35 research outputs found
Restricting exchangeable nonparametric distributions
Distributions over exchangeable matrices with infinitely many columns, such
as the Indian buffet process, are useful in constructing nonparametric latent
variable models. However, the distribution implied by such models over the
number of features exhibited by each data point may be poorly- suited for many
modeling tasks. In this paper, we propose a class of exchangeable nonparametric
priors obtained by restricting the domain of existing models. Such models allow
us to specify the distribution over the number of features per data point, and
can achieve better performance on data sets where the number of features is not
well-modeled by the original distribution
ClusterCluster: Parallel Markov Chain Monte Carlo for Dirichlet Process Mixtures
The Dirichlet process (DP) is a fundamental mathematical tool for Bayesian
nonparametric modeling, and is widely used in tasks such as density estimation,
natural language processing, and time series modeling. Although MCMC inference
methods for the DP often provide a gold standard in terms asymptotic accuracy,
they can be computationally expensive and are not obviously parallelizable. We
propose a reparameterization of the Dirichlet process that induces conditional
independencies between the atoms that form the random measure. This conditional
independence enables many of the Markov chain transition operators for DP
inference to be simulated in parallel across multiple cores. Applied to mixture
modeling, our approach enables the Dirichlet process to simultaneously learn
clusters that describe the data and superclusters that define the granularity
of parallelization. Unlike previous approaches, our technique does not require
alteration of the model and leaves the true posterior distribution invariant.
It also naturally lends itself to a distributed software implementation in
terms of Map-Reduce, which we test in cluster configurations of over 50
machines and 100 cores. We present experiments exploring the parallel
efficiency and convergence properties of our approach on both synthetic and
real-world data, including runs on 1MM data vectors in 256 dimensions.Comment: 12 pages, 10 figures. Submitted to ICML 2013 during third submission
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Vector Autoregressive POMDP Model Learning and Planning for Human-Robot Collaboration
Human-robot collaboration (HRC) has emerged as a hot research area at the
intersection of control, robotics, and psychology in recent years. It is of
critical importance to obtain an expressive but meanwhile tractable model for
human beings in HRC. In this paper, we propose a model called Vector
Autoregressive POMDP (VAR-POMDP) model which is an extension of the traditional
POMDP model by considering the correlation among observations. The VAR-POMDP
model is more powerful in the expressiveness of features than the traditional
continuous observation POMDP since the traditional one is a special case of the
VAR-POMDP model. Meanwhile, the proposed VAR-POMDP model is also tractable, as
we show that it can be effectively learned from data and we can extend
point-based value iteration (PBVI) to VAR-POMDP planning. Particularly, in this
paper, we propose to use the Bayesian non-parametric learning to decide
potential human states and learn a VAR-POMDP model using data collected from
human demonstrations. Then, we consider planning with respect to PCTL which is
widely used as safety and reachability requirement in robotics. Finally, the
advantage of using the proposed model for HRC is validated by experimental
results using data collected from a driver-assistance test-bed
Discovering shared and individual latent structure in multiple time series
This paper proposes a nonparametric Bayesian method for exploratory data
analysis and feature construction in continuous time series. Our method focuses
on understanding shared features in a set of time series that exhibit
significant individual variability. Our method builds on the framework of
latent Diricihlet allocation (LDA) and its extension to hierarchical Dirichlet
processes, which allows us to characterize each series as switching between
latent ``topics'', where each topic is characterized as a distribution over
``words'' that specify the series dynamics. However, unlike standard
applications of LDA, we discover the words as we learn the model. We apply this
model to the task of tracking the physiological signals of premature infants;
our model obtains clinically significant insights as well as useful features
for supervised learning tasks.Comment: Additional supplementary section in tex fil
A constructive definition of the beta process
We derive a construction of the beta process that allows for the atoms with
significant measure to be drawn first. Our representation is based on an
extension of the Sethuraman (1994) construction of the Dirichlet process, and
therefore we refer to it as a stick-breaking construction. Our first proof uses
a limiting case argument of finite arrays. To this end, we present a finite
sieve approximation to the beta process that parallels that of Ishwaran &
Zarepour (2002) and prove its convergence to the beta process. We give a second
proof of the construction using Poisson process machinery. We use the Poisson
process to derive almost sure truncation bounds for the construction. We
conclude the paper by presenting an efficient sampling algorithm for
beta-Bernoulli and beta-negative binomial process models
HIRL: Hierarchical Inverse Reinforcement Learning for Long-Horizon Tasks with Delayed Rewards
Reinforcement Learning (RL) struggles in problems with delayed rewards, and
one approach is to segment the task into sub-tasks with incremental rewards. We
propose a framework called Hierarchical Inverse Reinforcement Learning (HIRL),
which is a model for learning sub-task structure from demonstrations. HIRL
decomposes the task into sub-tasks based on transitions that are consistent
across demonstrations. These transitions are defined as changes in local
linearity w.r.t to a kernel function. Then, HIRL uses the inferred structure to
learn reward functions local to the sub-tasks but also handle any global
dependencies such as sequentiality.
We have evaluated HIRL on several standard RL benchmarks: Parallel Parking
with noisy dynamics, Two-Link Pendulum, 2D Noisy Motion Planning, and a Pinball
environment. In the parallel parking task, we find that rewards constructed
with HIRL converge to a policy with an 80% success rate in 32% fewer time-steps
than those constructed with Maximum Entropy Inverse RL (MaxEnt IRL), and with
partial state observation, the policies learned with IRL fail to achieve this
accuracy while HIRL still converges. We further find that that the rewards
learned with HIRL are robust to environment noise where they can tolerate 1
stdev. of random perturbation in the poses in the environment obstacles while
maintaining roughly the same convergence rate. We find that HIRL rewards can
converge up-to 6x faster than rewards constructed with IRL.Comment: 12 page
Detecting Unknown Behaviors by Pre-defined Behaviours: An Bayesian Non-parametric Approach
An automatic mouse behavior recognition system can considerably reduce the
workload of experimenters and facilitate the analysis process. Typically,
supervised approaches, unsupervised approaches and semi-supervised approaches
are applied for behavior recognition purpose under a setting which has all of
predefined behaviors. In the real situation, however, as mouses can show
various types of behaviors, besides the predefined behaviors that we want to
analyze, there are many undefined behaviors existing. Both supervised
approaches and conventional semi-supervised approaches cannot identify these
undefined behaviors. Though unsupervised approaches can detect these undefined
behaviors, a post-hoc labeling is needed. In this paper, we propose a
semi-supervised infinite Gaussian mixture model (SsIGMM), to incorporate both
labeled and unlabelled information in learning process while considering
undefined behaviors. It also generates the distribution of the predefined and
undefined behaviors by mixture Gaussians, which can be used for further
analysis. In our experiments, we confirmed the superiority of SsIGMM for
segmenting and labelling mouse-behavior videos
Concept Modeling with Superwords
In information retrieval, a fundamental goal is to transform a document into
concepts that are representative of its content. The term "representative" is
in itself challenging to define, and various tasks require different
granularities of concepts. In this paper, we aim to model concepts that are
sparse over the vocabulary, and that flexibly adapt their content based on
other relevant semantic information such as textual structure or associated
image features. We explore a Bayesian nonparametric model based on nested beta
processes that allows for inferring an unknown number of strictly sparse
concepts. The resulting model provides an inherently different representation
of concepts than a standard LDA (or HDP) based topic model, and allows for
direct incorporation of semantic features. We demonstrate the utility of this
representation on multilingual blog data and the Congressional Record
Bayesian Nonparametric Dictionary Learning for Compressed Sensing MRI
We develop a Bayesian nonparametric model for reconstructing magnetic
resonance images (MRI) from highly undersampled k-space data. We perform
dictionary learning as part of the image reconstruction process. To this end,
we use the beta process as a nonparametric dictionary learning prior for
representing an image patch as a sparse combination of dictionary elements. The
size of the dictionary and the patch-specific sparsity pattern are inferred
from the data, in addition to other dictionary learning variables. Dictionary
learning is performed directly on the compressed image, and so is tailored to
the MRI being considered. In addition, we investigate a total variation penalty
term in combination with the dictionary learning model, and show how the
denoising property of dictionary learning removes dependence on regularization
parameters in the noisy setting. We derive a stochastic optimization algorithm
based on Markov Chain Monte Carlo (MCMC) for the Bayesian model, and use the
alternating direction method of multipliers (ADMM) for efficiently performing
total variation minimization. We present empirical results on several MRI,
which show that the proposed regularization framework can improve
reconstruction accuracy over other methods
A New Class of Time Dependent Latent Factor Models with Applications
In many applications, observed data are influenced by some combination of
latent causes. For example, suppose sensors are placed inside a building to
record responses such as temperature, humidity, power consumption and noise
levels. These random, observed responses are typically affected by many
unobserved, latent factors (or features) within the building such as the number
of individuals, the turning on and off of electrical devices, power surges,
etc. These latent factors are usually present for a contiguous period of time
before disappearing; further, multiple factors could be present at a time. This
paper develops new probabilistic methodology and inference methods for random
object generation influenced by latent features exhibiting temporal
persistence. Every datum is associated with subsets of a potentially infinite
number of hidden, persistent features that account for temporal dynamics in an
observation. The ensuing class of dynamic models constructed by adapting the
Indian Buffet Process --- a probability measure on the space of random,
unbounded binary matrices --- finds use in a variety of applications arising in
operations, signal processing, biomedicine, marketing, image analysis, etc.
Illustrations using synthetic and real data are provided