuals from a species assemblage. The problem of estimating generalized species accumulation curve is addressed in a nonparametric Poisson mixture model. A likelihood-based estimator is proposed and illustrated by real examples.
Changes in population size influence genetic diversity of the population and, as a result, leave a signature of these changes in individual genomes in the population. We are interested in the inverse problem of reconstructing past population dynamics from genomic data. We start with a standard framework based on the coalescent, a stochastic process that generates genealogies connecting randomly sampled individuals from the population of interest. These genealogies serve as a glue between the population demographic history and genomic sequences. It turns out that only the times of genealogical …
We develop a Bayesian nonparametric framework for modeling ordinal regression relationships which evolve in discrete time. The motivating application involves a key problem in fisheries research on estimating dynamically evolving relationships between age, length and maturity, the latter recorded on an ordinal scale. The methodology builds from nonparametric mixture modeling for the joint stochastic mechanism of covariates and latent continuous responses. This approach yields highly flexible inference for ordinal regression functions while at the same time avoiding the computational challenges…
The success of deep learning has inspired recent interests in applying neural networks in statistical inference. In this paper, we investigate the use of deep neural networks for nonparametric regression with measurement errors. We propose an efficient neural network design for estimating measurement error models, in which we use a fully connected feed-forward neural network (FNN) to approximate the regression function $f(x)$, a normalizing flow to approximate the prior distribution of $X$, and an inference network to approximate the posterior distribution of $X$. Our method utilizes recent ad…
University of Chicago（芝加哥大学）；Toyota Technological Institute at Chicago（芝加哥丰田技术研究院）
We present a framework for incorporating prior information into nonparametric estimation of graphical models. To avoid distributional assumptions, we restrict the graph to be a forest and build on the work of forest density estimation (FDE). We reformulate the FDE approach from a Bayesian perspective, and introduce prior distributions on the graphs. As two concrete examples, we apply this framework to estimating scale-free graphs and learning multiple graphs with similar structures. The resulting algorithms are equivalent to finding a maximum spanning tree of a weighted graph with a penalty te…
A nonparametric and locally adaptive Bayesian estimator is proposed for estimating a binary regression. Flexibility is obtained by modeling the binary regression as a mixture of probit regressions with the argument of each probit regression having a thin plate spline prior with its own smoothing parameter and with the mixture weights depending on the covariates. The estimator is compared to a single spline estimator and to a recently proposed locally adaptive estimator. The methodology is illustrated by applying it to both simulated and real examples.
Motivated by problems in data clustering, we establish general conditions under which families of nonparametric mixture models are identifiable, by introducing a novel framework involving clustering overfitted \emph{parametric} (i.e. misspecified) mixture models. These identifiability conditions generalize existing conditions in the literature, and are flexible enough to include for example mixtures of Gaussian mixtures. In contrast to the recent literature on estimating nonparametric mixtures, we allow for general nonparametric mixture components, and instead impose regularity assumptions on …
We present a Bayesian nonparametric system reliability model which scales well and provides a great deal of flexibility in modeling. The Bayesian approach naturally handles the disparate amounts of component and subsystem data that may exist. However, traditional Bayesian reliability models are quite computationally complex, relying on MCMC techniques. Our approach utilizes the conjugate properties of the beta-Stacy process, which is the fundamental building block of our model. These individual models are linked together using a method of moments estimation approach. This model is computationa…
Intensity estimation is a common problem in statistical analysis of spatial point pattern data. This paper proposes a nonparametric Bayesian method for estimating the spatial point process intensity based on mixture of finite mixture (MFM) model. MFM approach leads to a consistent estimate of the intensity of spatial point patterns in different areas while considering heterogeneity. An efficient Markov chain Monte Carlo (MCMC) algorithm is proposed for our method. Extensive simulation studies are carried out to examine empirical performance of the proposed method. The usage of our proposed met…
In this paper we propose a general method to derive an upper bound for the contraction rate of the posterior distribution for nonparametric inverse problems. We present a general theorem that allows us to derive con- traction rates for the parameter of interest from contraction rates of the related direct problem of estimating transformed parameter of interest. An interesting aspect of this approach is that it allows us to derive con- traction rates for priors that are not related to the singular value decomposition of the operator. We apply our result to several examples of linear inverse pro…
We propose an extension of non-parametric multivariate finite mixture models by dropping the standard conditional independence assumption and incorporating the independent component analysis (ICA) structure instead. We formulate an objective function in terms of penalized smoothed Kullback Leibler distance and introduce the nonlinear smoothed majorization-minimization independent component analysis (NSMM-ICA) algorithm for optimizing this function and estimating the model parameters. We have implemented a practical version of this algorithm, which utilizes the FastICA algorithm, in the R packa…
In many real problems, dependence structures more general than exchangeability are required. For instance, in some settings partial exchangeability is a more reasonable assumption. For this reason, vectors of dependent Bayesian nonparametric priors have recently gained popularity. They provide flexible models which are tractable from a computational and theoretical point of view. In this paper, we focus on their use for estimating survival functions with multiple-samples information. Our methodology allows to model the dependence among survival times of different groups of observations and ext…
A nonparametric Bayes approach is proposed for the problem of estimating a sparse sequence based on Gaussian random variables. We adopt the popular two-group prior with one component being a point mass at zero, and the other component being a mixture of Gaussian distributions. Although the Gaussian family has been shown to be suboptimal for this problem, we find that Gaussian mixtures, with a proper choice on the means and mixing weights, have the desired asymptotic behavior, e.g., the corresponding posterior concentrates on balls with the desired minimax rate. To achieve computation efficienc…
In this paper, the panel count data analysis for recurrent events is considered. Such analysis is useful for studying tumor or infection recurrences in both clinical trial and observational studies. A bivariate Gaussian Cox process model is proposed to jointly model the observation process and the recurrent event process. Bayesian nonparametric inference is proposed for simultaneously estimating regression parameters, bivariate frailty effects and baseline intensity functions. Inference is done through Markov chain Monte Carlo, with fully developed computational techniques. Predictive inferenc…
Based on a novel dynamic Whittle likelihood approximation for locally stationary processes, a Bayesian nonparametric approach to estimating the time-varying spectral density is proposed. This dynamic frequency-domain based likelihood approximation is able to depict the time-frequency evolution of the process by utilizing the moving periodogram previously introduced in the bootstrap literature. The posterior distribution is obtained by updating a bivariate extension of the Bernstein-Dirichlet process prior with the dynamic Whittle likelihood. Asymptotic properties such as sup-norm posterior con…
We present a nonparametric method for estimating the value and several derivatives of an unknown, sufficiently smooth real-valued function of real-valued arguments from a finite sample of points, where both the function arguments and the corresponding values are known only up to measurement errors having some assumed distribution and correlation structure. The method, Moving Taylor Bayesian Regression (MOTABAR), uses Bayesian updating to find the posterior mean of the coefficients of a Taylor polynomial of the function at a moving position of interest. When measurement errors are neglected, MO…
In a meta-analysis, it is important to specify a model that adequately describes the effect-size distribution of the underlying population of studies. The conventional normal fixed-effect and normal random-effects models assume a normal effect-size population distribution, conditionally on parameters and covariates. For estimating the mean overall effect size, such models may be adequate, but for prediction they surely are not if the effect size distribution exhibits non-normal behavior. To address this issue, we propose a Bayesian nonparametric meta-analysis model, which can describe a wider …
We propose a kernel mixture of polynomials prior for Bayesian nonparametric regression. The regression function is modeled by local averages of polynomials with kernel mixture weights. We obtain the minimax-optimal rate of contraction of the full posterior distribution up to a logarithmic factor that adapts to the smoothness level of the true function by estimating metric entropies of certain function classes. We also provide a frequentist sieve maximum likelihood estimator with a near-optimal convergence rate. We further investigate the application of the kernel mixture of polynomials to the …
We propose an adaptive design for early phase drug combination cancer trials with the goal of estimating the maximum tolerated dose (MTD). A nonparametric Bayesian model, using beta priors truncated to the set of partially ordered dose combinations, is used to describe the probability of dose limiting toxicity (DLT). Dose allocation between successive cohorts of patients is estimated using a modified Continual Reassessment scheme. The updated probabilities of DLT are calculated with a Gibbs sampler that employs a weighting mechanism to calibrate the influence of data versus the prior. At the e…
In this paper, we study the Bernstein polynomial model for estimating the multivariate distribution functions and densities with bounded support. As a mixture model of multivariate beta distributions, the maximum (approximate) likelihood estimate can be obtained using EM algorithm. A change-point method of choosing optimal degrees of the proposed Bernstein polynomial model is presented. Under some conditions the optimal rate of convergence in the mean $χ^2$-divergence of new density estimator is shown to be nearly parametric. The method is illustrated by an application to a real data set. Fini…
Basketball shot location data provide valuable summary information regarding players to coaches, sports analysts, fans, statisticians, as well as players themselves. Represented by spatial points, such data are naturally analyzed with spatial point process models. We present a novel nonparametric Bayesian method for learning the underlying intensity surface built upon a combination of Dirichlet process and Markov random field. Our method has the advantage of effectively encouraging local spatial homogeneity when estimating a globally heterogeneous intensity surface. Posterior inferences are pe…
The Koopman operator is a mathematical tool that allows for a linear description of non-linear systems, but working in infinite dimensional spaces. Dynamic Mode Decomposition and Extended Dynamic Mode Decomposition are amongst the most popular finite dimensional approximation. In this paper we capture their core essence as a dual version of the same framework, incorporating them into the Kernel framework. To do so, we leverage the RKHS as a suitable space for learning the Koopman dynamics, thanks to its intrinsic finite-dimensional nature, shaped by data. We finally establish a strong link bet…
Non-parametric supervised learning algorithms represent a succinct class of supervised learning algorithms where the learning parameters are highly flexible and whose values are directly dependent on the size of the training data. In this paper, we comparatively study the properties of four nonparametric algorithms, K-Nearest Neighbours (KNNs), Support Vector Machines (SVMs), Decision trees and Random forests. The supervised learning task is a regression estimate of the time-lapse in medical insurance reimbursement. Our study is concerned precisely with how well each of the nonparametric regre…
When modeling a probability distribution with a Bayesian network, we are faced with the problem of how to handle continuous variables. Most previous work has either solved the problem by discretizing, or assumed that the data are generated by a single Gaussian. In this paper we abandon the normality assumption and instead use statistical methods for nonparametric density estimation. For a naive Bayesian classifier, we present experimental results on a variety of natural and artificial domains, comparing two methods of density estimation: assuming normality and modeling each conditional distrib…
Estimating the score, i.e., the gradient of log density function, from a set of samples generated by an unknown distribution is a fundamental task in inference and learning of probabilistic models that involve flexible yet intractable densities. Kernel estimators based on Stein's methods or score matching have shown promise, however their theoretical properties and relationships have not been fully-understood. We provide a unifying view of these estimators under the framework of regularized nonparametric regression. It allows us to analyse existing estimators and construct new ones with desira…
