Gradient descent can be surprisingly good at optimizing deep neural networks without overfitting and without explicit regularization. We find that the discrete steps of gradient descent implicitly regularize models by penalizing gradient descent trajectories that have large loss gradients. We call this Implicit Gradient Regularization (IGR) and we use backward error analysis to calculate the size of this regularization. We confirm empirically that implicit gradient regularization biases gradient descent toward flat minima, where test errors are small and solutions are robust to noisy parameter perturbations. Furthermore, we demonstrate that the implicit gradient regularization term can be used as an explicit regularizer, allowing us to control this gradient regularization directly. More broadly, our work indicates that backward error analysis is a useful theoretical approach to the perennial question of how learning rate, model size, and parameter regularization interact to determine the properties of overparameterized models optimized with gradient descent.

Accurate and comprehensive measurements of a range of sustainable development outcomes are fundamental inputs into both research and policy. We synthesize the growing literature that uses satellite imagery to understand these outcomes, with a focus on approaches that combine imagery with machine learning. We quantify the paucity of ground data on key human-related outcomes and the growing abundance and resolution (spatial, temporal, and spectral) of satellite imagery. We then review recent machine learning approaches to model-building in the context of scarce and noisy training data, highlighting how this noise often leads to incorrect assessment of models' predictive performance. We quantify recent model performance across multiple sustainable development domains, discuss research and policy applications, explore constraints to future progress, and highlight key research directions for the field.

The success of deep learning relies on the availability of large-scale annotated data sets, the acquisition of which can be costly, requiring expert domain knowledge. Semi-supervised learning (SSL) mitigates this challenge by exploiting the behavior of the neural function on large unlabeled data. The smoothness of the neural function is a commonly used assumption exploited in SSL. A successful example is the adoption of mixup strategy in SSL that enforces the global smoothness of the neural function by encouraging it to behave linearly when interpolating between training examples. Despite its empirical success, however, the theoretical underpinning of how mixup regularizes the neural function has not been fully understood. In this paper, we offer a theoretically substantiated proposition that mixup improves the smoothness of the neural function by bounding the Lipschitz constant of the gradient function of the neural networks. We then propose that this can be strengthened by simultaneously constraining the Lipschitz constant of the neural function itself through adversarial Lipschitz regularization, encouraging the neural function to behave linearly while also constraining the slope of this linear function. On three benchmark data sets and one real-world biomedical data set, we demonstrate that this combined regularization results in improved generalization performance of SSL when learning from a small amount of labeled data. We further demonstrate the robustness of the presented method against single-step adversarial attacks. Our code is available at https://github.com/Prasanna1991/Mixup-LR.

Deep neural networks (DNNs) have proven to be powerful tools for processing unstructured data. However for high-dimensional data, like images, they are inherently vulnerable to adversarial attacks. Small almost invisible perturbations added to the input can be used to fool DNNs. Various attacks, hardening methods and detection methods have been introduced in recent years. Notoriously, Carlini-Wagner (CW) type attacks computed by iterative minimization belong to those that are most difficult to detect. In this work, we demonstrate that such iterative minimization attacks can by used as detectors themselves. Thus, in some sense we show that one can fight fire with fire. This work also outlines a mathematical proof that under certain assumptions this detector provides asymptotically optimal separation of original and attacked images. In numerical experiments, we obtain AUROC values up to 99.73% for our detection method. This distinctly surpasses state of the art detection rates for CW attacks from the literature. We also give numerical evidence that our method is robust against the attacker's choice of the method of attack.

The problem of monotone missing data has been broadly studied during the last two decades and has many applications in different fields such as bioinformatics or statistics. Commonly used imputation techniques require multiple iterations through the data before yielding convergence. Moreover, those approaches may introduce extra noises and biases to the subsequent modeling. In this work, we derive exact formulas and propose a novel algorithm to compute the maximum likelihood estimators (MLEs) of a multiple class, monotone missing dataset when all the covariance matrices of all categories are assumed to be equal, namely EPEM. We then illustrate an application of our proposed methods in Linear Discriminant Analysis (LDA). As the computation is exact, our EPEM algorithm does not require multiple iterations through the data as other imputation approaches, thus promising to handle much less time-consuming than other methods. This effectiveness was validated by empirical results when EPEM reduced the error rates significantly and required a short computation time compared to several imputation-based approaches. We also release all codes and data of our experiments in one GitHub repository to contribute to the research community related to this problem.

Much as replacing hand-designed features with learned functions has revolutionized how we solve perceptual tasks, we believe learned algorithms will transform how we train models. In this work we focus on general-purpose learned optimizers capable of training a wide variety of problems with no user-specified hyperparameters. We introduce a new, neural network parameterized, hierarchical optimizer with access to additional features such as validation loss to enable automatic regularization. Most learned optimizers have been trained on only a single task, or a small number of tasks. We train our optimizers on thousands of tasks, making use of orders of magnitude more compute, resulting in optimizers that generalize better to unseen tasks. The learned optimizers not only perform well, but learn behaviors that are distinct from existing first order optimizers. For instance, they generate update steps that have implicit regularization and adapt as the problem hyperparameters (e.g. batch size) or architecture (e.g. neural network width) change. Finally, these learned optimizers show evidence of being useful for out of distribution tasks such as training themselves from scratch.

Extreme multi-label classification (XMLC) is a learning task of tagging instances with a small subset of relevant labels chosen from an extremely large pool of possible labels. Problems of this scale can be efficiently handled by organizing labels as a tree, like in hierarchical softmax used for multi-class problems. In this paper, we thoroughly investigate probabilistic label trees (PLTs) which can be treated as a generalization of hierarchical softmax for multi-label problems. We first introduce the PLT model and discuss training and inference procedures and their computational costs. Next, we prove the consistency of PLTs for a wide spectrum of performance metrics. To this end, we upperbound their regret by a function of surrogate-loss regrets of node classifiers. Furthermore, we consider a problem of training PLTs in a fully online setting, without any prior knowledge of training instances, their features, or labels. In this case, both node classifiers and the tree structure are trained online. We prove a specific equivalence between the fully online algorithm and an algorithm with a tree structure given in advance. Finally, we discuss several implementations of PLTs and introduce a new one, napkinXC, which we empirically evaluate and compare with state-of-the-art algorithms.

Improper or erroneous labelling can pose a hindrance to reliable generalization for supervised learning. This can have negative consequences, especially for critical fields such as healthcare. We propose an effective new approach for learning under extreme label noise, based on under-trained deep ensembles. Each ensemble member is trained with a subset of the training data, to acquire a general overview of the decision boundary separation, without focusing on potentially erroneous details. The accumulated knowledge of the ensemble is combined to form new labels, that determine a better class separation than the original labels. A new model is trained with these labels to generalize reliably despite the label noise. We focus on a healthcare setting and extensively evaluate our approach on the task of sleep apnea detection. For comparison with related work, we additionally evaluate on the task of digit recognition. In our experiments, we observed performance improvement in accuracy from 6.7\% up-to 49.3\% for the task of digit classification and in kappa from 0.02 up-to 0.55 for the task of sleep apnea detection.

This paper studies the problem of detecting novel or unexpected instances in text classification. In traditional text classification, the classes appeared in testing must have been seen in training. However, in many applications, this is not the case because in testing, we may see unexpected instances that are not from any of the training classes. In this paper, we propose a significantly more effective approach that converts the original problem to a pair-wise matching problem and then outputs how probable two instances belong to the same class. Under this approach, we present two models. The more effective model uses two embedding matrices of a pair of instances as two channels of a CNN. The output probabilities from such pairs are used to judge whether a test instance is from a seen class or is novel/unexpected. Experimental results show that the proposed method substantially outperforms the state-of-the-art baselines.

Machine learning can be used to make sense of healthcare data. Probabilistic machine learning models help provide a complete picture of observed data in healthcare. In this review, we examine how probabilistic machine learning can advance healthcare. We consider challenges in the predictive model building pipeline where probabilistic models can be beneficial including calibration and missing data. Beyond predictive models, we also investigate the utility of probabilistic machine learning models in phenotyping, in generative models for clinical use cases, and in reinforcement learning.