Unsupervised domain adaptation aims to address the problem of classifying unlabeled samples from the target domain whilst labeled samples are only available from the source domain and the data distributions are different in these two domains. As a result, classifiers trained from labeled samples in the source domain suffer from significant performance drop when directly applied to the samples from the target domain. To address this issue, different approaches have been proposed to learn domain-invariant features or domain-specific classifiers. In either case, the lack of labeled samples in the target domain can be an issue which is usually overcome by pseudo-labeling. Inaccurate pseudo-labeling, however, could result in catastrophic error accumulation during learning. In this paper, we propose a novel selective pseudo-labeling strategy based on structured prediction. The idea of structured prediction is inspired by the fact that samples in the target domain are well clustered within the deep feature space so that unsupervised clustering analysis can be used to facilitate accurate pseudo-labeling. Experimental results on four datasets (i.e. Office-Caltech, Office31, ImageCLEF-DA and Office-Home) validate our approach outperforms contemporary state-of-the-art methods.

We propose to address multi-label learning by jointly estimating the distribution of positive and negative instances for all labels. By a shared mapping function, each label's positive and negative instances are mapped into a new space forming a mixture distribution of two components (positive and negative). Due to the dependency among labels, positive instances are mapped close if they share common labels, while positive and negative embeddings of the same label are pushed away. The distribution is learned in the new space, and thus well presents both the distance between instances in their original feature space and their common membership w.r.t. different categories. By measuring the density function values, new instances mapped to the new space can easily identify their membership to possible multiple categories. We use neural networks for learning the mapping function and use the expectations of the positive and negative embedding as prototypes of the positive and negative components for each label, respectively. Therefore, we name our proposed method PNML (prototypical networks for multi-label learning). Extensive experiments verify that PNML significantly outperforms the state-of-the-arts.

Interest has been rising lately towards methods representing data in non-Euclidean spaces, e.g. hyperbolic or spherical, that provide specific inductive biases useful for certain real-world data properties, e.g. scale-free, hierarchical or cyclical. However, the popular graph neural networks are currently limited in modeling data only via Euclidean geometry and associated vector space operations. Here, we bridge this gap by proposing mathematically grounded generalizations of graph convolutional networks (GCN) to (products of) constant curvature spaces. We do this by i) introducing a unified formalism that can interpolate smoothly between all geometries of constant curvature, ii) leveraging gyro-barycentric coordinates that generalize the classic Euclidean concept of the center of mass. Our class of models smoothly recover their Euclidean counterparts when the curvature goes to zero from either side. Empirically, we outperform Euclidean GCNs in the tasks of node classification and distortion minimization for symbolic data exhibiting non-Euclidean behavior, according to their discrete curvature.

We introduce a framework for studying how distributional assumptions on the process by which data is partitioned into a training and test set can be leveraged to provide accurate estimation or learning algorithms, even for worst-case datasets. We consider a setting of $n$ datapoints, $x_1,\ldots,x_n$, together with a specified distribution, $P$, over partitions of these datapoints into a training set, test set, and irrelevant set. An algorithm takes as input a description of $P$ (or sample access), the indices of the test and training sets, and the datapoints in the training set, and returns a model or estimate that will be evaluated on the datapoints in the test set. We evaluate an algorithm in terms of its worst-case expected performance: the expected performance over potential test/training sets, for worst-case datapoints, $x_1,\ldots,x_n.$ This framework is a departure from more typical distributional assumptions on the datapoints (e.g. that data is drawn independently, or according to an exchangeable process), and can model a number of natural data collection processes, including processes with dependencies such as "snowball sampling" and "chain sampling", and settings where test and training sets satisfy chronological constraints (e.g. the test instances were observed after the training instances). Within this framework, we consider the setting where datapoints are bounded real numbers, and the goal is to estimate the mean of the test set. We give an efficient algorithm that returns a weighted combination of the training set---whose weights depend on the distribution, $P$, and on the training and test set indices---and show that the worst-case expected error achieved by this algorithm is at most a multiplicative $\pi/2$ factor worse than the optimal of such algorithms. The algorithm, and its proof, leverage a surprising connection to the Grothendieck problem.

This paper focuses on the problem of unsupervised alignment of hierarchical data such as ontologies or lexical databases. This is a problem that appears across areas, from natural language processing to bioinformatics, and is typically solved by appeal to outside knowledge bases and label-textual similarity. In contrast, we approach the problem from a purely geometric perspective: given only a vector-space representation of the items in the two hierarchies, we seek to infer correspondences across them. Our work derives from and interweaves hyperbolic-space representations for hierarchical data, on one hand, and unsupervised word-alignment methods, on the other. We first provide a set of negative results showing how and why Euclidean methods fail in this hyperbolic setting. We then propose a novel approach based on optimal transport over hyperbolic spaces, and show that it outperforms standard embedding alignment techniques in various experiments on cross-lingual WordNet alignment and ontology matching tasks.

Traditional text classifiers are limited to predicting over a fixed set of labels. However, in many real-world applications the label set is frequently changing. For example, in intent classification, new intents may be added over time while others are removed. We propose to address the problem of dynamic text classification by replacing the traditional, fixed-size output layer with a learned, semantically meaningful metric space. Here the distances between textual inputs are optimized to perform nearest-neighbor classification across overlapping label sets. Changing the label set does not involve removing parameters, but rather simply adding or removing support points in the metric space. Then the learned metric can be fine-tuned with only a few additional training examples. We demonstrate that this simple strategy is robust to changes in the label space. Furthermore, our results show that learning a non-Euclidean metric can improve performance in the low data regime, suggesting that further work on metric spaces may benefit low-resource research.

In many applications of machine learning, the training and test set data come from different distributions, or domains. A number of domain generalization strategies have been introduced with the goal of achieving good performance on out-of-distribution data. In this paper, we propose an adversarial approach to the problem. We propose a process that enforces pair-wise domain invariance while training a feature extractor over a diverse set of domains. We show that this process ensures invariance to any distribution that can be expressed as a mixture of the training domains. Following this insight, we then introduce an adversarial approach in which pair-wise divergences are estimated and minimized. Experiments on two domain generalization benchmarks for object recognition (i.e., PACS and VLCS) show that the proposed method yields higher average accuracy on the target domains in comparison to previously introduced adversarial strategies, as well as recently proposed methods based on learning invariant representations.

For joint inference over multiple variables, a variety of structured prediction techniques have been developed to model correlations among variables and thereby improve predictions. However, many classical approaches suffer from one of two primary drawbacks: they either lack the ability to model high-order correlations among variables while maintaining computationally tractable inference, or they do not allow to explicitly model known correlations. To address this shortcoming, we introduce `Graph Structured Prediction Energy Networks,' for which we develop inference techniques that allow to both model explicit local and implicit higher-order correlations while maintaining tractability of inference. We apply the proposed method to tasks from the natural language processing and computer vision domain and demonstrate its general utility.

We introduce the Convolutional Conditional Neural Process (ConvCNP), a new member of the Neural Process family that models translation equivariance in the data. Translation equivariance is an important inductive bias for many learning problems including time series modelling, spatial data, and images. The model embeds data sets into an infinite-dimensional function space as opposed to a finite-dimensional vector space. To formalize this notion, we extend the theory of neural representations of sets to include functional representations, and demonstrate that any translation-equivariant embedding can be represented using a convolutional deep set. We evaluate ConvCNPs in several settings, demonstrating that they achieve state-of-the-art performance compared to existing NPs. We demonstrate that building in translation equivariance enables zero-shot generalization to challenging, out-of-domain tasks.

Chatter detection has become a prominent subject of interest due to its effect on cutting tool life, surface finish and spindle of machine tool. Most of the existing methods in chatter detection literature are based on signal processing and signal decomposition. In this study, we use topological features of data simulating cutting tool vibrations, combined with four supervised machine learning algorithms to diagnose chatter in the milling process. Persistence diagrams, a method of representing topological features, are not easily used in the context of machine learning, so they must be transformed into a form that is more amenable. Specifically, we will focus on two different methods for featurizing persistence diagrams, Carlsson coordinates and template functions. In this paper, we provide classification results for simulated data from various cutting configurations, including upmilling and downmilling, in addition to the same data with some added noise. Our results show that Carlsson Coordinates and Template Functions yield accuracies as high as 96% and 95%, respectively. We also provide evidence that these topological methods are noise robust descriptors for chatter detection.