19,087 research outputs found
Automatic Debiased Machine Learning of Causal and Structural Effects
Many causal and structural effects depend on regressions. Examples include
average treatment effects, policy effects, average derivatives, regression
decompositions, economic average equivalent variation, and parameters of
economic structural models. The regressions may be high dimensional. Plugging
machine learners into identifying equations can lead to poor inference due to
bias and/or model selection. This paper gives automatic debiasing for
estimating equations and valid asymptotic inference for the estimators of
effects of interest. The debiasing is automatic in that its construction uses
the identifying equations without the full form of the bias correction and is
performed by machine learning. Novel results include convergence rates for
Lasso and Dantzig learners of the bias correction, primitive conditions for
asymptotic inference for important examples, and general conditions for GMM. A
variety of regression learners and identifying equations are covered. Automatic
debiased machine learning (Auto-DML) is applied to estimating the average
treatment effect on the treated for the NSW job training data and to estimating
demand elasticities from Nielsen scanner data while allowing preferences to be
correlated with prices and income
Group Lasso estimation of high-dimensional covariance matrices
In this paper, we consider the Group Lasso estimator of the covariance matrix
of a stochastic process corrupted by an additive noise. We propose to estimate
the covariance matrix in a high-dimensional setting under the assumption that
the process has a sparse representation in a large dictionary of basis
functions. Using a matrix regression model, we propose a new methodology for
high-dimensional covariance matrix estimation based on empirical contrast
regularization by a group Lasso penalty. Using such a penalty, the method
selects a sparse set of basis functions in the dictionary used to approximate
the process, leading to an approximation of the covariance matrix into a low
dimensional space. Consistency of the estimator is studied in Frobenius and
operator norms and an application to sparse PCA is proposed
Sparsity and cosparsity for audio declipping: a flexible non-convex approach
This work investigates the empirical performance of the sparse synthesis
versus sparse analysis regularization for the ill-posed inverse problem of
audio declipping. We develop a versatile non-convex heuristics which can be
readily used with both data models. Based on this algorithm, we report that, in
most cases, the two models perform almost similarly in terms of signal
enhancement. However, the analysis version is shown to be amenable for real
time audio processing, when certain analysis operators are considered. Both
versions outperform state-of-the-art methods in the field, especially for the
severely saturated signals
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