2,754 research outputs found
Algorithms for Approximate Minimization of the Difference Between Submodular Functions, with Applications
We extend the work of Narasimhan and Bilmes [30] for minimizing set functions
representable as a difference between submodular functions. Similar to [30],
our new algorithms are guaranteed to monotonically reduce the objective
function at every step. We empirically and theoretically show that the
per-iteration cost of our algorithms is much less than [30], and our algorithms
can be used to efficiently minimize a difference between submodular functions
under various combinatorial constraints, a problem not previously addressed. We
provide computational bounds and a hardness result on the mul- tiplicative
inapproximability of minimizing the difference between submodular functions. We
show, however, that it is possible to give worst-case additive bounds by
providing a polynomial time computable lower-bound on the minima. Finally we
show how a number of machine learning problems can be modeled as minimizing the
difference between submodular functions. We experimentally show the validity of
our algorithms by testing them on the problem of feature selection with
submodular cost features.Comment: 17 pages, 8 figures. A shorter version of this appeared in Proc.
Uncertainty in Artificial Intelligence (UAI), Catalina Islands, 201
Hierarchical Subquery Evaluation for Active Learning on a Graph
To train good supervised and semi-supervised object classifiers, it is
critical that we not waste the time of the human experts who are providing the
training labels. Existing active learning strategies can have uneven
performance, being efficient on some datasets but wasteful on others, or
inconsistent just between runs on the same dataset. We propose perplexity based
graph construction and a new hierarchical subquery evaluation algorithm to
combat this variability, and to release the potential of Expected Error
Reduction.
Under some specific circumstances, Expected Error Reduction has been one of
the strongest-performing informativeness criteria for active learning. Until
now, it has also been prohibitively costly to compute for sizeable datasets. We
demonstrate our highly practical algorithm, comparing it to other active
learning measures on classification datasets that vary in sparsity,
dimensionality, and size. Our algorithm is consistent over multiple runs and
achieves high accuracy, while querying the human expert for labels at a
frequency that matches their desired time budget.Comment: CVPR 201
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