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.

Input: Consider Input: In many applications data is naturally presented in terms of orderings of some basic elements or symbols. Reasoning about such data requires a notion of similarity capable of handling sequences of different lengths. In this paper we describe a family of Mercer kernel functions for such sequentially structured data. The family is characterized by a decomposable structure in terms of symbol-level and structure-level similarities, representing a specific combination of kernels which allows for efficient computation. We provide an experimental evaluation on sequential classification tasks comparing kernels from our family of kernels to a state of the art sequence kernel called the Global Alignment kernel which has been shown to outperform Dynamic Time Warping.

Output: On a Family of Decomposable Kernels on Sequences On a Family of Decomposable Kernels on Sequences

Input: Consider Input: Korf, Reid, and Edelkamp introduced a formula to predict the number of nodes IDA* will expand on a single iteration for a given consistent heuristic, and experimentally demonstrated that it could make very accurate predictions. In this paper we show that, in addition to requiring the heuristic to be consistent, their formula's predictions are accurate only at levels of the brute-force search tree where the heuristic values obey the unconditional distribution that they defined and then used in their formula. We then propose a new formula that works well without these requirements, i.e., it can make accurate predictions of IDA*'s performance for inconsistent heuristics and if the heuristic values in any level do not obey the unconditional distribution. In order to achieve this we introduce the conditional distribution of heuristic values which is a generalization of their unconditional heuristic distribution. We also provide extensions of our formula that handle individual start states and the augmentation of IDA* with bidirectional pathmax (BPMX), a technique for propagating heuristic values when inconsistent heuristics are used. Experimental results demonstrate the accuracy of our new method and all its variations.

Output: Predicting the Performance of IDA* using Conditional Distributions

Input: Consider Input: Unsupervised training of deep generative models containing latent variables and performing inference remains a challenging problem for complex, high dimensional distributions. One basic approach to this problem is the so called Helmholtz machine and it involves training an auxiliary model that helps to perform approximate inference jointly with the generative model which is to be fitted to the training data. The top-down generative model is typically realized as a directed model that starts from some prior at the top, down to the empirical distribution at the bottom. The approximate inference model runs in the opposite direction and is typically trained to efficiently infer high probability latent states given some observed data. Here we propose a new method, referred to as geometric mean matching (GMM), that is based on the idea that the generative model should be close to the class of distributions that can be modeled by our approximate inference distribution. We achieve this by interpreting both the top-down and the bottom-up directed models as approximate inference distributions and by defining the target distribution we fit to the training data to be the geometric mean of these two. We present an upper-bound for the log-likelihood of this model and we show that optimizing this bound will pressure the model to stay close to the approximate inference distributions. In the experimental section we demonstrate that we can use this approach to fit deep generative models with many layers of hidden binary stochastic variables to complex and high dimensional training distributions.
Output: Training opposing directed models using geometric mean matching