31,952 research outputs found
Mixed-Integer Convex Nonlinear Optimization with Gradient-Boosted Trees Embedded
Decision trees usefully represent sparse, high dimensional and noisy data.
Having learned a function from this data, we may want to thereafter integrate
the function into a larger decision-making problem, e.g., for picking the best
chemical process catalyst. We study a large-scale, industrially-relevant
mixed-integer nonlinear nonconvex optimization problem involving both
gradient-boosted trees and penalty functions mitigating risk. This
mixed-integer optimization problem with convex penalty terms broadly applies to
optimizing pre-trained regression tree models. Decision makers may wish to
optimize discrete models to repurpose legacy predictive models, or they may
wish to optimize a discrete model that particularly well-represents a data set.
We develop several heuristic methods to find feasible solutions, and an exact,
branch-and-bound algorithm leveraging structural properties of the
gradient-boosted trees and penalty functions. We computationally test our
methods on concrete mixture design instance and a chemical catalysis industrial
instance
Revisiting nested group testing procedures: new results, comparisons, and robustness
Group testing has its origin in the identification of syphilis in the US army
during World War II. Much of the theoretical framework of group testing was
developed starting in the late 1950s, with continued work into the 1990s.
Recently, with the advent of new laboratory and genetic technologies, there has
been an increasing interest in group testing designs for cost saving purposes.
In this paper, we compare different nested designs, including Dorfman, Sterrett
and an optimal nested procedure obtained through dynamic programming. To
elucidate these comparisons, we develop closed-form expressions for the optimal
Sterrett procedure and provide a concise review of the prior literature for
other commonly used procedures. We consider designs where the prevalence of
disease is known as well as investigate the robustness of these procedures when
it is incorrectly assumed. This article provides a technical presentation that
will be of interest to researchers as well as from a pedagogical perspective.
Supplementary material for this article is available online.Comment: Submitted for publication on May 3, 2016. Revised versio
Improving Table Compression with Combinatorial Optimization
We study the problem of compressing massive tables within the
partition-training paradigm introduced by Buchsbaum et al. [SODA'00], in which
a table is partitioned by an off-line training procedure into disjoint
intervals of columns, each of which is compressed separately by a standard,
on-line compressor like gzip. We provide a new theory that unifies previous
experimental observations on partitioning and heuristic observations on column
permutation, all of which are used to improve compression rates. Based on the
theory, we devise the first on-line training algorithms for table compression,
which can be applied to individual files, not just continuously operating
sources; and also a new, off-line training algorithm, based on a link to the
asymmetric traveling salesman problem, which improves on prior work by
rearranging columns prior to partitioning. We demonstrate these results
experimentally. On various test files, the on-line algorithms provide 35-55%
improvement over gzip with negligible slowdown; the off-line reordering
provides up to 20% further improvement over partitioning alone. We also show
that a variation of the table compression problem is MAX-SNP hard.Comment: 22 pages, 2 figures, 5 tables, 23 references. Extended abstract
appears in Proc. 13th ACM-SIAM SODA, pp. 213-222, 200
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Scheduling reentrant jobs on parallel machines with a remote server
This paper explores a specific combinatorial problem relating to re-entrant jobs on parallel primary machines, with a remote server machine. A middle operation is required by each job on the server before it returns to its primary processing machine. The problem is inspired by the logistics of a semi-automated micro-biology laboratory. The testing programme in the laboratory corresponds roughly to a hybrid flowshop, whose bottleneck stage is the subject of study. We demonstrate the NP-hard nature of the problem, and provide various structural features. A heuristic is developed and tested on randomly generated benchmark data. Results indicate solutions reliably within 1.5% of optimum. We also provide a greedy 2-approximation algorithm. Test on real-life data from the microbiology laboratory indicate a 20% saving relative to current practice, which is more than can be achieved currently with 3 instead of 2 people staffing the primary machines
BriskStream: Scaling Data Stream Processing on Shared-Memory Multicore Architectures
We introduce BriskStream, an in-memory data stream processing system (DSPSs)
specifically designed for modern shared-memory multicore architectures.
BriskStream's key contribution is an execution plan optimization paradigm,
namely RLAS, which takes relative-location (i.e., NUMA distance) of each pair
of producer-consumer operators into consideration. We propose a branch and
bound based approach with three heuristics to resolve the resulting nontrivial
optimization problem. The experimental evaluations demonstrate that BriskStream
yields much higher throughput and better scalability than existing DSPSs on
multi-core architectures when processing different types of workloads.Comment: To appear in SIGMOD'1
Let's Make Block Coordinate Descent Go Fast: Faster Greedy Rules, Message-Passing, Active-Set Complexity, and Superlinear Convergence
Block coordinate descent (BCD) methods are widely-used for large-scale
numerical optimization because of their cheap iteration costs, low memory
requirements, amenability to parallelization, and ability to exploit problem
structure. Three main algorithmic choices influence the performance of BCD
methods: the block partitioning strategy, the block selection rule, and the
block update rule. In this paper we explore all three of these building blocks
and propose variations for each that can lead to significantly faster BCD
methods. We (i) propose new greedy block-selection strategies that guarantee
more progress per iteration than the Gauss-Southwell rule; (ii) explore
practical issues like how to implement the new rules when using "variable"
blocks; (iii) explore the use of message-passing to compute matrix or Newton
updates efficiently on huge blocks for problems with a sparse dependency
between variables; and (iv) consider optimal active manifold identification,
which leads to bounds on the "active set complexity" of BCD methods and leads
to superlinear convergence for certain problems with sparse solutions (and in
some cases finite termination at an optimal solution). We support all of our
findings with numerical results for the classic machine learning problems of
least squares, logistic regression, multi-class logistic regression, label
propagation, and L1-regularization
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