275 research outputs found
Spectrum-Aware Adjustment: A New Debiasing Framework with Applications to Principal Components Regression
We introduce a new debiasing framework for high-dimensional linear regression
that bypasses the restrictions on covariate distributions imposed by modern
debiasing technology. We study the prevalent setting where the number of
features and samples are both large and comparable. In this context,
state-of-the-art debiasing technology uses a degrees-of-freedom correction to
remove shrinkage bias of regularized estimators and conduct inference. However,
this method requires that the observed samples are i.i.d., the covariates
follow a mean zero Gaussian distribution, and reliable covariance matrix
estimates for observed features are available. This approach struggles when (i)
covariates are non-Gaussian with heavy tails or asymmetric distributions, (ii)
rows of the design exhibit heterogeneity or dependencies, and (iii) reliable
feature covariance estimates are lacking.
To address these, we develop a new strategy where the debiasing correction is
a rescaled gradient descent step (suitably initialized) with step size
determined by the spectrum of the sample covariance matrix. Unlike prior work,
we assume that eigenvectors of this matrix are uniform draws from the
orthogonal group. We show this assumption remains valid in diverse situations
where traditional debiasing fails, including designs with complex row-column
dependencies, heavy tails, asymmetric properties, and latent low-rank
structures. We establish asymptotic normality of our proposed estimator
(centered and scaled) under various convergence notions. Moreover, we develop a
consistent estimator for its asymptotic variance. Lastly, we introduce a
debiased Principal Component Regression (PCR) technique using our
Spectrum-Aware approach. In varied simulations and real data experiments, we
observe that our method outperforms degrees-of-freedom debiasing by a margin
Evidence of the side jump mechanism in the anomalous Hall effect in paramagnets
Persistent confusion has existed between the intrinsic (Berry curvature) and
the side jump mechanisms of anomalous Hall effect (AHE) in ferromagnets. We
provide unambiguous identification of the side jump mechanism, in addition to
the skew scattering contribution in epitaxial paramagnetic NiCu
thin films, in which the intrinsic contribution is by definition excluded.
Furthermore, the temperature dependence of the AHE further reveals that the
side jump mechanism is dominated by the elastic scattering
- …