We propose a method called clustered conformal prediction that clusters together classes having "similar" conformal

Neural Information Processing Systems http://nips.cc/

Since our manually collected test sets are rather small, we decided to avoid tuning hyperparameters on them as this would require holding out a non-trivial number of data points.

Bayesian optimization (BO) is a popular technique for sample-efficient optimization of black-box functions. In many applications, the parameters being tuned come with a carefully engineered default configuration, and practitioners only want to deviate from this default when necessary. Standard BO, however, does not aim to minimize deviation from the default and, in practice, often pushes weakly relevant parameters to the boundary of the search space. This makes it difficult to distinguish between important and spurious changes and increases the burden of vetting recommendations when the optimization objective omits relevant operational considerations. We introduce BONSAI, a default-aware BO policy that prunes low-impact deviations from a default configuration while explicitly controlling the loss in acquisition value. BONSAI is compatible with a variety of acquisition functions, including expected improvement and upper confidence bound (GP-UCB). We theoretically bound the regret incurred by BONSAI, showing that, under certain conditions, it enjoys the same no-regret property as vanilla GP-UCB. Across many real-world applications, we empirically find that BONSAI substantially reduces the number of non-default parameters in recommended configurations while maintaining competitive optimization performance, with little effect on wall time.

In most applications,E " Y to begin with (ally are potential maximizer for some vector of costs, otherwise theyare not included in the set), and all points inY havepositive mass. Ittherefore also satisfies this property. We recall that we assume thatθ yields a unique maximum to the linear program onC. As a consequence, all convergent subsequences ofyn converge to the same limity pθq: it is the unique accumulation point of this sequence.Itfollowsdirectlythat yn convergesto y pθq,asitlivesinacompactset,whichyieldsthe desired result. Using different reference vectorsv yield different perturbed operations, andv " p1,2,...,dq is commonlyused.

Gathering training data is a key step of any supervised learning task, and it is both critical and expensive. Critical, because the quantity and quality of the training data has a high impact on the performance of the learned function. Expensive, because most practical cases rely on humans-in-the-loop to label the data. The process of determining the correct labels is much more expensive than comparing two items to see whether they belong to the same class. Thus motivated, we propose a setting for training data gathering where the human experts perform the comparatively cheap task of answering pairwise queries, and the computer groups the items into classes (which can be labeled cheaply at the very end of the process). Given the items, we consider two random models for the classes: one where the set partition they form is drawn uniformly, the other one where each item chooses its class independently following a fixed distribution. In the first model, we characterize the algorithms that minimize the average number of queries required to cluster the items and analyze their complexity. In the second model, we analyze a specific algorithm family, propose as a conjecture that they reach the minimum average number of queries and compare their performance to a random approach. We also propose solutions to handle errors or inconsistencies in the experts' answers.

To explore the relationship between dependency distance (DD) and hierarchical distance (HD) in Japanese, we compared the probability distributions of DD and HD with and without sentence length fixed, and analyzed the changes in mean dependency distance (MDD) and mean hierarchical distance (MHD) as sentence length increases, along with their correlation coefficient based on the Balanced Corpus of Contemporary Written Japanese. It was found that the valency of the predicates is the underlying factor behind the trade-off relation between MDD and MHD in Japanese. Native speakers of Japanese regulate the linear complexity and hierarchical complexity through the valency of the predicates, and the relative sizes of MDD and MHD depend on whether the threshold of valency has been reached. Apart from the cognitive load, the valency of the predicates also affects the probability distributions of DD and HD. The effect of the valency of the predicates on the distribution of HD is greater than on that of DD, which leads to differences in their probability distributions and causes the mean of MDD to be lower than that of MHD.