15,323 research outputs found
Optimal Sparse Decision Trees
Decision tree algorithms have been among the most popular algorithms for
interpretable (transparent) machine learning since the early 1980's. The
problem that has plagued decision tree algorithms since their inception is
their lack of optimality, or lack of guarantees of closeness to optimality:
decision tree algorithms are often greedy or myopic, and sometimes produce
unquestionably suboptimal models. Hardness of decision tree optimization is
both a theoretical and practical obstacle, and even careful mathematical
programming approaches have not been able to solve these problems efficiently.
This work introduces the first practical algorithm for optimal decision trees
for binary variables. The algorithm is a co-design of analytical bounds that
reduce the search space and modern systems techniques, including data
structures and a custom bit-vector library. Our experiments highlight
advantages in scalability, speed, and proof of optimality.Comment: 33rd Conference on Neural Information Processing Systems (NeurIPS
2019), Vancouver, Canad
Efficient Database Generation for Data-driven Security Assessment of Power Systems
Power system security assessment methods require large datasets of operating
points to train or test their performance. As historical data often contain
limited number of abnormal situations, simulation data are necessary to
accurately determine the security boundary. Generating such a database is an
extremely demanding task, which becomes intractable even for small system
sizes. This paper proposes a modular and highly scalable algorithm for
computationally efficient database generation. Using convex relaxation
techniques and complex network theory, we discard large infeasible regions and
drastically reduce the search space. We explore the remaining space by a highly
parallelizable algorithm and substantially decrease computation time. Our
method accommodates numerous definitions of power system security. Here we
focus on the combination of N-k security and small-signal stability.
Demonstrating our algorithm on IEEE 14-bus and NESTA 162-bus systems, we show
how it outperforms existing approaches requiring less than 10% of the time
other methods require.Comment: Database publicly available at:
https://github.com/johnnyDEDK/OPs_Nesta162Bus - Paper accepted for
publication at IEEE Transactions on Power System
Bidirectional branch and bound for controlled variable selection. Part III: local average loss minimization
The selection of controlled variables (CVs) from available measurements through
exhaustive search is computationally forbidding for large-scale processes. We
have recently proposed novel bidirectional branch and bound (B-3) approaches for
CV selection using the minimum singular value (MSV) rule and the local worst-
case loss criterion in the framework of self-optimizing control. However, the
MSV rule is approximate and worst-case scenario may not occur frequently in
practice. Thus, CV selection by minimizing local average loss can be deemed as
most reliable. In this work, the B-3 approach is extended to CV selection based
on local average loss metric. Lower bounds on local average loss and, fast
pruning and branching algorithms are derived for the efficient B-3 algorithm.
Random matrices and binary distillation column case study are used to
demonstrate the computational efficiency of the proposed method
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