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]: Proposed methods for prediction interval estimation so far focus on cases where input variables are numerical. In datasets with solely nominal input variables, we observe records with the exact same input x, but different real valued outputs due to the inherent noise in the system. Existing prediction interval estimation methods do not use representations that can accurately model such inherent noise in the case of nominal inputs. We propose a new prediction interval estimation method tailored for this type of data, which is prevalent in biology and medicine. We call this method Distribution Adaptive Prediction Interval Estimation given Nominal inputs (DAPIEN) and has four main phases. First, we select a distribution function that can best represent the inherent noise of the system for all unique inputs. Then we infer the parameters θi (e.g. θi = [meani, variancei]) of the selected distribution function for all unique input vectors xi and generate a new corresponding training set using pairs of xi , θi. III). Then, we train a model to predict θ given a new xu. Finally, we calculate the prediction interval for a new sample using the inverse of the cumulative distribution function once the parameters θ is predicted by the trained model. We compared DAPIEN to the commonly used Bootstrap method on three synthetic datasets. Our results show that DAPIEN provides tighter prediction intervals while preserving the requested coverage when compared to Bootstrap. This work can facilitate broader usage of regression methods in medicine and biology where it is necessary to provide tight prediction intervals while preserving coverage when input variables are nominal.
[EX A]: DICTION INTERVAL ESTIMATION USING NOMINAL VARIABLES

[EX Q]: Linear-time computational techniques have been developed for combining evidence which is available on a number of contending hypotheses. They offer a means of making the computation-intensive calculations involved more efficient in certain circumstances. Unfortunately, they restrict the orthogonal sum of evidential functions to the dichotomous structure − applies only to elements and their complements. In this paper, we present a novel evidence structure in terms of a triplet and a set of algorithms for evidential reasoning. The merit of this structure is that it divides a set of evidence into three subsets, distinguishing trivial evidential elements from important ones − focusing some particular elements. It avoids the deficits of the dichotomous structure in representing the preference of evidence and estimating the basic probability assignment of evidence. We have established a formalism for this structure and the general formulae for combining pieces of evidence in the form of the triplet, which have been theoretically and empirically justified.
[EX A]:
An Efficient Triplet-based Algorithm for Evidential Reasoning