Universal Feature Selection for Simultaneous Interpretability of Multitask Datasets

Extracting meaningful features from complex, high-dimensional datasets across scientific domains remains challenging. Current methods often struggle with scalability, limiting their applicability to large datasets, or make restrictive assumptions about feature-property relationships, hindering their ability to capture complex interactions. BoUTS's general and scalable feature selection algorithm surpasses these limitations to identify both universal features relevant to all datasets and task-specific features predictive for specific subsets. Evaluated on seven diverse chemical regression datasets, BoUTS achieves state-of-the-art feature sparsity while maintaining prediction accuracy comparable to specialized methods. Notably, BoUTS's universal features enable domain-specific knowledge transfer between datasets, and suggest deep connections in seemingly-disparate chemical datasets. We expect these results to have important repercussions in manually-guided inverse problems. Beyond its current application, BoUTS holds immense potential for elucidating data-poor systems by leveraging information from similar data-rich systems. BoUTS represents a significant leap in cross-domain feature selection, potentially leading to advancements in various scientific fields.

Unified Binary and Multiclass Margin-Based Classification

The notion of margin loss has been central to the development and analysis of algorithms for binary classification. To date, however, there remains no consensus as to the analogue of the margin loss for multiclass classification. In this work, we show that a broad range of multiclass loss functions, including many popular ones, can be expressed in the relative margin form, a generalization of the margin form of binary losses. The relative margin form is broadly useful for understanding and analyzing multiclass losses as shown by our prior work (Wang and Scott, 2020, 2021). To further demonstrate the utility of this way of expressing multiclass losses, we use it to extend the seminal result of Bartlett et al. (2006) on classification-calibration of binary margin losses to multiclass. We then analyze the class of Fenchel-Young losses, and expand the set of these losses that are known to be classification-calibrated.

Fusing Sparsity with Deep Learning for Rotating Scatter Mask Gamma Imaging

Many nuclear safety applications need fast, portable, and accurate imagers to better locate radiation sources. The Rotating Scatter Mask (RSM) system is an emerging device with the potential to meet these needs. The main challenge is the under-determined nature of the data acquisition process: the dimension of the measured signal is far less than the dimension of the image to be reconstructed. To address this challenge, this work aims to fuse model-based sparsity-promoting regularization and a data-driven deep neural network denoising image prior to perform image reconstruction. An efficient algorithm is developed and produces superior reconstructions relative to current approaches.

Mixture Proportion Estimation Beyond Irreducibility

The task of mixture proportion estimation (MPE) is to estimate the weight of a component distribution in a mixture, given observations from both the component and mixture. Previous work on MPE adopts the irreducibility assumption, which ensures identifiablity of the mixture proportion. In this paper, we propose a more general sufficient condition that accommodates several settings of interest where irreducibility does not hold. We further present a resampling-based meta-algorithm that takes any existing MPE algorithm designed to work under irreducibility and adapts it to work under our more general condition. Our approach empirically exhibits improved estimation performance relative to baseline methods and to a recently proposed regrouping-based algorithm.

Label Embedding by Johnson-Lindenstrauss Matrices

We present a simple and scalable framework for extreme multiclass classification based on Johnson-Lindenstrauss matrices (JLMs). Using the columns of a JLM to embed the labels, a $C$-class classification problem is transformed into a regression problem with $\cO(\log C)$ output dimension. We derive an excess risk bound, revealing a tradeoff between computational efficiency and prediction accuracy, and further show that under the Massart noise condition, the penalty for dimension reduction vanishes. Our approach is easily parallelizable, and experimental results demonstrate its effectiveness and scalability in large-scale applications.

Learning from Label Proportions by Learning with Label Noise

Learning from label proportions (LLP) is a weakly supervised classification problem where data points are grouped into bags, and the label proportions within each bag are observed instead of the instance-level labels. The task is to learn a classifier to predict the individual labels of future individual instances. Prior work on LLP for multi-class data has yet to develop a theoretically grounded algorithm. In this work, we provide a theoretically grounded approach to LLP based on a reduction to learning with label noise, using the forward correction (FC) loss of \citet{Patrini2017MakingDN}. We establish an excess risk bound and generalization error analysis for our approach, while also extending the theory of the FC loss which may be of independent interest. Our approach demonstrates improved empirical performance in deep learning scenarios across multiple datasets and architectures, compared to the leading existing methods.

Supervised PCA: A Multiobjective Approach

Methods for supervised principal component analysis (SPCA) aim to incorporate label information into principal component analysis (PCA), so that the extracted features are more useful for a prediction task of interest. Prior work on SPCA has focused primarily on optimizing prediction error, and has neglected the value of maximizing variance explained by the extracted features. We propose a new method for SPCA that addresses both of these objectives jointly, and demonstrate empirically that our approach dominates existing approaches, i.e., outperforms them with respect to both prediction error and variation explained. Our approach accommodates arbitrary supervised learning losses and, through a statistical reformulation, provides a novel low-rank extension of generalized linear models.

Consistent Estimation of Identifiable Nonparametric Mixture Models from Grouped Observations

Recent research has established sufficient conditions for finite mixture models to be identifiable from grouped observations. These conditions allow the mixture components to be nonparametric and have substantial (or even total) overlap. This work proposes an algorithm that consistently estimates any identifiable mixture model from grouped observations. Our analysis leverages an oracle inequality for weighted kernel density estimators of the distribution on groups, together with a general result showing that consistent estimation of the distribution on groups implies consistent estimation of mixture components. A practical implementation is provided for paired observations, and the approach is shown to outperform existing methods, especially when mixture components overlap significantly.

Learning from Label Proportions: A Mutual Contamination Framework

Learning from label proportions (LLP) is a weakly supervised setting for classification in which unlabeled training instances are grouped into bags, and each bag is annotated with the proportion of each class occurring in that bag. Prior work on LLP has yet to establish a consistent learning procedure, nor does there exist a theoretically justified, general purpose training criterion. In this work we address these two issues by posing LLP in terms of mutual contamination models (MCMs), which have recently been applied successfully to study various other weak supervision settings. In the process, we establish several novel technical results for MCMs, including unbiased losses and generalization error bounds under non-iid sampling plans. We also point out the limitations of a common experimental setting for LLP, and propose a new one based on our MCM framework.

Calibrated Surrogate Losses for Adversarially Robust Classification

Adversarially robust classification seeks a classifier that is insensitive to adversarial perturbations of test patterns. This problem is often formulated via a minimax objective, where the target loss is the worst-case value of the 0-1 loss subject to a bound on the size of perturbation. Recent work has proposed convex surrogates for the adversarial 0-1 loss, in an effort to make optimization more tractable. In this work, we consider the question of which surrogate losses are calibrated with respect to the adversarial 0-1 loss, meaning that minimization of the former implies minimization of the latter. We show that no convex surrogate loss is calibrated with respect to the adversarial 0-1 loss when restricted to the class of linear models. We further introduce a class of nonconvex losses and offer necessary and sufficient conditions for losses in this class to be calibrated.