Suppose we run online SGD for t iterations to estimate linear regression parameter beta^* \in R^d. Consider high-dim regime, so we impose t << d. Can we use SGD output to construct CIs for <v, beta^*> for a new test point v, whose width decays as d^{-alpha} for some alpha > 0?.

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This gives a practically meaningful inference result for SGD in the very high-d regime (samples (n) and dimension (d) -> infty with n/d -> 0) .Arxiv - . Joint work with @krizna_b and Promit Ghosal.

We construct non-asymptotic, CLT-based CIs for <v, beta^*> (Th 2.3), and show (under mild assumptions on E[XX^T]) that if d^{2/3} << t << d, the lr can be tuned so that both CLT error rate and width of CI decay as d^{-alpha} for some alpha > 0 (Remark 3).

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