60,750 research outputs found
Design of Experiments for Screening
The aim of this paper is to review methods of designing screening
experiments, ranging from designs originally developed for physical experiments
to those especially tailored to experiments on numerical models. The strengths
and weaknesses of the various designs for screening variables in numerical
models are discussed. First, classes of factorial designs for experiments to
estimate main effects and interactions through a linear statistical model are
described, specifically regular and nonregular fractional factorial designs,
supersaturated designs and systematic fractional replicate designs. Generic
issues of aliasing, bias and cancellation of factorial effects are discussed.
Second, group screening experiments are considered including factorial group
screening and sequential bifurcation. Third, random sampling plans are
discussed including Latin hypercube sampling and sampling plans to estimate
elementary effects. Fourth, a variety of modelling methods commonly employed
with screening designs are briefly described. Finally, a novel study
demonstrates six screening methods on two frequently-used exemplars, and their
performances are compared
On the Power of Adaptivity in Matrix Completion and Approximation
We consider the related tasks of matrix completion and matrix approximation
from missing data and propose adaptive sampling procedures for both problems.
We show that adaptive sampling allows one to eliminate standard incoherence
assumptions on the matrix row space that are necessary for passive sampling
procedures. For exact recovery of a low-rank matrix, our algorithm judiciously
selects a few columns to observe in full and, with few additional measurements,
projects the remaining columns onto their span. This algorithm exactly recovers
an rank matrix using observations,
where is a coherence parameter on the column space of the matrix. In
addition to completely eliminating any row space assumptions that have pervaded
the literature, this algorithm enjoys a better sample complexity than any
existing matrix completion algorithm. To certify that this improvement is due
to adaptive sampling, we establish that row space coherence is necessary for
passive sampling algorithms to achieve non-trivial sample complexity bounds.
For constructing a low-rank approximation to a high-rank input matrix, we
propose a simple algorithm that thresholds the singular values of a zero-filled
version of the input matrix. The algorithm computes an approximation that is
nearly as good as the best rank- approximation using
samples, where is a slightly different coherence parameter on the matrix
columns. Again we eliminate assumptions on the row space
OBOE: Collaborative Filtering for AutoML Model Selection
Algorithm selection and hyperparameter tuning remain two of the most
challenging tasks in machine learning. Automated machine learning (AutoML)
seeks to automate these tasks to enable widespread use of machine learning by
non-experts. This paper introduces OBOE, a collaborative filtering method for
time-constrained model selection and hyperparameter tuning. OBOE forms a matrix
of the cross-validated errors of a large number of supervised learning models
(algorithms together with hyperparameters) on a large number of datasets, and
fits a low rank model to learn the low-dimensional feature vectors for the
models and datasets that best predict the cross-validated errors. To find
promising models for a new dataset, OBOE runs a set of fast but informative
algorithms on the new dataset and uses their cross-validated errors to infer
the feature vector for the new dataset. OBOE can find good models under
constraints on the number of models fit or the total time budget. To this end,
this paper develops a new heuristic for active learning in time-constrained
matrix completion based on optimal experiment design. Our experiments
demonstrate that OBOE delivers state-of-the-art performance faster than
competing approaches on a test bed of supervised learning problems. Moreover,
the success of the bilinear model used by OBOE suggests that AutoML may be
simpler than was previously understood
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