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Miscellaneous Aspects of Machine Learning/Supervised Learning

Yufei CUI, Ziquan Liu, Yixin Chen, Yuchen Lu, Xinyue Yu, Xue (Steve) Liu, Tei-Wei Kuo, Miguel Rodrigues, Chun Jason Xue, Antoni Chan

Multiple Instance Learning (MIL) is a crucial weakly supervised learning method applied across various domains, e.g., medical diagnosis based on whole slide images (WSIs). Recent advancements in MIL algorithms have yielded exceptional performance when the training and test data originate from the same domain, such as WSIs obtained from the same hospital. However, this paper reveals a performance deterioration of MIL models when tested on an out-of-domain test set, exemplified by WSIs sourced from a novel hospital. To address this challenge, this paper introduces the Retrieval-AugMented MIL (RAM-MIL) framework, which integrates Optimal Transport (OT) as the distance metric for nearest neighbor retrieval. The development of RAM-MIL is driven by two key insights. First, a theoretical discovery indicates that reducing the input's intrinsic dimension can minimize the approximation error in attention-based MIL. Second, previous studies highlight a link between input intrinsic dimension and the feature merging process with the retrieved data. Empirical evaluations conducted on WSI classification demonstrate that the proposed RAM-MIL framework achieves state-of-the-art performance in both in-domain scenarios, where the training and retrieval data are in the same domain, and more crucially, in out-of-domain scenarios, where the (unlabeled) retrieval data originates from a different domain. Furthermore, the use of the transportation matrix derived from OT renders the retrieval results interpretable at the instance level, in contrast to the vanilla $l_2$ distance, and allows for visualization for human experts. *Code can be found at \url{https://github.com/ralphc1212/ram-mil*.

Miscellaneous Aspects of Machine Learning/Supervised Learning

Jacob Zavatone-Veth, Cengiz Pehlevan

In recent years, significant attention in deep learning theory has been devoted to analyzing when models that interpolate their training data can still generalize well to unseen examples. Many insights have been gained from studying models with multiple layers of Gaussian random features, for which one can compute precise generalization asymptotics. However, few works have considered the effect of weight anisotropy; most assume that the random features are generated using independent and identically distributed Gaussian weights, and allow only for structure in the input data. Here, we use the replica trick from statistical physics to derive learning curves for models with many layers of structured Gaussian features. We show that allowing correlations between the rows of the first layer of features can aid generalization, while structure in later layers is generally detrimental. Our results shed light on how weight structure affects generalization in a simple class of solvable models.

Miscellaneous Aspects of Machine Learning/Supervised Learning

Zitai Wang, Qianqian Xu, Zhiyong Yang, Yuan He, Xiaochun Cao, Qingming Huang

Real-world datasets are typically imbalanced in the sense that only a few classes have numerous samples, while many classes are associated with only a few samples. As a result, a naive ERM learning process will be biased towards the majority classes, making it difficult to generalize to the minority classes. To address this issue, one simple but effective approach is to modify the loss function to emphasize the learning on minority classes, such as re-weighting the losses or adjusting the logits via class-dependent terms. However, existing generalization analysis of such losses is still coarse-grained and fragmented, failing to explain some empirical results. To bridge this gap between theory and practice, we propose a novel technique named data-dependent contraction to capture how these modified losses handle different classes. On top of this technique, a fine-grained generalization bound is established for imbalanced learning, which helps reveal the mystery of re-weighting and logit-adjustment in a unified manner. Furthermore, a principled learning algorithm is developed based on the theoretical insights. Finally, the empirical results on benchmark datasets not only validate the theoretical results but also demonstrate the effectiveness of the proposed method.

Miscellaneous Aspects of Machine Learning/Supervised Learning

Naoki Nishikawa, Yuichi Ike, Kenji Yamanishi

Machine learning for point clouds has been attracting much attention, with many applications in various fields, such as shape recognition and material science. For enhancing the accuracy of such machine learning methods, it is often effective to incorporate global topological features, which are typically extracted by persistent homology. In the calculation of persistent homology for a point cloud, we choose a filtration for the point cloud, an increasing sequence of spaces. Since the performance of machine learning methods combined with persistent homology is highly affected by the choice of a filtration, we need to tune it depending on data and tasks. In this paper, we propose a framework that learns a filtration adaptively with the use of neural networks. In order to make the resulting persistent homology isometry-invariant, we develop a neural network architecture with such invariance. Additionally, we show a theoretical result on a finite-dimensional approximation of filtration functions, which justifies the proposed network architecture. Experimental results demonstrated the efficacy of our framework in several classification tasks.

Miscellaneous Aspects of Machine Learning/Supervised Learning

Wittawat Jitkrittum, Neha Gupta, Aditya Menon, Harikrishna Narasimhan, Ankit Rawat, Sanjiv Kumar

Cascades are a classical strategy to enable inference cost to vary adaptively across samples, wherein a sequence of classifiers are invoked in turn. A deferral rule determines whether to invoke the next classifier in the sequence, or to terminate prediction. One simple deferral rule employs the confidence of the current classifier, e.g., based on the maximum predicted softmax probability. Despite being oblivious to the structure of the cascade --- e.g., not modelling the errors of downstream models --- such confidence-based deferral often works remarkably well in practice. In this paper, we seek to better understand the conditions under which confidence-based deferral may fail, and when alternate deferral strategies can perform better. We first present a theoretical characterisation of the optimal deferral rule, which precisely characterises settings under which confidence-based deferral may suffer. We then study post-hoc deferral mechanisms, and demonstrate they can significantly improve upon confidence-based deferral in settings where (i) downstream models are specialists that only work well on a subset of inputs, (ii) samples are subject to label noise, and (iii) there is distribution shift between the train and test set.

Miscellaneous Aspects of Machine Learning/Supervised Learning

Nora Schneider, Shirin Goshtasbpour, Fernando Perez-Cruz

We propose a novel algorithm for data augmentation in nonlinear over-parametrized regression. Our data augmentation algorithm borrows from the literature on causality. Contrary to the current state-of-the-art solutions that rely on modifications of Mixup algorithm, we extend the recently proposed distributionally robust Anchor regression (AR) method for data augmentation. Our Anchor Data Augmentation (ADA) uses several replicas of the modified samples in AR to provide more training examples, leading to more robust regression predictions. We apply ADA to linear and nonlinear regression problems using neural networks. ADA is competitive with state-of-the-art C-Mixup solutions.

Miscellaneous Aspects of Machine Learning/Supervised Learning

Jiaming Qiu, Xiongtao Dai

We extend metric learning by studying the Riemannian manifold structure of the underlying data space induced by similarity measures between data points. The key quantity of interest here is the Riemannian metric, which characterizes the Riemannian geometry and defines straight lines and derivatives on the manifold. Being able to estimate the Riemannian metric allows us to gain insights into the underlying manifold and compute geometric features such as the geodesic curves. We model the observed similarity measures as noisy responses generated from a function of the intrinsic geodesic distance between data points. A new local regression approach is proposed to learn the Riemannian metric tensor and its derivatives based on a Taylor expansion for the squared geodesic distances, accommodating different types of data such as continuous, binary, or comparative responses. We develop theoretical foundation for our method by deriving the rates of convergence for the asymptotic bias and variance of the estimated metric tensor. The proposed method is shown to be versatile in simulation studies and real data applications involving taxi trip time in New York City and MNIST digits.

Miscellaneous Aspects of Machine Learning/Supervised Learning

Erik Schultheis, Marek Wydmuch, Wojciech Kotlowski, Rohit Babbar, Krzysztof Dembczynski

Extreme multi-label classification (XMLC) is the task of selecting a small subset of relevant labels from a very large set of possible labels. As such, it is characterized by long-tail labels, i.e., most labels have very few positive instances. With standard performance measures such as precision@k, a classifier can ignore tail labels and still report good performance. However, it is often argued that correct predictions in the tail are more "interesting" or "rewarding," but the community has not yet settled on a metric capturing this intuitive concept. The existing propensity-scored metrics fall short on this goal by confounding the problems of long-tail and missing labels. In this paper, we analyze generalized metrics budgeted "at k" as an alternative solution. To tackle the challenging problem of optimizing these metrics, we formulate it in the expected test utility (ETU) framework, which aims to optimize the expected performance on a given test set. We derive optimal prediction rules and construct their computationally efficient approximations with provable regret guarantees and being robust against model misspecification. Our algorithm, based on block coordinate descent, scales effortlessly to XMLC problems and obtains promising results in terms of long-tail performance.