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.

[Q]: Metric learning seeks a transformation of the feature space that enhances prediction quality for the given task at hand. In this work we provide PAC-style sample complexity rates for supervised metric learning. We give matching lowerand upper-bounds showing that the sample complexity scales with the representation dimension when no assumptions are made about the underlying data distribution. However, by leveraging the structure of the data distribution, we show that one can achieve rates that are fine-tuned to a specific notion of intrinsic complexity for a given dataset. Our analysis reveals that augmenting the metric learning optimization criterion with a simple norm-based regularization can help adapt to a dataset’s intrinsic complexity, yielding better generalization. Experiments on benchmark datasets validate our analysis and show that regularizing the metric can help discern the signal even when the data contains high amounts of noise.
[A]: Sample Complexity of Learning Mahalanobis Distance Metrics


[Q]: We describe how to use propositional model counting for a quantitative analysis of product configuration data. Our approach computes valuable meta information such as the total number of valid configurations or the relative frequency of components. This information can be used to assess the severity of documentation errors or to measure documentation quality. As an application example we show how we apply these methods to product documentation formulas of the Mercedes-Benz line of vehicles. In order to process these large formulas we developed and implemented a new model counter for non-CNF formulas. Our model counter can process formulas, whose CNF representations could not be processed up till now.
[A]: Model Counting in Product Configuration


[Q]: We present a new system S for handling uncertainty in a quantified modal logic (first-order modal logic). The system is based on both probability theory and proof theory. The system is derived from Chisholm’s epistemology. We concretize Chisholm’s system by grounding his undefined and primitive (i.e. foundational) concept of reasonableness in probability and proof theory. S can be useful in systems that have to interact with humans and provide justifications for their uncertainty. As a demonstration of the system, we apply the system to provide a solution to the lottery paradox. Another advantage of the system is that it can be used to provide uncertainty values for counterfactual statements. Counterfactuals are statements that an agent knows for sure are false. Among other cases, counterfactuals are useful when systems have to explain their actions to users (If I had not done α, then φ would have happened). Uncertainties for counterfactuals fall out naturally from our system. Efficient reasoning in just simple first-order logic is a hard problem. Resolution-based first-order reasoning systems have made significant progress over the last several decades in building systems that have solved non-trivial tasks (even unsolved conjectures in mathematics). We present a sketch of a novel algorithm for reasoning that extends firstorder resolution. Finally, while there have been many systems of uncertainty for propositional logics, first-order logics and propositional modal logics, there has been very little work in building systems of uncertainty for first-order modal logics. The work described below is in progress; and once finished will address this lack.
[A]:
Strength Factors: An Uncertainty System for a Quantified Modal Logic