Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
134 tokens/sec
GPT-4o
9 tokens/sec
Gemini 2.5 Pro Pro
47 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Differentially Private Ordinary Least Squares (1507.02482v4)

Published 9 Jul 2015 in cs.DS, cs.CR, and cs.LG

Abstract: Linear regression is one of the most prevalent techniques in machine learning, however, it is also common to use linear regression for its \emph{explanatory} capabilities rather than label prediction. Ordinary Least Squares (OLS) is often used in statistics to establish a correlation between an attribute (e.g. gender) and a label (e.g. income) in the presence of other (potentially correlated) features. OLS assumes a particular model that randomly generates the data, and derives \emph{$t$-values} --- representing the likelihood of each real value to be the true correlation. Using $t$-values, OLS can release a \emph{confidence interval}, which is an interval on the reals that is likely to contain the true correlation, and when this interval does not intersect the origin, we can \emph{reject the null hypothesis} as it is likely that the true correlation is non-zero. Our work aims at achieving similar guarantees on data under differentially private estimators. First, we show that for well-spread data, the Gaussian Johnson-Lindenstrauss Transform (JLT) gives a very good approximation of $t$-values, secondly, when JLT approximates Ridge regression (linear regression with $l_2$-regularization) we derive, under certain conditions, confidence intervals using the projected data, lastly, we derive, under different conditions, confidence intervals for the "Analyze Gauss" algorithm (Dwork et al, STOC 2014).

Citations (111)

Summary

We haven't generated a summary for this paper yet.