41,744 research outputs found
Removing the influence of a group variable in high-dimensional predictive modelling
In many application areas, predictive models are used to support or make
important decisions. There is increasing awareness that these models may
contain spurious or otherwise undesirable correlations. Such correlations may
arise from a variety of sources, including batch effects, systematic
measurement errors, or sampling bias. Without explicit adjustment, machine
learning algorithms trained using these data can produce poor out-of-sample
predictions which propagate these undesirable correlations. We propose a method
to pre-process the training data, producing an adjusted dataset that is
statistically independent of the nuisance variables with minimum information
loss. We develop a conceptually simple approach for creating an adjusted
dataset in high-dimensional settings based on a constrained form of matrix
decomposition. The resulting dataset can then be used in any predictive
algorithm with the guarantee that predictions will be statistically independent
of the group variable. We develop a scalable algorithm for implementing the
method, along with theory support in the form of independence guarantees and
optimality. The method is illustrated on some simulation examples and applied
to two case studies: removing machine-specific correlations from brain scan
data, and removing race and ethnicity information from a dataset used to
predict recidivism. That the motivation for removing undesirable correlations
is quite different in the two applications illustrates the broad applicability
of our approach.Comment: Update. 18 pages, 3 figure
Tensor Analysis and Fusion of Multimodal Brain Images
Current high-throughput data acquisition technologies probe dynamical systems
with different imaging modalities, generating massive data sets at different
spatial and temporal resolutions posing challenging problems in multimodal data
fusion. A case in point is the attempt to parse out the brain structures and
networks that underpin human cognitive processes by analysis of different
neuroimaging modalities (functional MRI, EEG, NIRS etc.). We emphasize that the
multimodal, multi-scale nature of neuroimaging data is well reflected by a
multi-way (tensor) structure where the underlying processes can be summarized
by a relatively small number of components or "atoms". We introduce
Markov-Penrose diagrams - an integration of Bayesian DAG and tensor network
notation in order to analyze these models. These diagrams not only clarify
matrix and tensor EEG and fMRI time/frequency analysis and inverse problems,
but also help understand multimodal fusion via Multiway Partial Least Squares
and Coupled Matrix-Tensor Factorization. We show here, for the first time, that
Granger causal analysis of brain networks is a tensor regression problem, thus
allowing the atomic decomposition of brain networks. Analysis of EEG and fMRI
recordings shows the potential of the methods and suggests their use in other
scientific domains.Comment: 23 pages, 15 figures, submitted to Proceedings of the IEE
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