62,027 research outputs found
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
Accelerated forgetting of contextual details due to focal medio-dorsal thalamic lesion
Effects of thalamic nuclei damage and related white matter tracts on memory performance are still debated. This is particularly evident for the medio-dorsal thalamus which has been less clear in predicting amnesia than anterior thalamus changes. The current study addresses this issue by assessing 7 thalamic stroke patients with consistent unilateral lesions focal to the left medio-dorsal nuclei for immediate and delayed memory performance on standard visual and verbal tests of anterograde memory, and over the long-term (>24 h) on an object-location associative memory task. Thalamic patients showed selective impairment to delayed recall, but intact recognition memory. Patients also showed accelerated forgetting of contextual details after a 24 h delay, compared to controls. Importantly, the mammillothalamic tract was intact in all patients, which suggests a role for the medio-dorsal nuclei in recall and early consolidation memory processes
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