35,300 research outputs found
Large-scale Nonlinear Variable Selection via Kernel Random Features
We propose a new method for input variable selection in nonlinear regression.
The method is embedded into a kernel regression machine that can model general
nonlinear functions, not being a priori limited to additive models. This is the
first kernel-based variable selection method applicable to large datasets. It
sidesteps the typical poor scaling properties of kernel methods by mapping the
inputs into a relatively low-dimensional space of random features. The
algorithm discovers the variables relevant for the regression task together
with learning the prediction model through learning the appropriate nonlinear
random feature maps. We demonstrate the outstanding performance of our method
on a set of large-scale synthetic and real datasets.Comment: Final version for proceedings of ECML/PKDD 201
Bayesian Approximate Kernel Regression with Variable Selection
Nonlinear kernel regression models are often used in statistics and machine
learning because they are more accurate than linear models. Variable selection
for kernel regression models is a challenge partly because, unlike the linear
regression setting, there is no clear concept of an effect size for regression
coefficients. In this paper, we propose a novel framework that provides an
effect size analog of each explanatory variable for Bayesian kernel regression
models when the kernel is shift-invariant --- for example, the Gaussian kernel.
We use function analytic properties of shift-invariant reproducing kernel
Hilbert spaces (RKHS) to define a linear vector space that: (i) captures
nonlinear structure, and (ii) can be projected onto the original explanatory
variables. The projection onto the original explanatory variables serves as an
analog of effect sizes. The specific function analytic property we use is that
shift-invariant kernel functions can be approximated via random Fourier bases.
Based on the random Fourier expansion we propose a computationally efficient
class of Bayesian approximate kernel regression (BAKR) models for both
nonlinear regression and binary classification for which one can compute an
analog of effect sizes. We illustrate the utility of BAKR by examining two
important problems in statistical genetics: genomic selection (i.e. phenotypic
prediction) and association mapping (i.e. inference of significant variants or
loci). State-of-the-art methods for genomic selection and association mapping
are based on kernel regression and linear models, respectively. BAKR is the
first method that is competitive in both settings.Comment: 22 pages, 3 figures, 3 tables; theory added; new simulations
presented; references adde
Machine Learning and Integrative Analysis of Biomedical Big Data.
Recent developments in high-throughput technologies have accelerated the accumulation of massive amounts of omics data from multiple sources: genome, epigenome, transcriptome, proteome, metabolome, etc. Traditionally, data from each source (e.g., genome) is analyzed in isolation using statistical and machine learning (ML) methods. Integrative analysis of multi-omics and clinical data is key to new biomedical discoveries and advancements in precision medicine. However, data integration poses new computational challenges as well as exacerbates the ones associated with single-omics studies. Specialized computational approaches are required to effectively and efficiently perform integrative analysis of biomedical data acquired from diverse modalities. In this review, we discuss state-of-the-art ML-based approaches for tackling five specific computational challenges associated with integrative analysis: curse of dimensionality, data heterogeneity, missing data, class imbalance and scalability issues
Random Feature-based Online Multi-kernel Learning in Environments with Unknown Dynamics
Kernel-based methods exhibit well-documented performance in various nonlinear
learning tasks. Most of them rely on a preselected kernel, whose prudent choice
presumes task-specific prior information. Especially when the latter is not
available, multi-kernel learning has gained popularity thanks to its
flexibility in choosing kernels from a prescribed kernel dictionary. Leveraging
the random feature approximation and its recent orthogonality-promoting
variant, the present contribution develops a scalable multi-kernel learning
scheme (termed Raker) to obtain the sought nonlinear learning function `on the
fly,' first for static environments. To further boost performance in dynamic
environments, an adaptive multi-kernel learning scheme (termed AdaRaker) is
developed. AdaRaker accounts not only for data-driven learning of kernel
combination, but also for the unknown dynamics. Performance is analyzed in
terms of both static and dynamic regrets. AdaRaker is uniquely capable of
tracking nonlinear learning functions in environments with unknown dynamics,
and with with analytic performance guarantees. Tests with synthetic and real
datasets are carried out to showcase the effectiveness of the novel algorithms.Comment: 36 page
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