248 research outputs found
Modeling Persistent Trends in Distributions
We present a nonparametric framework to model a short sequence of probability
distributions that vary both due to underlying effects of sequential
progression and confounding noise. To distinguish between these two types of
variation and estimate the sequential-progression effects, our approach
leverages an assumption that these effects follow a persistent trend. This work
is motivated by the recent rise of single-cell RNA-sequencing experiments over
a brief time course, which aim to identify genes relevant to the progression of
a particular biological process across diverse cell populations. While
classical statistical tools focus on scalar-response regression or
order-agnostic differences between distributions, it is desirable in this
setting to consider both the full distributions as well as the structure
imposed by their ordering. We introduce a new regression model for ordinal
covariates where responses are univariate distributions and the underlying
relationship reflects consistent changes in the distributions over increasing
levels of the covariate. This concept is formalized as a "trend" in
distributions, which we define as an evolution that is linear under the
Wasserstein metric. Implemented via a fast alternating projections algorithm,
our method exhibits numerous strengths in simulations and analyses of
single-cell gene expression data.Comment: To appear in: Journal of the American Statistical Associatio
Stochastic Variational Inference
We develop stochastic variational inference, a scalable algorithm for
approximating posterior distributions. We develop this technique for a large
class of probabilistic models and we demonstrate it with two probabilistic
topic models, latent Dirichlet allocation and the hierarchical Dirichlet
process topic model. Using stochastic variational inference, we analyze several
large collections of documents: 300K articles from Nature, 1.8M articles from
The New York Times, and 3.8M articles from Wikipedia. Stochastic inference can
easily handle data sets of this size and outperforms traditional variational
inference, which can only handle a smaller subset. (We also show that the
Bayesian nonparametric topic model outperforms its parametric counterpart.)
Stochastic variational inference lets us apply complex Bayesian models to
massive data sets
Tree block coordinate descent for map in graphical models
abstract URL: http://jmlr.csail.mit.edu/proceedings/papers/v5/sontag09a.htmlA number of linear programming relaxations have been proposed for finding most likely settings of the variables (MAP) in large probabilistic models. The relaxations are often succinctly expressed in the dual and reduce to different types of reparameterizations of the original model. The dual objectives are typically solved by performing local block coordinate descent steps. In this work, we show how to perform block coordinate descent on spanning trees of the graphical model. We also show how all of the earlier dual algorithms are related to each other, giving transformations from one type of reparameterization to another while maintaining monotonicity relative to a common objective function. Finally, we quantify when the MAP solution can and cannot be decoded directly from the dual LP relaxation
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