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.
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Question: The paper addresses the problem of learning a regression model parameterized by a fixedrank positive semidefinite matrix. The focus is on the nonlinear nature of the search space and on scalability to high-dimensional problems. The mathematical developments rely on the theory of gradient descent algorithms adapted to the Riemannian geometry that underlies the set of fixed-rank positive semidefinite matrices. In contrast with previous contributions in the literature, no restrictions are imposed on the range space of the learned matrix. The resulting algorithms maintain a linear complexity in the problem size and enjoy important invariance properties. We apply the proposed algorithms to the problem of learning a distance function parameterized by a positive semidefinite matrix. Good performance is observed on classical benchmarks.

Answer: Regression on fixed-rank positive semidefinite matrices: a Riemannian approach

Question: Positive unlabeled (PU) learning is useful in various practical situations, where there is a need to learn a classifier for a class of interest from an unlabeled data set, which may contain anomalies as well as samples from unknown classes. The learning task can be formulated as an optimization problem under the framework of statistical learning theory. Recent studies have theoretically analyzed its properties and generalization performance, nevertheless, little effort has been made to consider the problem of scalability, especially when large sets of unlabeled data are available. In this work we propose a novel scalable PU learning algorithm that is theoretically proven to provide the optimal solution, while showing superior computational and memory performance. Experimental evaluation confirms the theoretical evidence and shows that the proposed method can be successfully applied to a large variety of real-world problems involving PU learning.

Answer: Efficient Training for Positive Unlabeled Learning

Question: In this work, we study an important problem: learning programs from input-output<lb>examples. We propose a novel method to learn a neural program operating a<lb>domain-specific non-differentiable machine, and demonstrate that this method<lb>can be applied to learn programs that are significantly more complex than the<lb>ones synthesized before: programming language parsers from input-output pairs<lb>without knowing the underlying grammar. The main challenge is to train the neural<lb>program without supervision on execution traces. To tackle it, we propose: (1)<lb>LL machines and neural programs operating them to effectively regularize the<lb>space of the learned programs; and (2) a two-phase reinforcement learning-based<lb>search technique to train the model. Our evaluation demonstrates that our approach<lb>can successfully learn to parse programs in both an imperative language and a<lb>functional language, and achieve 100% test accuracy, while existing approaches'<lb>accuracies are almost 0%. This is the first successful demonstration of applying<lb>reinforcement learning to train a neural program operating a non-differentiable<lb>machine that can fully generalize to test sets on a non-trivial task.

Answer:
Learning Neural Programs To Parse Programs