Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Towards Linear Algebra over Normalized Data   Providing machine learning (ML) over relational data is a mainstream
requirement for data analytics systems. While almost all the ML tools require
the input data to be presented as a single table, many datasets are
multi-table, which forces data scientists to join those tables first, leading
to data redundancy and runtime waste. Recent works on "factorized" ML mitigate
this issue for a few specific ML algorithms by pushing ML through joins. But
their approaches require a manual rewrite of ML implementations. Such piecemeal
methods create a massive development overhead when extending such ideas to
other ML algorithms. In this paper, we show that it is possible to mitigate
this overhead by leveraging a popular formal algebra to represent the
computations of many ML algorithms: linear algebra. We introduce a new logical
data type to represent normalized data and devise a framework of algebraic
rewrite rules to convert a large set of linear algebra operations over
denormalized data into operations over normalized data. We show how this
enables us to automatically "factorize" several popular ML algorithms, thus
unifying and generalizing several prior works. We prototype our framework in
the popular ML environment R and an industrial R-over-RDBMS tool. Experiments
with both synthetic and real normalized data show that our framework also
yields significant speed-ups, up to 36x on real data.

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The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
2
The categories of this paper are: math