59,747 research outputs found
On the usage of the probability integral transform to reduce the complexity of multi-way fuzzy decision trees in Big Data classification problems
We present a new distributed fuzzy partitioning method to reduce the
complexity of multi-way fuzzy decision trees in Big Data classification
problems. The proposed algorithm builds a fixed number of fuzzy sets for all
variables and adjusts their shape and position to the real distribution of
training data. A two-step process is applied : 1) transformation of the
original distribution into a standard uniform distribution by means of the
probability integral transform. Since the original distribution is generally
unknown, the cumulative distribution function is approximated by computing the
q-quantiles of the training set; 2) construction of a Ruspini strong fuzzy
partition in the transformed attribute space using a fixed number of equally
distributed triangular membership functions. Despite the aforementioned
transformation, the definition of every fuzzy set in the original space can be
recovered by applying the inverse cumulative distribution function (also known
as quantile function). The experimental results reveal that the proposed
methodology allows the state-of-the-art multi-way fuzzy decision tree (FMDT)
induction algorithm to maintain classification accuracy with up to 6 million
fewer leaves.Comment: Appeared in 2018 IEEE International Congress on Big Data (BigData
Congress). arXiv admin note: text overlap with arXiv:1902.0935
Approximate Computation and Implicit Regularization for Very Large-scale Data Analysis
Database theory and database practice are typically the domain of computer
scientists who adopt what may be termed an algorithmic perspective on their
data. This perspective is very different than the more statistical perspective
adopted by statisticians, scientific computers, machine learners, and other who
work on what may be broadly termed statistical data analysis. In this article,
I will address fundamental aspects of this algorithmic-statistical disconnect,
with an eye to bridging the gap between these two very different approaches. A
concept that lies at the heart of this disconnect is that of statistical
regularization, a notion that has to do with how robust is the output of an
algorithm to the noise properties of the input data. Although it is nearly
completely absent from computer science, which historically has taken the input
data as given and modeled algorithms discretely, regularization in one form or
another is central to nearly every application domain that applies algorithms
to noisy data. By using several case studies, I will illustrate, both
theoretically and empirically, the nonobvious fact that approximate
computation, in and of itself, can implicitly lead to statistical
regularization. This and other recent work suggests that, by exploiting in a
more principled way the statistical properties implicit in worst-case
algorithms, one can in many cases satisfy the bicriteria of having algorithms
that are scalable to very large-scale databases and that also have good
inferential or predictive properties.Comment: To appear in the Proceedings of the 2012 ACM Symposium on Principles
of Database Systems (PODS 2012
- …