To mitigate the bias exhibited by machine learning models, fairness criteria can be integrated into the training process to ensure fair treatment across all demographics, but it often comes at the expense of model performance. Understanding such tradeoffs, therefore, underlies the design of fair algorithms. To this end, this paper provides a complete characterization of the inherent tradeoff of demographic parity on classification problems, under the most general multi-group, multi-class, and noisy setting. Specifically, we show that the minimum error rate achievable by randomized and attribute-aware fair classifiers is given by the optimal value of a Wasserstein-barycenter problem. On the practical side, our findings lead to a simple post-processing algorithm that derives fair classifiers from score functions, which yields the optimal fair classifier when the score is Bayes optimal. We provide suboptimality analysis and sample complexity for our algorithm, and demonstrate its effectiveness on benchmark datasets.
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Fully-unsupervised Person and Vehicle Re-Identification have received increasing attention due to their broad applicability in surveillance, forensics, event understanding, and smart cities, without requiring any manual annotation. However, most of the prior art has been evaluated in datasets that have just a couple thousand samples. Such small-data setups often allow the use of costly techniques in time and memory footprints, such as Re-Ranking, to improve clustering results. Moreover, some previous work even pre-selects the best clustering hyper-parameters for each dataset, which is unrealistic in a large-scale fully-unsupervised scenario. In this context, this work tackles a more realistic scenario and proposes two strategies to learn from large-scale unlabeled data. The first strategy performs a local neighborhood sampling to reduce the dataset size in each iteration without violating neighborhood relationships. A second strategy leverages a novel Re-Ranking technique, which has a lower time upper bound complexity and reduces the memory complexity from O(n^2) to O(kn) with k << n. To avoid the pre-selection of specific hyper-parameter values for the clustering algorithm, we also present a novel scheduling algorithm that adjusts the density parameter during training, to leverage the diversity of samples and keep the learning robust to noisy labeling. Finally, due to the complementary knowledge learned by different models, we also introduce a co-training strategy that relies upon the permutation of predicted pseudo-labels, among the backbones, with no need for any hyper-parameters or weighting optimization. The proposed methodology outperforms the state-of-the-art methods in well-known benchmarks and in the challenging large-scale Veri-Wild dataset, with a faster and memory-efficient Re-Ranking strategy, and a large-scale, noisy-robust, and ensemble-based learning approach.
Verifying the correct behavior of robots in contact tasks is challenging due to model uncertainties associated with contacts. Standard methods for testing often fall short since all (uncountable many) solutions cannot be obtained. Instead, we propose to formally and efficiently verify robot behaviors in contact tasks using reachability analysis, which enables checking all the reachable states against user-provided specifications. To this end, we extend the state of the art in reachability analysis for hybrid (mixed discrete and continuous) dynamics subject to discrete-time input trajectories. In particular, we present a novel and scalable guard intersection approach to reliably compute the complex behavior caused by contacts. We model robots subject to contacts as hybrid automata in which crucial time delays are included. The usefulness of our approach is demonstrated by verifying safe human-robot interaction in the presence of constrained collisions, which was out of reach for existing methods.
Attention models are typically learned by optimizing one of three standard loss functions that are variously called -- soft attention, hard attention, and latent variable marginal likelihood (LVML) attention. All three paradigms are motivated by the same goal of finding two models -- a `focus' model that `selects' the right \textit{segment} of the input and a `classification' model that processes the selected segment into the target label. However, they differ significantly in the way the selected segments are aggregated, resulting in distinct dynamics and final results. We observe a unique signature of models learned using these paradigms and explain this as a consequence of the evolution of the classification model under gradient descent when the focus model is fixed. We also analyze these paradigms in a simple setting and derive closed-form expressions for the parameter trajectory under gradient flow. With the soft attention loss, the focus model improves quickly at initialization and splutters later on. On the other hand, hard attention loss behaves in the opposite fashion. Based on our observations, we propose a simple hybrid approach that combines the advantages of the different loss functions and demonstrates it on a collection of semi-synthetic and real-world datasets
The increasing use of machine learning in high-stakes domains -- where people's livelihoods are impacted -- creates an urgent need for interpretable, fair, and highly accurate algorithms. With these needs in mind, we propose a mixed integer optimization (MIO) framework for learning optimal classification trees -- one of the most interpretable models -- that can be augmented with arbitrary fairness constraints. In order to better quantify the "price of interpretability", we also propose a new measure of model interpretability called decision complexity that allows for comparisons across different classes of machine learning models. We benchmark our method against state-of-the-art approaches for fair classification on popular datasets; in doing so, we conduct one of the first comprehensive analyses of the trade-offs between interpretability, fairness, and predictive accuracy. Given a fixed disparity threshold, our method has a price of interpretability of about 4.2 percentage points in terms of out-of-sample accuracy compared to the best performing, complex models. However, our method consistently finds decisions with almost full parity, while other methods rarely do.
We introduce and study a scale of operator classes on the annulus that is motivated by the $\mathcal{C}_{\rho}$ classes of $\rho$-contractions of Nagy and Foia\c{s}. In particular, our classes are defined in terms of the contractivity of the double-layer potential integral operator over the annulus. We prove that if, in addition, complete contractivity is assumed, then one obtains a complete characterization involving certain variants of the $\mathcal{C}_{\rho}$ classes. Recent work of Crouzeix-Greenbaum and Schwenninger-de Vries allows us to also obtain relevant K-spectral estimates, generalizing existing results from the literature on the annulus. Finally, we exhibit a special case where these estimates can be significantly strengthened.
Modern machine learning approaches to classification, including AdaBoost, support vector machines, and deep neural networks, utilize surrogate loss techniques to circumvent the computational complexity of minimizing empirical classification risk. These techniques are also useful for causal policy learning problems, since estimation of individualized treatment rules can be cast as a weighted (cost-sensitive) classification problem. Consistency of the surrogate loss approaches studied in Zhang (2004) and Bartlett et al. (2006) crucially relies on the assumption of correct specification, meaning that the specified set of classifiers is rich enough to contain a first-best classifier. This assumption is, however, less credible when the set of classifiers is constrained by interpretability or fairness, leaving the applicability of surrogate loss based algorithms unknown in such second-best scenarios. This paper studies consistency of surrogate loss procedures under a constrained set of classifiers without assuming correct specification. We show that in the setting where the constraint restricts the classifier's prediction set only, hinge losses (i.e., $\ell_1$-support vector machines) are the only surrogate losses that preserve consistency in second-best scenarios. If the constraint additionally restricts the functional form of the classifier, consistency of a surrogate loss approach is not guaranteed even with hinge loss. We therefore characterize conditions for the constrained set of classifiers that can guarantee consistency of hinge risk minimizing classifiers. Exploiting our theoretical results, we develop robust and computationally attractive hinge loss based procedures for a monotone classification problem.
Social media offer plenty of information to perform market research in order to meet the requirements of customers. One way how this research is conducted is that a domain expert gathers and categorizes user-generated content into a complex and fine-grained class structure. In many of such cases, little data meets complex annotations. It is not yet fully understood how this can be leveraged successfully for classification. We examine the classification accuracy of expert labels when used with a) many fine-grained classes and b) few abstract classes. For scenario b) we compare abstract class labels given by the domain expert as baseline and by automatic hierarchical clustering. We compare this to another baseline where the entire class structure is given by a completely unsupervised clustering approach. By doing so, this work can serve as an example of how complex expert annotations are potentially beneficial and can be utilized in the most optimal way for opinion mining in highly specific domains. By exploring across a range of techniques and experiments, we find that automated class abstraction approaches in particular the unsupervised approach performs remarkably well against domain expert baseline on text classification tasks. This has the potential to inspire opinion mining applications in order to support market researchers in practice and to inspire fine-grained automated content analysis on a large scale.
Modern neural network training relies heavily on data augmentation for improved generalization. After the initial success of label-preserving augmentations, there has been a recent surge of interest in label-perturbing approaches, which combine features and labels across training samples to smooth the learned decision surface. In this paper, we propose a new augmentation method that leverages the first and second moments extracted and re-injected by feature normalization. We replace the moments of the learned features of one training image by those of another, and also interpolate the target labels. As our approach is fast, operates entirely in feature space, and mixes different signals than prior methods, one can effectively combine it with existing augmentation methods. We demonstrate its efficacy across benchmark data sets in computer vision, speech, and natural language processing, where it consistently improves the generalization performance of highly competitive baseline networks.
Graph convolutional networks (GCNs) have been successfully applied in node classification tasks of network mining. However, most of these models based on neighborhood aggregation are usually shallow and lack the "graph pooling" mechanism, which prevents the model from obtaining adequate global information. In order to increase the receptive field, we propose a novel deep Hierarchical Graph Convolutional Network (H-GCN) for semi-supervised node classification. H-GCN first repeatedly aggregates structurally similar nodes to hyper-nodes and then refines the coarsened graph to the original to restore the representation for each node. Instead of merely aggregating one- or two-hop neighborhood information, the proposed coarsening procedure enlarges the receptive field for each node, hence more global information can be learned. Comprehensive experiments conducted on public datasets demonstrate the effectiveness of the proposed method over the state-of-art methods. Notably, our model gains substantial improvements when only a few labeled samples are provided.
In this paper, we propose the joint learning attention and recurrent neural network (RNN) models for multi-label classification. While approaches based on the use of either model exist (e.g., for the task of image captioning), training such existing network architectures typically require pre-defined label sequences. For multi-label classification, it would be desirable to have a robust inference process, so that the prediction error would not propagate and thus affect the performance. Our proposed model uniquely integrates attention and Long Short Term Memory (LSTM) models, which not only addresses the above problem but also allows one to identify visual objects of interests with varying sizes without the prior knowledge of particular label ordering. More importantly, label co-occurrence information can be jointly exploited by our LSTM model. Finally, by advancing the technique of beam search, prediction of multiple labels can be efficiently achieved by our proposed network model.
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