1,471 research outputs found
Poisson Latent Feature Calculus for Generalized Indian Buffet Processes
The purpose of this work is to describe a unified, and indeed simple,
mechanism for non-parametric Bayesian analysis, construction and generative
sampling of a large class of latent feature models which one can describe as
generalized notions of Indian Buffet Processes(IBP). This is done via the
Poisson Process Calculus as it now relates to latent feature models. The IBP
was ingeniously devised by Griffiths and Ghahramani in (2005) and its
generative scheme is cast in terms of customers entering sequentially an Indian
Buffet restaurant and selecting previously sampled dishes as well as new
dishes. In this metaphor dishes corresponds to latent features, attributes,
preferences shared by individuals. The IBP, and its generalizations, represent
an exciting class of models well suited to handle high dimensional statistical
problems now common in this information age. The IBP is based on the usage of
conditionally independent Bernoulli random variables, coupled with completely
random measures acting as Bayesian priors, that are used to create sparse
binary matrices. This Bayesian non-parametric view was a key insight due to
Thibaux and Jordan (2007). One way to think of generalizations is to to use
more general random variables. Of note in the current literature are models
employing Poisson and Negative-Binomial random variables. However, unlike their
closely related counterparts, generalized Chinese restaurant processes, the
ability to analyze IBP models in a systematic and general manner is not yet
available. The limitations are both in terms of knowledge about the effects of
different priors and in terms of models based on a wider choice of random
variables. This work will not only provide a thorough description of the
properties of existing models but also provide a simple template to devise and
analyze new models.Comment: This version provides more details for the multivariate extensions in
section 5. We highlight the case of a simple multinomial distribution and
showcase a multivariate Levy process prior we call a stable-Beta Dirichlet
process. Section 4.1.1 expande
A Simple Class of Bayesian Nonparametric Autoregression Models
We introduce a model for a time series of continuous outcomes, that can be expressed as fully nonparametric regression or density regression on lagged terms. The model is based on a dependent Dirichlet process prior on a family of random probability measures indexed by the lagged covariates. The approach is also extended to sequences of binary responses. We discuss implementation and applications of the models to a sequence of waiting times between eruptions of the Old Faithful Geyser, and to a dataset consisting of sequences of recurrence indicators for tumors in the bladder of several patients.MIUR 2008MK3AFZFONDECYT 1100010NIH/NCI R01CA075981Mathematic
Robot Introspection with Bayesian Nonparametric Vector Autoregressive Hidden Markov Models
Robot introspection, as opposed to anomaly detection typical in process
monitoring, helps a robot understand what it is doing at all times. A robot
should be able to identify its actions not only when failure or novelty occurs,
but also as it executes any number of sub-tasks. As robots continue their quest
of functioning in unstructured environments, it is imperative they understand
what is it that they are actually doing to render them more robust. This work
investigates the modeling ability of Bayesian nonparametric techniques on
Markov Switching Process to learn complex dynamics typical in robot contact
tasks. We study whether the Markov switching process, together with Bayesian
priors can outperform the modeling ability of its counterparts: an HMM with
Bayesian priors and without. The work was tested in a snap assembly task
characterized by high elastic forces. The task consists of an insertion subtask
with very complex dynamics. Our approach showed a stronger ability to
generalize and was able to better model the subtask with complex dynamics in a
computationally efficient way. The modeling technique is also used to learn a
growing library of robot skills, one that when integrated with low-level
control allows for robot online decision making.Comment: final version submitted to humanoids 201
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