4,122 research outputs found
Random Forests for Big Data
Big Data is one of the major challenges of statistical science and has
numerous consequences from algorithmic and theoretical viewpoints. Big Data
always involve massive data but they also often include online data and data
heterogeneity. Recently some statistical methods have been adapted to process
Big Data, like linear regression models, clustering methods and bootstrapping
schemes. Based on decision trees combined with aggregation and bootstrap ideas,
random forests were introduced by Breiman in 2001. They are a powerful
nonparametric statistical method allowing to consider in a single and versatile
framework regression problems, as well as two-class and multi-class
classification problems. Focusing on classification problems, this paper
proposes a selective review of available proposals that deal with scaling
random forests to Big Data problems. These proposals rely on parallel
environments or on online adaptations of random forests. We also describe how
related quantities -- such as out-of-bag error and variable importance -- are
addressed in these methods. Then, we formulate various remarks for random
forests in the Big Data context. Finally, we experiment five variants on two
massive datasets (15 and 120 millions of observations), a simulated one as well
as real world data. One variant relies on subsampling while three others are
related to parallel implementations of random forests and involve either
various adaptations of bootstrap to Big Data or to "divide-and-conquer"
approaches. The fifth variant relates on online learning of random forests.
These numerical experiments lead to highlight the relative performance of the
different variants, as well as some of their limitations
Network Sampling: From Static to Streaming Graphs
Network sampling is integral to the analysis of social, information, and
biological networks. Since many real-world networks are massive in size,
continuously evolving, and/or distributed in nature, the network structure is
often sampled in order to facilitate study. For these reasons, a more thorough
and complete understanding of network sampling is critical to support the field
of network science. In this paper, we outline a framework for the general
problem of network sampling, by highlighting the different objectives,
population and units of interest, and classes of network sampling methods. In
addition, we propose a spectrum of computational models for network sampling
methods, ranging from the traditionally studied model based on the assumption
of a static domain to a more challenging model that is appropriate for
streaming domains. We design a family of sampling methods based on the concept
of graph induction that generalize across the full spectrum of computational
models (from static to streaming) while efficiently preserving many of the
topological properties of the input graphs. Furthermore, we demonstrate how
traditional static sampling algorithms can be modified for graph streams for
each of the three main classes of sampling methods: node, edge, and
topology-based sampling. Our experimental results indicate that our proposed
family of sampling methods more accurately preserves the underlying properties
of the graph for both static and streaming graphs. Finally, we study the impact
of network sampling algorithms on the parameter estimation and performance
evaluation of relational classification algorithms
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