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.
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Question: A two–step Christoffel function based solution is proposed to distribution regression problem. On the first step, to model distribution of observations inside a bag, build Christoffel function for each bag of observations. Then, on the second step, build outcome variable Christoffel function, but use the bag’s Christoffel function value at given point as the weight for the bag’s outcome. The approach allows the result to be obtained in closed form and then to be evaluated numerically. While most of existing approaches minimize some kind an error between outcome and prediction, the proposed approach is conceptually different, because it uses Christoffel function for knowledge representation, what is conceptually equivalent working with probabilities only. To receive possible outcomes and their probabilities Gauss quadrature for second–step measure can be built, then the nodes give possible outcomes and normalized weights – outcome probabilities. A library providing numerically stable polynomial basis for these calculations is available, what make the proposed approach practical.

Answer: Multiple–Instance Learning: Christoffel Function Approach to Distribution Regression Problem


Question: 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.

Answer: Online Dynamic Programming


Question: This paper proposes a novel approach for relation extraction from free text which is trained to jointly use information from the text and from existing knowledge. Our model is based on two scoring functions that operate by learning low-dimensional embeddings of words and of entities and relationships from a knowledge base. We empirically show on New York Times articles aligned with Freebase relations that our approach is able to efficiently use the extra information provided by a large subset of Freebase data (4M entities, 23k relationships) to improve over existing methods that rely on text features alone.

Answer:
Connecting Language and Knowledge Bases with Embedding Models for Relation Extraction