25,943 research outputs found
A Tutorial on Bayesian Nonparametric Models
A key problem in statistical modeling is model selection, how to choose a
model at an appropriate level of complexity. This problem appears in many
settings, most prominently in choosing the number ofclusters in mixture models
or the number of factors in factor analysis. In this tutorial we describe
Bayesian nonparametric methods, a class of methods that side-steps this issue
by allowing the data to determine the complexity of the model. This tutorial is
a high-level introduction to Bayesian nonparametric methods and contains
several examples of their application.Comment: 28 pages, 8 figure
Gaussian Process Structural Equation Models with Latent Variables
In a variety of disciplines such as social sciences, psychology, medicine and
economics, the recorded data are considered to be noisy measurements of latent
variables connected by some causal structure. This corresponds to a family of
graphical models known as the structural equation model with latent variables.
While linear non-Gaussian variants have been well-studied, inference in
nonparametric structural equation models is still underdeveloped. We introduce
a sparse Gaussian process parameterization that defines a non-linear structure
connecting latent variables, unlike common formulations of Gaussian process
latent variable models. The sparse parameterization is given a full Bayesian
treatment without compromising Markov chain Monte Carlo efficiency. We compare
the stability of the sampling procedure and the predictive ability of the model
against the current practice.Comment: 12 pages, 6 figure
Automatic Differentiation Variational Inference
Probabilistic modeling is iterative. A scientist posits a simple model, fits
it to her data, refines it according to her analysis, and repeats. However,
fitting complex models to large data is a bottleneck in this process. Deriving
algorithms for new models can be both mathematically and computationally
challenging, which makes it difficult to efficiently cycle through the steps.
To this end, we develop automatic differentiation variational inference (ADVI).
Using our method, the scientist only provides a probabilistic model and a
dataset, nothing else. ADVI automatically derives an efficient variational
inference algorithm, freeing the scientist to refine and explore many models.
ADVI supports a broad class of models-no conjugacy assumptions are required. We
study ADVI across ten different models and apply it to a dataset with millions
of observations. ADVI is integrated into Stan, a probabilistic programming
system; it is available for immediate use
- …