heavy-tailed distributions are ubiquitous in modern statistical analysis and machine learning problems. this talk gives a simple principle for robust high-dimensional statistical inference via an appropriate shrinkage on the data. this widens the scope of high-dimensional techniques, reducing the moment conditions from sub-exponential or sub-gaussian distributions to merely bounded second moment. as an illustration of this principle, we focus on robust estimation of the low-rank matrix from the trace regression model. it encompasses four popular problems: sparse linear models, compressed sensing, matrix completion, and multi-task regression. under only bounded $2+\delta$ moment condition, the proposed robust methodology yields an estimator that possesses the same statistical error rates as previous literature with sub-gaussian errors. we also illustrate the idea for estimation of large covariance matrix. the benefits of shrinkage are also demonstrated by financial, economic, and simulated data.