user: 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: String Kernel (SK) techniques, especially those using gapped k-mers as features (gk), have obtained great success in classifying sequences like DNA, protein, and text. However, the state-of-the-art gk-SK runs extremely slow when we increase the dictionary size (⌃) or allow more number of mismatches (M). This is because current gk-SK uses a trie-based algorithm to calculate co-occurrence of mismatched substrings resulting in a time cost proportional to O(⌃ ). We propose a fast algorithm for calculating Gapped k-mer Kernel using Counting (GaKCo). GaKCo uses associative arrays to calculate the co-occurrence of substrings using cumulative counting. This algorithm is fast, scalable to larger ⌃ and M , and naturally parallelizable. We provide a rigorous asymptotic analysis that compares GaKCo with the state-of-the-art gk-SK. Theoretically, the time cost of GaKCo is independent of the ⌃ term that slows down the trie-based approach. Experimentally, we observe that GaKCo achieves the same accuracy as the state-of-the-art and outperforms its speed by factors of 2, 100, and 4, on classifying sequences of DNA (5 datasets), protein (12 datasets), and character-based English text (2 datasets), respectively .

Answer: GaKCo: a Fast Gapped k-mer string Kernel using Counting


Question: 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.

Answer: Sample Complexity of Learning Mahalanobis Distance Metrics


Question: Heuristics used for solving hard real-time search problems have regions with depressions. Such regions are bounded areas of the search space in which the heuristic function is inaccurate compared to the actual cost to reach a solution. Early real-time search algorithms, like LRTA∗, easily become trapped in those regions since the heuristic values of their states may need to be updated multiple times, which results in costly solutions. State-of-the-art real-time search algorithms, like LSS-LRTA∗ or LRTA∗(k), improve LRTA∗’s mechanism to update the heuristic, resulting in improved performance. Those algorithms, however, do not guide search towards avoiding depressed regions. This paper presents depression avoidance, a simple real-time search principle to guide search towards avoiding states that have been marked as part of a heuristic depression. We propose two ways in which depression avoidance can be implemented: mark-and-avoid and move-to-border. We implement these strategies on top of LSS-LRTA∗ and RTAA∗, producing 4 new real-time heuristic search algorithms: aLSS-LRTA∗, daLSS-LRTA∗, aRTAA∗, and daRTAA∗. When the objective is to find a single solution by running the real-time search algorithm once, we show that daLSS-LRTA∗ and daRTAA∗ outperform their predecessors sometimes by one order of magnitude. Of the four new algorithms, daRTAA∗ produces the best solutions given a fixed deadline on the average time allowed per planning episode. We prove all our algorithms have good theoretical properties: in finite search spaces, they find a solution if one exists, and converge to an optimal after a number of trials.

Answer:

assistant: Avoiding and Escaping Depressions in Real-Time Heuristic Search