19 research outputs found
Computationally Tractable Algorithms for Finding a Subset of Non-defective Items from a Large Population
In the classical non-adaptive group testing setup, pools of items are tested
together, and the main goal of a recovery algorithm is to identify the
"complete defective set" given the outcomes of different group tests. In
contrast, the main goal of a "non-defective subset recovery" algorithm is to
identify a "subset" of non-defective items given the test outcomes. In this
paper, we present a suite of computationally efficient and analytically
tractable non-defective subset recovery algorithms. By analyzing the
probability of error of the algorithms, we obtain bounds on the number of tests
required for non-defective subset recovery with arbitrarily small probability
of error. Our analysis accounts for the impact of both the additive noise
(false positives) and dilution noise (false negatives). By comparing with the
information theoretic lower bounds, we show that the upper bounds on the number
of tests are order-wise tight up to a factor, where is the number
of defective items. We also provide simulation results that compare the
relative performance of the different algorithms and provide further insights
into their practical utility. The proposed algorithms significantly outperform
the straightforward approaches of testing items one-by-one, and of first
identifying the defective set and then choosing the non-defective items from
the complement set, in terms of the number of measurements required to ensure a
given success rate.Comment: In this revision: Unified some proofs and reorganized the paper,
corrected a small mistake in one of the proofs, added more reference
IMLI: An Incremental Framework for MaxSAT-Based Learning of Interpretable Classification Rules
The wide adoption of machine learning in the critical domains such as medical
diagnosis, law, education had propelled the need for interpretable techniques
due to the need for end users to understand the reasoning behind decisions due
to learning systems. The computational intractability of interpretable learning
led practitioners to design heuristic techniques, which fail to provide sound
handles to tradeoff accuracy and interpretability.
Motivated by the success of MaxSAT solvers over the past decade, recently
MaxSAT-based approach, called MLIC, was proposed that seeks to reduce the
problem of learning interpretable rules expressed in Conjunctive Normal Form
(CNF) to a MaxSAT query. While MLIC was shown to achieve accuracy similar to
that of other state of the art black-box classifiers while generating small
interpretable CNF formulas, the runtime performance of MLIC is significantly
lagging and renders approach unusable in practice. In this context, authors
raised the question: Is it possible to achieve the best of both worlds, i.e., a
sound framework for interpretable learning that can take advantage of MaxSAT
solvers while scaling to real-world instances?
In this paper, we take a step towards answering the above question in
affirmation. We propose IMLI: an incremental approach to MaxSAT based framework
that achieves scalable runtime performance via partition-based training
methodology. Extensive experiments on benchmarks arising from UCI repository
demonstrate that IMLI achieves up to three orders of magnitude runtime
improvement without loss of accuracy and interpretability.Comment: 10 pages, published in the proceedings of AAAI/ACM Conference on AI,
Ethics, and Society (AIES 2019