Optimal subsampling designs
Preprint, 2023

Subsampling is commonly used to overcome computational and economical bottlenecks in the analysis of finite populations and massive datasets. Existing methods are often limited in scope and use optimality criteria (e.g., A-optimality) with well-known deficiencies, such as lack of invariance to the measurement-scale of the data and parameterisation of the model. A unified theory of optimal subsampling design is still lacking. We present a theory of optimal design for general data subsampling problems, including finite population inference, parametric density estimation, and regression modelling. Our theory encompasses and generalises most existing methods in the field of optimal subdata selection based on unequal probability sampling and inverse probability weighting. We derive optimality conditions for a general class of optimality criteria, and present corresponding algorithms for finding optimal sampling schemes under Poisson and multinomial sampling designs. We present a novel class of transformation- and parameterisation-invariant linear optimality criteria which enjoy the best of two worlds: the computational tractability of A-optimality and invariance properties similar to D-optimality. The methodology is illustrated on an application in the traffic safety domain. In our experiments, the proposed invariant linear optimality criteria achieve 92-99% D-efficiency with 90-95% lower computational demand. In contrast, the A-optimality criterion has only 46% and 60% D-efficiency on two of the examples.

L-optimality

inverse probability weighting

A-optimality

D-optimality

unequal probability sampling

M-estimation

Författare

Henrik Imberg

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Marina Axelson-Fisk

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Johan Jonasson

Chalmers, Matematiska vetenskaper, Analys och sannolikhetsteori

Statistical sampling in machine learning

Stiftelsen Wilhelm och Martina Lundgrens Vetenskapsfond (2019-3132), 2019-05-01 -- 2019-12-31.

Stiftelsen Wilhelm och Martina Lundgrens Vetenskapsfond (2020-3446), 2020-05-01 -- 2020-12-31.

Ämneskategorier

Beräkningsmatematik

Sannolikhetsteori och statistik

Fundament

Grundläggande vetenskaper

DOI

10.48550/arXiv.2304.03019

Mer information

Skapat

2023-04-11