Phylodynamics is an area of population genetics that uses genetic sequence data to estimate past population dynamics. Modern state-of-the-art Bayesian nonparametric methods for recovering population size trajectories of unknown form use either change-point models or Gaussian process priors. Change-point models suffer from computational issues when the number of change-points is unknown and needs to be estimated. Gaussian process-based methods lack local adaptivity and cannot accurately recover trajectories that exhibit features such as abrupt changes in trend or varying levels of smoothness. We propose a novel, locally-adaptive approach to Bayesian nonparametric phylodynamic inference that has the flexibility to accommodate a large class of functional behaviors. Local adaptivity results from modeling the log-transformed effective population size a priori as a horseshoe Markov random field, a recently proposed statistical model that blends together the best properties of the change-point and Gaussian process modeling paradigms. We use simulated data to assess model performance, and find that our proposed method results in reduced bias and increased precision when compared to contemporary methods. We also use our models to reconstruct past changes in genetic diversity of human hepatitis C virus in Egypt and to estimate population size changes of ancient and modern steppe bison. These analyses show that our new method captures features of the population size trajectories that were missed by the state-of-the-art methods.
Spike-and-slab and horseshoe regression are arguably the most popular Bayesian variable selection approaches for linear regression models. However, their performance can deteriorate if outliers and heteroskedasticity are present in the data, which are common features in many real-world statistics and machine learning applications. In this work, we propose a Bayesian nonparametric approach to linear regression that performs variable selection while accounting for outliers and heteroskedasticity. Our proposed model is an instance of a Dirichlet process scale mixture model with the advantage that…
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 present a locally adaptive nonparametric curve fitting method that operates within a fully Bayesian framework. This method uses shrinkage priors to induce sparsity in order-k differences in the latent trend function, providing a combination of local adaptation and global control. Using a scale mixture of normals representation of shrinkage priors, we make explicit connections between our method and kth order Gaussian Markov random field smoothing. We call the resulting processes shrinkage prior Markov random fields (SPMRFs). We use Hamiltonian Monte Carlo to approximate the posterior distri…
Modeling Nonlinear Ability Trajectories and Learner Heterogeneity in Online Learning: A Bayesian Nonparametric Dynamic IRT Framework
Shenzhen University（深圳大学）；University of California, Los Angeles（加州大学洛杉矶分校）；University of Wisconsin-Madison（威斯康星大学麦迪逊分校）；Michigan State University（密歇根州立大学）
The goal of phylodynamics, an area on the intersection of phylogenetics and population genetics, is to reconstruct population size dynamics from genetic data. Recently, a series of nonparametric Bayesian methods have been proposed for such demographic reconstructions. These methods rely on prior specifications based on Gaussian processes and proceed by approximating the posterior distribution of population size trajectories via Markov chain Monte Carlo (MCMC) methods. In this paper, we adapt an integrated nested Laplace approximation (INLA), a recently proposed approximate Bayesian inference f…
We propose a model of brain atrophy as a function of high-dimensional genetic information and low dimensional covariates such as gender, age, APOE gene, and disease status. A nonparametric single-index Bayesian model of high dimension is proposed to model the relationship with B-spline series prior on the unknown functions and Dirichlet process scale mixture of centered normal prior on the distributions of the random effects. The posterior rate of contraction without the random effect is established for a fixed number of regions and time points with increasing sample size. We implement an effi…
Layer 6 AI（Layer 6人工智能公司）；University of Toronto（多伦多大学）；Vector Institute（向量研究所）
Skills or low-level policies in reinforcement learning are temporally extended actions that can speed up learning and enable complex behaviours. Recent work in offline reinforcement learning and imitation learning has proposed several techniques for skill discovery from a set of expert trajectories. While these methods are promising, the number K of skills to discover is always a fixed hyperparameter, which requires either prior knowledge about the environment or an additional parameter search to tune it. We first propose a method for offline learning of options (a particular skill framework) …
We propose a flexible stochastic framework for modeling the market share dynamics over time in a multiple markets setting, where firms interact within and between markets. Firms undergo stochastic idiosyncratic shocks, which contract their shares, and compete to consolidate their position by acquiring new ones in both the market where they operate and in new markets. The model parameters can meaningfully account for phenomena such as barriers to entry and exit, fixed and sunk costs, costs of expanding to new sectors with different technologies and competitive advantage among firms. The constru…
We present a method for learning options from segmented demonstration trajectories. The trajectories are first segmented into skills using nonparametric Bayesian clustering and a reward function for each segment is then learned using inverse reinforcement learning. From this, a set of inferred trajectories for the demonstration are generated. Option initiation sets and termination conditions are learned from these trajectories using the one-class support vector machine clustering algorithm. We demonstrate our method in the four rooms domain, where an agent is able to autonomously discover usab…
Bayesian ACCESS for Understanding Latent Epidemic Trajectories from Publicly Released Suppressed Data: Application to U.S. Opioid-related Overdose Mortality
The University of Texas Health Science Center at Houston（休斯顿德克萨斯大学健康科学中心）
The observed sequence variation at a locus informs about the evolutionary history of the sample and past population size dynamics. The Kingman coalescent is used in a generative model of molecular sequence variation to infer evolutionary parameters. However, it is well understood that inference under this model does not scale well with sample size. Here, we build on recent work based on a lower resolution coalescent process, the Tajima coalescent, to model longitudinal samples. While the Kingman coalescent models the ancestry of labeled individuals, the heterochronous Tajima coalescent models …
Standard models assign disease progression to discrete categories or stages based on well-characterized clinical markers. However, such a system is potentially at odds with our understanding of the underlying biology, which in highly complex systems may support a (near-)continuous evolution of disease from inception to terminal state. To learn such a continuous disease score one could infer a latent variable from dynamic "omics" data such as RNA-seq that correlates with an outcome of interest such as survival time. However, such analyses may be confounded by additional data such as clinical co…
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 promising approach is to model the trajectory as being generated by a set of Switching Linear Dynamical Systems and inferring a meaningful segmentation by inspecting the transition points characterized by the switching dynamics. With respect to the learning, a nonparametric Bayesian approach is employed utilizing a Gibbs sampler.
Aalto University（阿尔托大学）；University of Tübingen（蒂宾根大学）
Recent machine learning advances have proposed black-box estimation of unknown continuous-time system dynamics directly from data. However, earlier works are based on approximative ODE solutions or point estimates. We propose a novel Bayesian nonparametric model that uses Gaussian processes to infer posteriors of unknown ODE systems directly from data. We derive sparse variational inference with decoupled functional sampling to represent vector field posteriors. We also introduce a probabilistic shooting augmentation to enable efficient inference from arbitrarily long trajectories. The method …
We develop a fully Bayesian framework for function-on-scalars regression with many predictors. The functional data response is modeled nonparametrically using unknown basis functions, which produces a flexible and data-adaptive functional basis. We incorporate shrinkage priors that effectively remove unimportant scalar covariates from the model and reduce sensitivity to the number of (unknown) basis functions. For variable selection in functional regression, we propose a decision theoretic posterior summarization technique, which identifies a subset of covariates that retains nearly the predic…
University of Cambridge（剑桥大学）；The Alan Turing Institute（艾伦·图灵研究所）；University of California Los Angeles（加州大学洛杉矶分校）
Analyzing electronic health records (EHR) poses significant challenges because often few samples are available describing a patient's health and, when available, their information content is highly diverse. The problem we consider is how to integrate sparsely sampled longitudinal data, missing measurements informative of the underlying health status and fixed demographic information to produce estimated survival distributions updated through a patient's follow up. We propose a nonparametric probabilistic model that generates survival trajectories from an ensemble of Bayesian trees that learns …
We develop a Gaussian process ("GP") framework for modeling mortality rates and mortality improvement factors. GP regression is a nonparametric, data-driven approach for determining the spatial dependence in mortality rates and jointly smoothing raw rates across dimensions, such as calendar year and age. The GP model quantifies uncertainty associated with smoothed historical experience and generates full stochastic trajectories for out-of-sample forecasts. Our framework is well suited for updating projections when newly available data arrives, and for dealing with "edge" issues where credibili…
In mixed longitudinal studies, a group of subjects enter the study at different ages (cross-sectional) and are followed for successive years (longitudinal). In the context of such studies, we consider nonparametric covariance estimation with samples of noisy and partially observed functional trajectories. The proposed algorithm is based on a noniterative sequential-aggregation scheme with only basic matrix operations and closed-form solutions in each step. The good performance of the proposed method is supported by both theory and numerical experiments. We also apply the proposed procedure to …
In 2015 the US federal government sponsored a dengue forecasting competition using historical case data from Iquitos, Peru and San Juan, Puerto Rico. Competitors were evaluated on several aspects of out-of-sample forecasts including the targets of peak week, peak incidence during that week and total season incidence across each of several seasons. Our team was one of the top performers of that competition, outperforming all other teams in multiple targets/locals. In this paper we report on our methodology, a large component of which, surprisingly, ignores the known biology of epidemics at larg…
In the near future, millions of load curves measuring the electricity consumption of French households in small time grids (probably half hours) will be available. All these collected load curves represent a huge amount of information which could be exploited using survey sampling techniques. In particular, the total consumption of a specific cus- tomer group (for example all the customers of an electricity supplier) could be estimated using unequal probability random sampling methods. Unfortunately, data collection may undergo technical problems resulting in missing values. In this paper we s…
In this paper, I propose a general algorithm for multiple change point analysis via multivariate distribution-free nonparametric testing based on the concept of ranks that are defined by measure transportation. Multivariate ranks and the usual one-dimensional ranks both share an important property: they are both distribution-free. This finding allows for the creation of nonparametric tests that are distribution-free under the null hypothesis. This method has applications in a variety of fields, and in this paper I implement this algorithm to a microarray dataset for individuals with bladder tu…
Johns Hopkins University（约翰斯·霍普金斯大学）；University of California Santa Barbara（加州大学圣巴巴拉分校）；Harvard University（哈佛大学）
Interacting particle or agent systems that display a rich variety of swarming behaviours are ubiquitous in science and engineering. A fundamental and challenging goal is to understand the link between individual interaction rules and swarming. In this paper, we study the data-driven discovery of a second-order particle swarming model that describes the evolution of $N$ particles in $\mathbb{R}^d$ under radial interactions. We propose a learning approach that models the latent radial interaction function as Gaussian processes, which can simultaneously fulfill two inference goals: one is the non…
