  Estimating the number of distinct values (NDV) in a column is useful for many
tasks in database systems, such as columnstore compression and data profiling.
In this work, we focus on how to derive accurate NDV estimations from random
(online/offline) samples. Such efficient estimation is critical for tasks where
it is prohibitive to scan the data even once. Existing sample-based estimators
typically rely on heuristics or assumptions and do not have robust performance
across different datasets as the assumptions on data can easily break. On the
other hand, deriving an estimator from a principled formulation such as maximum
likelihood estimation is very challenging due to the complex structure of the
formulation. We propose to formulate the NDV estimation task in a supervised
learning framework, and aim to learn a model as the estimator. To this end, we
need to answer several questions: i) how to make the learned model workload
agnostic; ii) how to obtain training data; iii) how to perform model training.
We derive conditions of the learning framework under which the learned model is
workload agnostic, in the sense that the model/estimator can be trained with
synthetically generated training data, and then deployed into any data
warehouse simply as, e.g., user-defined functions (UDFs), to offer efficient
(within microseconds on CPU) and accurate NDV estimations for unseen tables and
workloads. We compare the learned estimator with the state-of-the-art
sample-based estimators on nine real-world datasets to demonstrate its superior
estimation accuracy. We publish our code for training data generation, model
training, and the learned estimator online for reproducibility.
