  There is a great need for robust techniques in data mining and machine
learning contexts where many standard techniques such as principal component
analysis and linear discriminant analysis are inherently susceptible to
outliers. Furthermore, standard robust procedures assume that less than half
the observation rows of a data matrix are contaminated, which may not be a
realistic assumption when the number of observed features is large. This work
looks at the problem of estimating covariance and precision matrices under
cellwise contamination. We consider using a robust pairwise covariance matrix
as an input to various regularisation routines, such as the graphical lasso,
QUIC and CLIME. To ensure the input covariance matrix is positive semidefinite,
we use a method that transforms a symmetric matrix of pairwise covariances to
the nearest covariance matrix. The result is a potentially sparse precision
matrix that is resilient to moderate levels of cellwise contamination. Since
this procedure is not based on subsampling it scales well as the number of
variables increases.
