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 consider the problem of repeatedly solving a variant of the same dynamic programming problem in successive trials. An instance of the type of problems we consider is to find the optimal binary search tree. At the beginning of each trial, the learner probabilistically chooses a tree with the n keys at the internal nodes and the n+ 1 gaps between keys at the leaves. It is then told the frequencies of the keys and gaps and is charged by the average search cost for the chosen tree. The problem is online because the frequencies can change between trials. The goal is to develop algorithms with the property that their total average search cost (loss) in all trials is close to the total loss of the best tree chosen in hind sight for all trials. The challenge, of course, is that the algorithm has to deal with exponential number of trees. We develop a methodology for tackling such problems for a wide class of dynamic programming algorithms. Our framework allows us to extend online learning algorithms like Hedge [9] and Component Hedge [15] to a significantly wider class of combinatorial objects than was possible before.
Example Output: Online Dynamic Programming

Example Input: The First-Order Variable Elimination (FOVE) algorithm allows exact inference to be applied directly to probabilistic relational models, and has proven to be vastly superior to the application of standard inference methods on a grounded propositional model. Still, FOVE operators can be applied under restricted conditions, often forcing one to resort to propositional inference. This paper aims to extend the applicability of FOVE by providing two new model conversion operators: the first and the primary is joint formula conversion and the second is just-different counting conversion. These new operations allow efficient inference methods to be applied directly on relational models, where no existing efficient method could be applied hitherto. In addition, aided by these capabilities, we show how to adapt FOVE to provide exact solutions to Maximum Expected Utility (MEU) queries over relational models for decision under uncertainty. Experimental evaluations show our algorithms to provide significant speedup over the alternatives.
Example Output: Extended Lifted Inference with Joint Formulas

Example Input: A novel method for learning optimal, orthonormal wavelet bases for representing 1and 2D signals, based on parallels between the wavelet transform and fully connected artificial neural networks, is described. The structural similarities between these two concepts are reviewed and combined to a “wavenet”, allowing for the direct learning of optimal wavelet filter coefficient through stochastic gradient descent with back-propagation over ensembles of training inputs, where conditions on the filter coefficients for constituting orthonormal wavelet bases are cast as quadratic regularisations terms. We describe the practical implementation of this method [1], and study its performance for high-energy physics collision events for QCD 2 → 2 processes. It is shown that an optimal solution is found, even in a high-dimensional search space, and the implications of the result are discussed.
Example Output:
Learning optimal wavelet bases using a neural network approach