This paper aims to provide understandings for the effect of an over-parameterized model, e.g. a deep neural network, memorizing instance-dependent noisy labels. We first quantify the harms caused by memorizing noisy instances, and show the disparate impacts of noisy labels for sample instances with different representation frequencies. We then analyze how several popular solutions for learning with noisy labels mitigate this harm at the instance level. Our analysis reveals that existing approaches lead to disparate treatments when handling noisy instances. While higher-frequency instances often enjoy a high probability of an improvement by applying these solutions, lower-frequency instances do not. Our analysis reveals new understandings for when these approaches work, and provides theoretical justifications for previously reported empirical observations. This observation requires us to rethink the distribution of label noise across instances and calls for different treatments for instances in different regimes.

Machine learning models trained with purely observational data and the principle of empirical risk minimization (Vapnik 1992) can fail to generalize to unseen domains. In this paper, we focus on the case where the problem arises through spurious correlation between the observed domains and the actual task labels. We find that many domain generalization methods do not explicitly take this spurious correlation into account. Instead, especially in more application-oriented research areas like medical imaging or robotics, data augmentation techniques that are based on heuristics are used to learn domain invariant features. To bridge the gap between theory and practice, we develop a causal perspective on the problem of domain generalization. We argue that causal concepts can be used to explain the success of data augmentation by describing how they can weaken the spurious correlation between the observed domains and the task labels. We demonstrate that data augmentation can serve as a tool for simulating interventional data. We use these theoretical insights to derive a simple algorithm that is able to select data augmentation techniques that will lead to better domain generalization.

Data subset selection from a large number of training instances has been a successful approach toward efficient and cost-effective machine learning. However, models trained on a smaller subset may show poor generalization ability. In this paper, our goal is to design an algorithm for selecting a subset of the training data, so that the model can be trained quickly, without significantly sacrificing on accuracy. More specifically, we focus on data subset selection for $L_2$ regularized regression problems and provide a novel problem formulation which seeks to minimize the training loss with respect to both the trainable parameters and the subset of training data, subject to error bounds on the validation set. We tackle this problem using several technical innovations. First, we represent this problem with simplified constraints using the dual of the original training problem and show that the objective of this new representation is a monotone and $\alpha$-submodular function, for a wide variety of modeling choices. Such properties lead us to develop SELCON, an efficient majorization-minimization algorithm for data subset selection, that admits an approximation guarantee even when the training provides an imperfect estimate of the trained model. Finally, our experiments on several datasets show that SELCON trades off accuracy and efficiency more effectively than the current state-of-the-art.

Democratization of machine learning requires architectures that automatically adapt to new problems. Neural Differential Equations (NDEs) have emerged as a popular modeling framework by removing the need for ML practitioners to choose the number of layers in a recurrent model. While we can control the computational cost by choosing the number of layers in standard architectures, in NDEs the number of neural network evaluations for a forward pass can depend on the number of steps of the adaptive ODE solver. But, can we force the NDE to learn the version with the least steps while not increasing the training cost? Current strategies to overcome slow prediction require high order automatic differentiation, leading to significantly higher training time. We describe a novel regularization method that uses the internal cost heuristics of adaptive differential equation solvers combined with discrete adjoint sensitivities to guide the training process towards learning NDEs that are easier to solve. This approach opens up the blackbox numerical analysis behind the differential equation solver's algorithm and directly uses its local error estimates and stiffness heuristics as cheap and accurate cost estimates. We incorporate our method without any change in the underlying NDE framework and show that our method extends beyond Ordinary Differential Equations to accommodate Neural Stochastic Differential Equations. We demonstrate how our approach can halve the prediction time and, unlike other methods which can increase the training time by an order of magnitude, we demonstrate similar reduction in training times. Together this showcases how the knowledge embedded within state-of-the-art equation solvers can be used to enhance machine learning.

There has been much interest in recent years in developing learning algorithms that can learn accurate classifiers from data with noisy labels. A widely-studied noise model is that of \emph{class-conditional noise} (CCN), wherein a label $y$ is flipped to a label $\tilde{y}$ with some associated noise probability that depends on both $y$ and $\tilde{y}$. In the multiclass setting, all previously proposed algorithms under the CCN model involve changing the training process, by introducing a `noise-correction' to the surrogate loss to be minimized over the noisy training examples. In this paper, we show that this is really unnecessary: one can simply perform class probability estimation (CPE) on the noisy examples, e.g.\ using a standard (multiclass) logistic regression algorithm, and then apply noise-correction only in the final prediction step. This means that the training algorithm itself does not need any change, and one can simply use standard off-the-shelf implementations with no modification to the code for training. Our approach can handle general multiclass loss matrices, including the usual 0-1 loss but also other losses such as those used for ordinal regression problems. We also provide a quantitative regret transfer bound, which bounds the target regret on the true distribution in terms of the CPE regret on the noisy distribution; in doing so, we extend the notion of strong properness introduced for binary losses by Agarwal (2014) to the multiclass case. Our bound suggests that the sample complexity of learning under CCN increases as the noise matrix approaches singularity. We also provide fixes and potential improvements for noise estimation methods that involve computing anchor points. Our experiments confirm our theoretical findings.

The performance of modern algorithms on certain computer vision tasks such as object recognition is now close to that of humans. This success was achieved at the price of complicated architectures depending on millions of parameters and it has become quite challenging to understand how particular predictions are made. Interpretability methods propose to give us this understanding. In this paper, we study LIME, perhaps one of the most popular. On the theoretical side, we show that when the number of generated examples is large, LIME explanations are concentrated around a limit explanation for which we give an explicit expression. We further this study for elementary shape detectors and linear models. As a consequence of this analysis, we uncover a connection between LIME and integrated gradients, another explanation method. More precisely, the LIME explanations are similar to the sum of integrated gradients over the superpixels used in the preprocessing step of LIME.

It is well-known that, for separable data, the regularised two-class logistic regression or support vector machine re-normalised estimate converges to the maximal margin classifier as the regularisation hyper-parameter $\lambda$ goes to 0. The fact that different loss functions may lead to the same solution is of theoretical and practical relevance as margin maximisation allows more straightforward considerations in terms of generalisation and geometric interpretation. We investigate the case where this convergence property is not guaranteed to hold and show that it can be fully characterised by the distribution of error terms in the latent variable interpretation of linear classifiers. In particular, if errors follow a regularly varying distribution, then the regularised and re-normalised estimate does not converge to the maximal margin classifier. This shows that classification with fat tails has a qualitatively different behaviour, which should be taken into account when considering real-life data.