Recently, non-Euclidean spaces became popular for embedding structured data. Following hyperbolic and spherical spaces, more general product spaces have been proposed. However, searching for the best configuration of a product space is a resource-intensive procedure, which reduces the practical applicability of the idea. We introduce a novel concept of overlaying spaces that does not have the problem of configuration search and outperforms the competitors in structured data embedding tasks, when the aim is to preserve all distances. On the other hand, for local loss functions (e.g., for ranking losses), the dot-product similarity, which is often overlooked in graph embedding literature since it cannot be converted to a metric, outperforms all metric spaces. We discuss advantages of the dot product over proper metric spaces.

Metric space magnitude, an active subject of research in algebraic topology, originally arose in the context of biology, where it was used to represent the effective number of distinct species in an environment. In a more general setting, the magnitude of a metric space is a real number that aims to quantify the effective number of distinct points in the space. The contribution of each point to a metric space's global magnitude, which is encoded by the {\em weighting vector}, captures much of the underlying geometry of the original metric space. Surprisingly, when the metric space is Euclidean, the weighting vector also serves as an effective tool for boundary detection. This allows the weighting vector to serve as the foundation of novel algorithms for classic machine learning tasks such as classification, outlier detection and active learning. We demonstrate, using experiments and comparisons on classic benchmark datasets, the promise of the proposed magnitude and weighting vector-based approaches.

The goal in extreme multi-label classification (XMC) is to tag an instance with a small subset of relevant labels from an extremely large set of possible labels. In addition to the computational burden arising from large number of training instances, features and labels, problems in XMC are faced with two statistical challenges, (i) large number of 'tail-labels' -- those which occur very infrequently, and (ii) missing labels as it is virtually impossible to manually assign every relevant label to an instance. In this work, we derive an unbiased estimator for general formulation of loss functions which decompose over labels, and then infer the forms for commonly used loss functions such as hinge- and squared-hinge-loss and binary cross-entropy loss. We show that the derived unbiased estimators, in the form of appropriate weighting factors, can be easily incorporated in state-of-the-art algorithms for extreme classification, thereby scaling to datasets with hundreds of thousand labels. However, empirically, we find a slightly altered version that gives more relative weight to tail labels to perform even better. We suspect is due to the label imbalance in the dataset, which is not explicitly addressed by our theoretically derived estimator. Minimizing the proposed loss functions leads to significant improvement over existing methods (up to 20% in some cases) on benchmark datasets in XMC.

Many inference problems in structured prediction can be modeled as maximizing a score function on a space of labels, where graphs are a natural representation to decompose the total score into a sum of unary (nodes) and pairwise (edges) scores. Given a generative model with an undirected connected graph $G$ and true vector of binary labels, it has been previously shown that when $G$ has good expansion properties, such as complete graphs or $d$-regular expanders, one can exactly recover the true labels (with high probability and in polynomial time) from a single noisy observation of each edge and node. We analyze the previously studied generative model by Globerson et al. (2015) under a notion of statistical parity. That is, given a fair binary node labeling, we ask the question whether it is possible to recover the fair assignment, with high probability and in polynomial time, from single edge and node observations. We find that, in contrast to the known trade-offs between fairness and model performance, the addition of the fairness constraint improves the probability of exact recovery. We effectively explain this phenomenon and empirically show how graphs with poor expansion properties, such as grids, are now capable to achieve exact recovery with high probability. Finally, as a byproduct of our analysis, we provide a tighter minimum-eigenvalue bound than that of Weyl's inequality.

Sequence classification is the supervised learning task of building models that predict class labels of unseen sequences of symbols. Although accuracy is paramount, in certain scenarios interpretability is a must. Unfortunately, such trade-off is often hard to achieve since we lack human-independent interpretability metrics. We introduce a novel sequence learning algorithm, that combines (i) linear classifiers - which are known to strike a good balance between predictive power and interpretability, and (ii) background knowledge embeddings. We extend the classic subsequence feature space with groups of symbols which are generated by background knowledge injected via word or graph embeddings, and use this new feature space to learn a linear classifier. We also present a new measure to evaluate the interpretability of a set of symbolic features based on the symbol embeddings. Experiments on human activity recognition from wearables and amino acid sequence classification show that our classification approach preserves predictive power, while delivering more interpretable models.

Automated per-instance algorithm selection often outperforms single learners. Key to algorithm selection via meta-learning is often the (meta) features, which sometimes though do not provide enough information to train a meta-learner effectively. We propose a Siamese Neural Network architecture for automated algorithm selection that focuses more on 'alike performing' instances than meta-features. Our work includes a novel performance metric and method for selecting training samples. We introduce further the concept of 'Algorithm Performance Personas' that describe instances for which the single algorithms perform alike. The concept of 'alike performing algorithms' as ground truth for selecting training samples is novel and provides a huge potential as we believe. In this proposal, we outline our ideas in detail and provide the first evidence that our proposed metric is better suitable for training sample selection that standard performance metrics such as absolute errors.

Knowledge Graph Completion (KGC) has been proposed to improve Knowledge Graphs by filling in missing connections via link prediction or relation extraction. One of the main difficulties for KGC is a low resource problem. Previous approaches assume sufficient training triples to learn versatile vectors for entities and relations, or a satisfactory number of labeled sentences to train a competent relation extraction model. However, low resource relations are very common in KGs, and those newly added relations often do not have many known samples for training. In this work, we aim at predicting new facts under a challenging setting where only limited training instances are available. We propose a general framework called Weighted Relation Adversarial Network, which utilizes an adversarial procedure to help adapt knowledge/features learned from high resource relations to different but related low resource relations. Specifically, the framework takes advantage of a relation discriminator to distinguish between samples from different relations, and help learn relation-invariant features more transferable from source relations to target relations. Experimental results show that the proposed approach outperforms previous methods regarding low resource settings for both link prediction and relation extraction.

We study reinforcement learning in continuous state and action spaces endowed with a metric. We provide a refined analysis of the algorithm of Sinclair, Banerjee, and Yu (2019) and show that its regret scales with the \emph{zooming dimension} of the instance. This parameter, which originates in the bandit literature, captures the size of the subsets of near optimal actions and is always smaller than the covering dimension used in previous analyses. As such, our results are the first provably adaptive guarantees for reinforcement learning in metric spaces.

Gov. Ron DeSantis last week said the upward trend in confirmed cases is mostly a reflection of more testing being conducted combined with some spikes in some agriculture communities, but the number of tests conducted daily peaked three weeks ago and the percentage of positive tests is now over 6%, more than double the rate of 2.3% in late May.

We present Wasserstein Embedding for Graph Learning (WEGL), a novel and fast framework for embedding entire graphs in a vector space, in which various machine learning models are applicable for graph-level prediction tasks. We leverage new insights on defining similarity between graphs as a function of the similarity between their node embedding distributions. Specifically, we use the Wasserstein distance to measure the dissimilarity between node embeddings of different graphs. Different from prior work, we avoid pairwise calculation of distances between graphs and reduce the computational complexity from quadratic to linear in the number of graphs. WEGL calculates Monge maps from a reference distribution to each node embedding and, based on these maps, creates a fixed-sized vector representation of the graph. We evaluate our new graph embedding approach on various benchmark graph-property prediction tasks, showing state-of-the-art classification performance, while having superior computational efficiency.