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.

[EX Q]: This paper presents the input convex neural network architecture. These are scalar-valued (potentially deep) neural networks with constraints on the network parameters such that the output of the network is a convex function of (some of) the inputs. The networks allow for efficient inference via optimization over some inputs to the network given others, and can be applied to settings including structured prediction, data imputation, reinforcement learning, and others. In this paper we lay the basic groundwork for these models, proposing methods for inference, optimization and learning, and analyze their representational power. We show that many existing neural network architectures can be made input-convex with only minor modification, and develop specialized optimization algorithms tailored to this setting. Finally, we highlight the performance of the methods on multi-label prediction, image completion, and reinforcement learning problems, where we show improvement over the existing state of the art in many cases.
[EX A]: Input Convex Neural Networks

[EX Q]: We provide a general framework for computing lower-bounds on the sample complexity of recovering the underlying graphs of Ising models, given i.i.d. samples. While there have been recent results for specific graph classes, these involve fairly extensive technical arguments that are specialized to each specific graph class. In contrast, we isolate two key graph-structural ingredients that can then be used to specify sample complexity lower-bounds. Presence of these structural properties makes the graph class hard to learn. We derive corollaries of our main result that not only recover existing recent results, but also provide lower bounds for novel graph classes not considered previously. We also extend our framework to the random graph setting and derive corollaries for Erdos-Renyi graphs in a certain dense setting.
[EX A]: On the Information Theoretic Limits of Learning Ising Models

[EX Q]: In this paper, we present a heuristic operator which aims at simultaneously optimizing the orientations of all the edges in an interme diate Bayesian network structure during the search process. This is done by alternating between the space of directed acyclic graphs (DAGs) and the space of skeletons. The found orientations of the edges are based on a scoring function rather than on induced con ditional independences. This operator can be used as an extension to commonly employed search strategies. It is evaluated in experi ments with artificial and real-world data.
[EX A]:
On the Use of Skeletons when Learning in Bayesian Networks