We consider a variant of the contextual bandit problem. In standard contextual bandits, when a user arrives we get the user's complete feature vector and then assign a treatment (arm) to that user. In a number of applications (like healthcare), collecting features from users can be costly. To address this issue, we propose algorithms that avoid needless feature collection while maintaining strong regret guarantees.

Representation Learning of words and Knowledge Graphs (KG) into low dimensional vector spaces along with its applications to many real-world scenarios have recently gained momentum. In order to make use of multiple KG embeddings for knowledge-driven applications such as question answering, named entity disambiguation, knowledge graph completion, etc., alignment of different KG embedding spaces is necessary. In addition to multilinguality and domain-specific information, different KGs pose the problem of structural differences making the alignment of the KG embeddings more challenging. This paper provides a theoretical analysis and comparison of the state-of-the-art alignment methods between two embedding spaces representing entity-entity and entity-word. This paper also aims at assessing the capability and short-comings of the existing alignment methods on the pretext of different applications.

We propose a neural network-based approach that computes a stable and generalizing metric (LSiM), to compare field data from a variety of numerical simulation sources. Our method employs a Siamese network architecture that is motivated by the mathematical properties of a metric. We leverage a controllable data generation setup with partial differential equation (PDE) solvers to create increasingly different outputs from a reference simulation in a controlled environment. A central component of our learned metric is a specialized loss function that introduces knowledge about the correlation between single data samples into the training process. To demonstrate that the proposed approach outperforms existing simple metrics for vector spaces and other learned, image-based metrics, we evaluate the different methods on a large range of test data. Additionally, we analyze benefits for generalization and the impact of an adjustable training data difficulty. The robustness of LSiM is demonstrated via an evaluation on three real-world data sets.

In an ego-network, an individual (ego) organizes its friends (alters) in different groups (social circles). This social network can be efficiently analyzed after learning representations of the ego and its alters in a low-dimensional, real vector space. These representations are then easily exploited via statistical models for tasks such as social circle detection and prediction. Recent advances in language modeling via deep learning have inspired new methods for learning network representations. These methods can capture the global structure of networks. In this paper, we evolve these techniques to also encode the local structure of neighborhoods. Therefore, our local representations capture network features that are hidden in the global representation of large networks. We show that the task of social circle prediction benefits from a combination of global and local features generated by our technique.

The multi-armed bandit (MAB) setting is a useful abstraction of many online learning tasks which focuses on the trade-off between exploration and exploitation. In this setting, an online algorithm has a fixed set of alternatives ("arms"), and in each round it selects one arm and then observes the corresponding reward. While the case of small number of arms is by now well-understood, a lot of recent work has focused on multi-armed bandits with (infinitely) many arms, where one needs to assume extra structure in order to make the problem tractable. In particular, in the Lipschitz MAB problem there is an underlying similarity metric space, known to the algorithm, such that any two arms that are close in this metric space have similar payoffs. In this paper we consider the more realistic scenario in which the metric space is *implicit* -- it is defined by the available structure but not revealed to the algorithm directly.

It was recently shown that certain nonparametric regressors can escape the curse of dimensionality in the sense that their convergence rates adapt to the intrinsic dimension of data (\cite{BL:65, SK:77}). We prove some stronger results in more general settings. In particular, we consider a regressor which, by combining aspects of both tree-based regression and kernel regression, operates on a general metric space, yields a smooth function, and evaluates in time $O(\log n)$. We derive a tight convergence rate of the form $n {-2/(2 d)}$ where $d$ is the Assouad dimension of the input space. Papers published at the Neural Information Processing Systems Conference.

Motivated by recent developments in manifold-valued regression we propose a family of nonparametric kernel-smoothing estimators with metric-space valued output including a robust median type estimator and the classical Frechet mean. Depending on the choice of the output space and the chosen metric the estimator reduces to partially well-known procedures for multi-class classification, multivariate regression in Euclidean space, regression with manifold-valued output and even some cases of structured output learning. In this paper we focus on the case of regression with manifold-valued input and output. We show pointwise and Bayes consistency for all estimators in the family for the case of manifold-valued output and illustrate the robustness properties of the estimator with experiments. Papers published at the Neural Information Processing Systems Conference.

Unsupervised text encoding models have recently fueled substantial progress in NLP. The key idea is to use neural networks to convert words in texts to vector space representations based on word positions in a sentence and their contexts, which are suitable for end-to-end training of downstream tasks. We see a strikingly similar situation in spatial analysis, which focuses on incorporating both absolute positions and spatial contexts of geographic objects such as POIs into models. A general-purpose representation model for space is valuable for a multitude of tasks. However, no such general model exists to date beyond simply applying discretization or feed-forward nets to coordinates, and little effort has been put into jointly modeling distributions with vastly different characteristics, which commonly emerges from GIS data. Meanwhile, Nobel Prize-winning Neuroscience research shows that grid cells in mammals provide a multi-scale periodic representation that functions as a metric for location encoding and is critical for recognizing places and for path-integration. Therefore, we propose a representation learning model called Space2Vec to encode the absolute positions and spatial relationships of places. We conduct experiments on two real-world geographic data for two different tasks: 1) predicting types of POIs given their positions and context, 2) image classification leveraging their geo-locations. Results show that because of its multi-scale representations, Space2Vec outperforms well-established ML approaches such as RBF kernels, multi-layer feed-forward nets, and tile embedding approaches for location modeling and image classification tasks. Detailed analysis shows that all baselines can at most well handle distribution at one scale but show poor performances in other scales. In contrast, Space2Vec's multi-scale representation can handle distributions at different scales.

Our focus is on approximate nearest neighbor retrieval in metric and non-metric spaces. We employ a VP-tree and explore two simple yet effective learning-to prune approaches: density estimation through sampling and "stretching" of the triangle inequality. Both methods are evaluated using data sets with metric (Euclidean) and non-metric (KL-divergence and Itakura-Saito) distance functions. Conditions on spaces where the VP-tree is applicable are discussed. The VP-tree with a learned pruner is compared against the recently proposed state-of-the-art approaches: the bbtree, the multi-probe locality sensitive hashing (LSH), and permutation methods.

Few prior works study deep learning on point sets. PointNet is a pioneer in this direction. However, by design PointNet does not capture local structures induced by the metric space points live in, limiting its ability to recognize fine-grained patterns and generalizability to complex scenes. In this work, we introduce a hierarchical neural network that applies PointNet recursively on a nested partitioning of the input point set. By exploiting metric space distances, our network is able to learn local features with increasing contextual scales.