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 Input:
Surely we want solid foundations. What kind of castle can we build on sand? What is the point of devoting effort to balconies and minarets, if the foundation may be so weak as to allow the structure to collapse of its own weight? We want our foundations set on bedrock, designed to last for generations. Who would want an architect who cannot certify the soundness of the foundations of his buildings?

Ex Output:
Why Do We Need Foundations for Modelling Uncertainties?


Ex Input:
A BN20 network is a two level belief net in which parent interactions are modeled using the noisy-or interaction model. In this paper we discuss application of the SPI local expression language [1] to effi­ cient inference in large BN20 networks. In particular, we show that there is sig­ nificant structure which can be exploited to improve over the Quickscore result. We further describe how symbolic tech­ niques can provide information which can significantly reduce the computation required for computing all cause poste­ rior marginals. Finally, we present a novel approximation technique with pre­ liminary experimental results.

Ex Output:
Symbolic Probabilistic Inference in large BN20 networks


Ex Input:
In this paper we propose a simple yet powerful method for learning representations in supervised learning scenarios where an input datapoint is described by a set of feature vectors and its associated output may be given by soft labels indicating, for example, class probabilities. We represent an input datapoint as a K-dimensional vector, where each component is a mixture of probabilities over its corresponding set of feature vectors. Each probability indicates how likely a feature vector is to belong to one-out-of-K unknown prototype patterns. We propose a probabilistic model that parameterizes these prototype patterns in terms of hidden variables and therefore it can be trained with conventional approaches based on likelihood maximization. More importantly, both the model parameters and the prototype patterns can be learned from data in a discriminative way. We show that our model can be seen as a probabilistic generalization of learning vector quantization (LVQ). We apply our method to the problems of shape classification, hyperspectral imaging classification and people’s work class categorization, showing the superior performance of our method compared to the standard prototype-based classification approach and other competitive benchmarks.

Ex Output:

Discriminative Probabilistic Prototype Learning