3,430 research outputs found
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
Foundational principles for large scale inference: Illustrations through correlation mining
When can reliable inference be drawn in the "Big Data" context? This paper
presents a framework for answering this fundamental question in the context of
correlation mining, with implications for general large scale inference. In
large scale data applications like genomics, connectomics, and eco-informatics
the dataset is often variable-rich but sample-starved: a regime where the
number of acquired samples (statistical replicates) is far fewer than the
number of observed variables (genes, neurons, voxels, or chemical
constituents). Much of recent work has focused on understanding the
computational complexity of proposed methods for "Big Data." Sample complexity
however has received relatively less attention, especially in the setting when
the sample size is fixed, and the dimension grows without bound. To
address this gap, we develop a unified statistical framework that explicitly
quantifies the sample complexity of various inferential tasks. Sampling regimes
can be divided into several categories: 1) the classical asymptotic regime
where the variable dimension is fixed and the sample size goes to infinity; 2)
the mixed asymptotic regime where both variable dimension and sample size go to
infinity at comparable rates; 3) the purely high dimensional asymptotic regime
where the variable dimension goes to infinity and the sample size is fixed.
Each regime has its niche but only the latter regime applies to exa-scale data
dimension. We illustrate this high dimensional framework for the problem of
correlation mining, where it is the matrix of pairwise and partial correlations
among the variables that are of interest. We demonstrate various regimes of
correlation mining based on the unifying perspective of high dimensional
learning rates and sample complexity for different structured covariance models
and different inference tasks
Challenges of Big Data Analysis
Big Data bring new opportunities to modern society and challenges to data
scientists. On one hand, Big Data hold great promises for discovering subtle
population patterns and heterogeneities that are not possible with small-scale
data. On the other hand, the massive sample size and high dimensionality of Big
Data introduce unique computational and statistical challenges, including
scalability and storage bottleneck, noise accumulation, spurious correlation,
incidental endogeneity, and measurement errors. These challenges are
distinguished and require new computational and statistical paradigm. This
article give overviews on the salient features of Big Data and how these
features impact on paradigm change on statistical and computational methods as
well as computing architectures. We also provide various new perspectives on
the Big Data analysis and computation. In particular, we emphasis on the
viability of the sparsest solution in high-confidence set and point out that
exogeneous assumptions in most statistical methods for Big Data can not be
validated due to incidental endogeneity. They can lead to wrong statistical
inferences and consequently wrong scientific conclusions
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