You will be shown an abstract from a computer science research paper. Given this abstract, your task is to extract all unique entities with the following types:

- "Task": Applications, problems to solve, systems to construct. Examples include "information extraction", "machine reading system", "image segmentation".
- "Method": : Methods, models, systems to use, or tools, components of a system, frameworks. Examples include "language model", "CORENLP", "POS parser".
- "Metric": Metrics, measures, or entities that can express quality of a system / method. Examples include "F1", "BLEU", "Precision", "time complexity".
- "Material": Data, datasets, resources, Corpus, Knowledge base. Examples include "image data", "speech data", "stereo images", "CoNLL", "Wikipedia".
- "OtherScientificTerm": Phrases that are a scientific terms but do not fall into any of the above classes. Examples include "physical or geometric constraints", "qualitative prior knowledge", "tree kernel", "noise".
- "Generic": General terms or pronouns that may refer to a entity but are not themselves informative, often used as connection words. Examples include "model", "approach", "them".

Please return the output as a JSON object of the format: {"type1" : ["example_entity", ...], "type2" : ["example_entity", ...]}. The keys should be entity types and values should be lists of extracted entities belonging to the corresponding type. Entity types with no matching entities should be assigned an empty array [].

For instance, the output might look like: {"Task": ["speech recognition", ...], "Method": ["Conditional random field"], "Material": [], ...}.

Only output the JSON object and do not include any additional text.

Abstract:

We analyze a reweighted version of the Kikuchi approximation for estimating the log partition function of a product distribution defined over a region graph. We establish sufficient conditions for the concavity of our reweighted objective function in terms of weight assignments in the Kikuchi expansion, and show that a reweighted version of the sum product algorithm applied to the Kikuchi region graph will produce global optima of the Kikuchi approximation whenever the algorithm converges. When the region graph has two layers, corresponding to a Bethe approximation, we show that our sufficient conditions for concavity are also necessary. Finally, we provide an explicit characterization of the polytope of concavity in terms of the cycle structure of the region graph. We conclude with simulations that demonstrate the advantages of the reweighted Kikuchi approach.
{"Generic": [], "Material": [], "Method": ["Kikuchi approximation", "reweighted version of the Kikuchi approximation", "reweighted version of the sum product algorithm", "Bethe approximation"], "Metric": [], "OtherScientificTerm": ["cycle structure", "region graph", "Kikuchi region graph", "global optima", "Kikuchi expansion", "weight assignments", "concavity", "reweighted objective function"], "Task": ["log partition function of a product distribution"]}