In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.

Example Input: The problem of learning automata from example traces (but no equivalence or membership queries) is fundamental in automata learning theory and practice. In this paper we study this problem for finite state machines with inputs and outputs, and in particular for Moore machines. We introduce three algorithms for solving this problem: (1) the PTAP algorithm, which transforms a set of inputoutput traces into an incomplete Moore machine and then completes that machine with self-loops; (2) the PRPNI algorithm, which uses the well-known RPNI algorithm for automata learning to learn a product of automata encoding a Moore machine; and (3) the MooreMI algorithm, which directly learns a Moore machine using PTAP extended with state merging. We prove that MooreMI always learns the right machine when the training set is a characteristic sample, which is generally not true for the other two algorithms. We also compare the algorithms experimentally in terms of the size of the learned machine and several notions of accuracy, introduced in this paper. Finally, we compare with OSTIA, an algorithm that learns a more general class of transducers, and find that OSTIA generally does not learn a Moore machine, even when fed with a characteristic sample.
Example Output: Learning Moore Machines from Input-Output Traces

Example Input: We envision a machine learning service provider facing a continuous stream of problems with the same input domain, but with output domains that may differ. Clients present the provider with problems implicitly, by labeling a few example inputs, and then ask the provider to train models which reasonably extend their labelings to novel inputs. The provider wants to avoid constraining its users to a set of common labels, so it does not assume any particular correspondence between labels for a new task and labels for previously encountered tasks. To perform well in this setting, the provider needs a representation of the input domain which, in expectation, permits effective models for new problems to be learned efficiently from a small number of examples. While this bears a resemblance to settings considered in previous work on multitask and lifelong learning, our non-assumption of inter-task label correspondence leads to a novel algorithm: Lifelong Learner of Discriminative Representations (LLDR), which explicitly minimizes a proxy for the intra-task small-sample generalization error. We examine the relative benefits of our approach on a diverse set of real-world datasets in three significant scenarios: representation learning, multitask learning and lifelong learning.
Example Output: Lifelong Learning of Discriminative Representations

Example Input: In this work we focus on efficient heuristics for solving a class of stochastic planning problems that arise in a variety of business, investment, and industrial applications. The problem is best de scribed in terms of future buy and sell contracts. By buying less reliable, but less expensive, buy (supply) contracts, a company or a trader can cover a position of more reliable and more expen sive sell contracts. The goal is to maximize the expected net gain (profit) by constructing a close to optimum portfolio out of the available buy and sell contracts. This stochastic planning problem can be formulated as a two-stage stochastic linear programm ing problem with recourse. However, this formalization leads to solutions that are ex ponential in the number of possible failure com binations. Thus, this approach is not feasible for large scale problems. In this work we investi gate heuristic approximation techniques alleviat ing the efficiency problem. We primarily focus on the clustering approach and devise heuristics for finding clusterings leading to good approxi mations. We illustrate the quality and feasibility of the approach through experimental data.
Example Output:
A Clustering Approach to Solving Large Stochastic Matching Problems