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.

Example Input: We introduce a novel training principle for probabilistic models that is an alternative to maximum likelihood. The proposed Generative Stochastic Networks (GSN) framework is based on learning the transition operator of a Markov chain whose stationary distribution estimates the data distribution. The transition distribution of the Markov chain is conditional on the previous state, generally involving a small move, so this conditional distribution has fewer dominant modes, being unimodal in the limit of small moves. Thus, it is easier to learn because it is easier to approximate its partition function, more like learning to perform supervised function approximation, with gradients that can be obtained by backprop. We provide theorems that generalize recent work on the probabilistic interpretation of denoising autoencoders and obtain along the way an interesting justification for dependency networks and generalized pseudolikelihood, along with a definition of an appropriate joint distribution and sampling mechanism even when the conditionals are not consistent. GSNs can be used with missing inputs and can be used to sample subsets of variables given the rest. We validate these theoretical results with experiments on two image datasets using an architecture that mimics the Deep Boltzmann Machine Gibbs sampler but allows training to proceed with simple backprop, without the need for layerwise pretraining. P(X)
Example Output: Deep Generative Stochastic Networks Trainable by Backprop

Example Input: This papers shows that using separators, which is a pair of two complementary contractors, we can easily and efficiently solve the localization problem of a robot with sonar measurements in an unstructured environment. We introduce separators associated with the Minkowski sum and the Minkowski difference in order to facilitate the resolution. A test-case is given in order to illustrate the principle of the approach.
Example Output: Minkowski Operations of Sets with Application to Robot Localization

Example Input: This paper presents generalized probabilistic models for high-order projective dependency parsing and an algorithmic framework for learning these statistical models involving dependency trees. Partition functions and marginals for high-order dependency trees can be computed efficiently, by adapting our algorithms which extend the inside-outside algorithm to higher-order cases. To show the effectiveness of our algorithms, we perform experiments on three languages— English, Chinese and Czech, using maximum conditional likelihood estimation for model training and L-BFGS for parameter estimation. Our methods achieve competitive performance for English, and outperform all previously reported dependency parsers for Chinese and Czech.
Example Output:
Probabilistic Models for High-Order Projective Dependency Parsing