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: We present a neural network architecture to predict a point in color space from the sequence of characters in the color’s name. Using large scale color–name pairs obtained from an online color design forum, we evaluate our model on a “color Turing test” and find that, given a name, the colors predicted by our model are preferred by annotators to color names created by humans. Our datasets and demo system are available online at http://colorlab.us.

Answer: Character Sequence Models for Colorful Words


Question: For high level path planning, environments are usually modeled as distance graphs, and path planning problems are reduced to com­ puting the shortest path in distance graphs. One major drawback of this modeling is the inability to model uncertainties, which are of­ ten encountered in practice. In this paper, a new tool, called U-graph, is proposed for environment modeling. A U-graph is an ex­ tension of distance graphs with the ability to handle a kind of uncertainty. By model­ ing an uncertain environment as a U-graph, and a navigation problem as a Markovian decision process, we can precisely define a new optimality criterion for navigation plans, and more importantly, we can come up with a general algorithm for computing optimal plans for navigation tasks.

Answer:
High Level Path Planning with Uncertainty