arXiv subjects

Ibrahim Alabdulmohsin

Publications and source records attributed to Ibrahim Alabdulmohsin.

32 records · Page 2Linked to original sources

arXiv2022

Adapting to Latent Subgroup Shifts via Concepts and Proxies

We address the problem of unsupervised domain adaptation when the source domain differs from the target domain because of a shift in the distribution of a latent subgroup. When this subgroup confounds all observed data, neither covariate shift nor label shift assumptions apply. We show that the optimal target predictor can be non-parametrically identified with the help of concept and proxy variables available only in the source domain, and unlabeled data from the target. The identification results are constructive, immediately suggesting an algorithm for estimating the optimal predictor in the target. For continuous observations, when this algorithm becomes impractical, we propose a latent variable model specific to the data generation process at hand. We show how the approach degrades as the size of the shift changes, and verify that it outperforms both covariate and label shift adjustment.

stat.ML↗

arXiv2022

Layer-Stack Temperature Scaling

Recent works demonstrate that early layers in a neural network contain useful information for prediction. Inspired by this, we show that extending temperature scaling across all layers improves both calibration and accuracy. We call this procedure "layer-stack temperature scaling" (LATES). Informally, LATES grants each layer a weighted vote during inference. We evaluate it on five popular convolutional neural network architectures both in- and out-of-distribution and observe a consistent improvement over temperature scaling in terms of accuracy, calibration, and AUC. All conclusions are supported by comprehensive statistical analyses. Since LATES neither retrains the architecture nor introduces many more parameters, its advantages can be reaped without requiring additional data beyond what is used in temperature scaling. Finally, we show that combining LATES with Monte Carlo Dropout matches state-of-the-art results on CIFAR10/100.

cs.LG↗

arXiv2022

Fair Wrapping for Black-box Predictions

We introduce a new family of techniques to post-process ("wrap") a black-box classifier in order to reduce its bias. Our technique builds on the recent analysis of improper loss functions whose optimization can correct any twist in prediction, unfairness being treated as a twist. In the post-processing, we learn a wrapper function which we define as an $α$-tree, which modifies the prediction. We provide two generic boosting algorithms to learn $α$-trees. We show that our modification has appealing properties in terms of composition of $α$-trees, generalization, interpretability, and KL divergence between modified and original predictions. We exemplify the use of our technique in three fairness notions: conditional value-at-risk, equality of opportunity, and statistical parity; and provide experiments on several readily available datasets.

stat.ML↗

arXiv2022

Revisiting Neural Scaling Laws in Language and Vision

The remarkable progress in deep learning in recent years is largely driven by improvements in scale, where bigger models are trained on larger datasets for longer schedules. To predict the benefit of scale empirically, we argue for a more rigorous methodology based on the extrapolation loss, instead of reporting the best-fitting (interpolating) parameters. We then present a recipe for estimating scaling law parameters reliably from learning curves. We demonstrate that it extrapolates more accurately than previous methods in a wide range of architecture families across several domains, including image classification, neural machine translation (NMT) and language modeling, in addition to tasks from the BIG-Bench evaluation benchmark. Finally, we release a benchmark dataset comprising of 90 evaluation tasks to facilitate research in this domain.

cs.LG↗

arXiv2022

A Reduction to Binary Approach for Debiasing Multiclass Datasets

We propose a novel reduction-to-binary (R2B) approach that enforces demographic parity for multiclass classification with non-binary sensitive attributes via a reduction to a sequence of binary debiasing tasks. We prove that R2B satisfies optimality and bias guarantees and demonstrate empirically that it can lead to an improvement over two baselines: (1) treating multiclass problems as multi-label by debiasing labels independently and (2) transforming the features instead of the labels. Surprisingly, we also demonstrate that independent label debiasing yields competitive results in most (but not all) settings. We validate these conclusions on synthetic and real-world datasets from social science, computer vision, and healthcare.

cs.LG↗

arXiv2022

A Near-Optimal Algorithm for Debiasing Trained Machine Learning Models

We present a scalable post-processing algorithm for debiasing trained models, including deep neural networks (DNNs), which we prove to be near-optimal by bounding its excess Bayes risk. We empirically validate its advantages on standard benchmark datasets across both classical algorithms as well as modern DNN architectures and demonstrate that it outperforms previous post-processing methods while performing on par with in-processing. In addition, we show that the proposed algorithm is particularly effective for models trained at scale where post-processing is a natural and practical choice.

cs.LG↗

arXiv2021

The Impact of Reinitialization on Generalization in Convolutional Neural Networks

Recent results suggest that reinitializing a subset of the parameters of a neural network during training can improve generalization, particularly for small training sets. We study the impact of different reinitialization methods in several convolutional architectures across 12 benchmark image classification datasets, analyzing their potential gains and highlighting limitations. We also introduce a new layerwise reinitialization algorithm that outperforms previous methods and suggest explanations of the observed improved generalization. First, we show that layerwise reinitialization increases the margin on the training examples without increasing the norm of the weights, hence leading to an improvement in margin-based generalization bounds for neural networks. Second, we demonstrate that it settles in flatter local minima of the loss surface. Third, it encourages learning general rules and discourages memorization by placing emphasis on the lower layers of the neural network. Our takeaway message is that the accuracy of convolutional neural networks can be improved for small datasets using bottom-up layerwise reinitialization, where the number of reinitialized layers may vary depending on the available compute budget.

cs.LG↗

arXiv2021

A Generalized Lottery Ticket Hypothesis

We introduce a generalization to the lottery ticket hypothesis in which the notion of "sparsity" is relaxed by choosing an arbitrary basis in the space of parameters. We present evidence that the original results reported for the canonical basis continue to hold in this broader setting. We describe how structured pruning methods, including pruning units or factorizing fully-connected layers into products of low-rank matrices, can be cast as particular instances of this "generalized" lottery ticket hypothesis. The investigations reported here are preliminary and are provided to encourage further research along this direction.

cs.LG↗

arXiv2021

A Generalization of Classical Formulas in Numerical Integration and Series Convergence Acceleration

Summation formulas, such as the Euler-Maclaurin expansion or Gregory's quadrature, have found many applications in mathematics, ranging from accelerating series, to evaluating fractional sums and analyzing asymptotics, among others. We show that these summation formulas actually arise as particular instances of a single series expansion, including Euler's method for alternating series. This new summation formula gives rise to a family of polynomials, which contain both the Bernoulli and Gregory numbers in their coefficients. We prove some properties of those polynomials, such as recurrence identities and symmetries. Lastly, we present one case study, which illustrates one potential application of the new expansion for finite impulse response (FIR) filters.

math.NA↗

arXiv2020

What Do Neural Networks Learn When Trained With Random Labels?

We study deep neural networks (DNNs) trained on natural image data with entirely random labels. Despite its popularity in the literature, where it is often used to study memorization, generalization, and other phenomena, little is known about what DNNs learn in this setting. In this paper, we show analytically for convolutional and fully connected networks that an alignment between the principal components of network parameters and data takes place when training with random labels. We study this alignment effect by investigating neural networks pre-trained on randomly labelled image data and subsequently fine-tuned on disjoint datasets with random or real labels. We show how this alignment produces a positive transfer: networks pre-trained with random labels train faster downstream compared to training from scratch even after accounting for simple effects, such as weight scaling. We analyze how competing effects, such as specialization at later layers, may hide the positive transfer. These effects are studied in several network architectures, including VGG16 and ResNet18, on CIFAR10 and ImageNet.

stat.ML↗

arXiv2020

Fair Classification via Unconstrained Optimization

Achieving the Bayes optimal binary classification rule subject to group fairness constraints is known to be reducible, in some cases, to learning a group-wise thresholding rule over the Bayes regressor. In this paper, we extend this result by proving that, in a broader setting, the Bayes optimal fair learning rule remains a group-wise thresholding rule over the Bayes regressor but with a (possible) randomization at the thresholds. This provides a stronger justification to the post-processing approach in fair classification, in which (1) a predictor is learned first, after which (2) its output is adjusted to remove bias. We show how the post-processing rule in this two-stage approach can be learned quite efficiently by solving an unconstrained optimization problem. The proposed algorithm can be applied to any black-box machine learning model, such as deep neural networks, random forests and support vector machines. In addition, it can accommodate many fairness criteria that have been previously proposed in the literature, such as equalized odds and statistical parity. We prove that the algorithm is Bayes consistent and motivate it, furthermore, via an impossibility result that quantifies the tradeoff between accuracy and fairness across multiple demographic groups. Finally, we conclude by validating the algorithm on the Adult benchmark dataset.

cs.LG↗

arXiv2017

Fractional Parts and their Relations to the Values of the Riemann Zeta Function

A well-known result, due to Dirichlet and later generalized by de la Vallee-Poussin, expresses a relationship between the sum of fractional parts and the Euler-Mascheroni constant. In this paper, we prove an asymptotic relationship between the summation of the products of fractional parts with powers of integers on one hand, and the values of the Riemann zeta function, on the other hand. Dirichlet's classical result falls as a particular case of this more general theorem.

math.NT↗

arXiv2016

Uniform Generalization, Concentration, and Adaptive Learning

One fundamental goal in any learning algorithm is to mitigate its risk for overfitting. Mathematically, this requires that the learning algorithm enjoys a small generalization risk, which is defined either in expectation or in probability. Both types of generalization are commonly used in the literature. For instance, generalization in expectation has been used to analyze algorithms, such as ridge regression and SGD, whereas generalization in probability is used in the VC theory, among others. Recently, a third notion of generalization has been studied, called uniform generalization, which requires that the generalization risk vanishes uniformly in expectation across all bounded parametric losses. It has been shown that uniform generalization is, in fact, equivalent to an information-theoretic stability constraint, and that it recovers classical results in learning theory. It is achievable under various settings, such as sample compression schemes, finite hypothesis spaces, finite domains, and differential privacy. However, the relationship between uniform generalization and concentration remained unknown. In this paper, we answer this question by proving that, while a generalization in expectation does not imply a generalization in probability, a uniform generalization in expectation does imply concentration. We establish a chain rule for the uniform generalization risk of the composition of hypotheses and use it to derive a large deviation bound. Finally, we prove that the bound is tight.

cs.LG↗

arXiv2014

A Mathematical Theory of Learning

In this paper, a mathematical theory of learning is proposed that has many parallels with information theory. We consider Vapnik's General Setting of Learning in which the learning process is defined to be the act of selecting a hypothesis in response to a given training set. Such hypothesis can, for example, be a decision boundary in classification, a set of centroids in clustering, or a set of frequent item-sets in association rule mining. Depending on the hypothesis space and how the final hypothesis is selected, we show that a learning process can be assigned a numeric score, called learning capacity, which is analogous to Shannon's channel capacity and satisfies similar interesting properties as well such as the data-processing inequality and the information-cannot-hurt inequality. In addition, learning capacity provides the tightest possible bound on the difference between true risk and empirical risk of the learning process for all loss functions that are parametrized by the chosen hypothesis. It is also shown that the notion of learning capacity equivalently quantifies how sensitive the choice of the final hypothesis is to a small perturbation in the training set. Consequently, algorithmic stability is both necessary and sufficient for generalization. While the theory does not rely on concentration inequalities, we finally show that analogs to classical results in learning theory using the Probably Approximately Correct (PAC) model can be immediately deduced using this theory, and conclude with information-theoretic bounds to learning capacity.

cs.LG↗