  In recent years, multiple notions of algorithmic fairness have arisen. One
such notion is individual fairness (IF), which requires that individuals who
are similar receive similar treatment. In parallel, matrix estimation (ME) has
emerged as a natural paradigm for handling noisy data with missing values. In
this work, we connect the two concepts. We show that pre-processing data using
ME can improve an algorithm's IF without sacrificing performance. Specifically,
we show that using a popular ME method known as singular value thresholding
(SVT) to pre-process the data provides a strong IF guarantee under appropriate
conditions. We then show that, under analogous conditions, SVT pre-processing
also yields estimates that are consistent and approximately minimax optimal. As
such, the ME pre-processing step does not, under the stated conditions,
increase the prediction error of the base algorithm, i.e., does not impose a
fairness-performance trade-off. We verify these results on synthetic and real
data.
