As models are trained and deployed, developers need to be able to
systematically debug errors that emerge in the machine learning pipeline. We
present MDB, a debugging framework for interactively querying datasets and
models. MDB integrates functional programming with relational algebra to build
expressive queries over a database of datasets and model predictions. Queries
are reusable and easily modified, enabling debuggers to rapidly iterate and
refine queries to discover and characterize errors and model behaviors. We
evaluate MDB on object detection, bias discovery, image classification, and
data imputation tasks across self-driving videos, large language models, and
medical records. Our experiments show that MDB enables up to 10x faster and
40\% shorter queries than other baselines. In a user study, we find developers
can successfully construct complex queries that describe errors of machine
learning models.

MDB 是一个与功能编程和关系代数相结合的调试框架，可以构建数据库和模型预测的表达式查询，用于快速排除错误和发现模型行为。

MDB：数据集和模型的交互式查询

MDB: Interactively Querying Datasets and Models

The logic of nulls in databases has been subject of investigation since their
introduction in Codd's Relational Model, which is the foundation of the SQL
standard. We show a logical characterisation of a first-order fragment of SQL
with null values, by first focussing on a simple extension with null values of
standard relational algebra, which captures exactly the SQL fragment, and then
proposing two different domain relational calculi, in which the null value is a
term of the language but it does not appear as an element of the semantic
interpretation domain of the logics. In one calculus, a relation can be seen as
a set of partial tuples, while in the other (equivalent) calculus, a relation
is horizontally decomposed as a set of relations each one holding regular total
tuples. We extend Codd's theorem by proving the equivalence of the relational
algebra with both domain relational calculi in presence of SQL null values.

本论文通过与标准关系代数的空值扩展，提出了两种不同的领域关系演算，证明了在存在 SQL 空值的情况下关系代数与领域关系演算的等价性。其中一个演算是将关系视为部分元组的集合，而另一个是将关系水平分解为多个具有正规完全组的关系的集合。

关系代数和关系演算中的 SQL 空值

Relational Algebra and Calculus with SQL Null Values

Differential privacy (DP) provides formal guarantees that the output of a
database query does not reveal too much information about any individual
present in the database. While many differentially private algorithms have been
proposed in the scientific literature, there are only a few end-to-end
implementations of differentially private query engines. Crucially, existing
systems assume that each individual is associated with at most one database
record, which is unrealistic in practice. We propose a generic and scalable
method to perform differentially private aggregations on databases, even when
individuals can each be associated with arbitrarily many rows. We express this
method as an operator in relational algebra, and implement it in an SQL engine.
To validate this system, we test the utility of typical queries on industry
benchmarks, and verify its correctness with a stochastic test framework we
developed. We highlight the promises and pitfalls learned when deploying such a
system in practice, and we publish its core components as open-source software.

本文提出了一种通用可扩展的方法，用于在数据库上执行差分隐私聚合，即使个体可以与任意多个行关联，将其表达为关系代数操作符并在 SQL 引擎中实现，测试了 typial queries 在工业基准测试上的效用，并通过随机测试框架验证其正确性，描述了在实践中部署此类系统时学到的优点和缺点，并发布其核心组件作为开源软件。