Challenging Forgets: Unveiling the Worst-Case Forget Sets in Machine Unlearning

The trustworthy machine learning (ML) community is increasingly recognizing the crucial need for models capable of selectively 'unlearning' data points after training. This leads to the problem of machine unlearning (MU), aiming to eliminate the influence of chosen data points on model performance, while still maintaining the model's utility post-unlearning. Despite various MU methods for data influence erasure, evaluations have largely focused on random data forgetting, ignoring the vital inquiry into which subset should be chosen to truly gauge the authenticity of unlearning performance. To tackle this issue, we introduce a new evaluative angle for MU from an adversarial viewpoint. We propose identifying the data subset that presents the most significant challenge for influence erasure, i.e., pinpointing the worst-case forget set. Utilizing a bi-level optimization principle, we amplify unlearning challenges at the upper optimization level to emulate worst-case scenarios, while simultaneously engaging in standard training and unlearning at the lower level, achieving a balance between data influence erasure and model utility. Our proposal offers a worst-case evaluation of MU's resilience and effectiveness. Through extensive experiments across different datasets (including CIFAR-10, 100, CelebA, Tiny ImageNet, and ImageNet) and models (including both image classifiers and generative models), we expose critical pros and cons in existing (approximate) unlearning strategies. Our results illuminate the complex challenges of MU in practice, guiding the future development of more accurate and robust unlearning algorithms. The code is available at https://github.com/OPTML-Group/Unlearn-WorstCase.

Gradient Coding through Iterative Block Leverage Score Sampling

We generalize the leverage score sampling sketch for $\ell_2$-subspace embeddings, to accommodate sampling subsets of the transformed data, so that the sketching approach is appropriate for distributed settings. This is then used to derive an approximate coded computing approach for first-order methods; known as gradient coding, to accelerate linear regression in the presence of failures in distributed computational networks, \textit{i.e.} stragglers. We replicate the data across the distributed network, to attain the approximation guarantees through the induced sampling distribution. The significance and main contribution of this work, is that it unifies randomized numerical linear algebra with approximate coded computing, while attaining an induced $\ell_2$-subspace embedding through uniform sampling. The transition to uniform sampling is done without applying a random projection, as in the case of the subsampled randomized Hadamard transform. Furthermore, by incorporating this technique to coded computing, our scheme is an iterative sketching approach to approximately solving linear regression. We also propose weighting when sketching takes place through sampling with replacement, for further compression.

Minimum-Risk Recalibration of Classifiers

Recalibrating probabilistic classifiers is vital for enhancing the reliability and accuracy of predictive models. Despite the development of numerous recalibration algorithms, there is still a lack of a comprehensive theory that integrates calibration and sharpness (which is essential for maintaining predictive power). In this paper, we introduce the concept of minimum-risk recalibration within the framework of mean-squared-error (MSE) decomposition, offering a principled approach for evaluating and recalibrating probabilistic classifiers. Using this framework, we analyze the uniform-mass binning (UMB) recalibration method and establish a finite-sample risk upper bound of order $\tilde{O}(B/n + 1/B^2)$ where $B$ is the number of bins and $n$ is the sample size. By balancing calibration and sharpness, we further determine that the optimal number of bins for UMB scales with $n^{1/3}$, resulting in a risk bound of approximately $O(n^{-2/3})$. Additionally, we tackle the challenge of label shift by proposing a two-stage approach that adjusts the recalibration function using limited labeled data from the target domain. Our results show that transferring a calibrated classifier requires significantly fewer target samples compared to recalibrating from scratch. We validate our theoretical findings through numerical simulations, which confirm the tightness of the proposed bounds, the optimal number of bins, and the effectiveness of label shift adaptation.

Robustness-preserving Lifelong Learning via Dataset Condensation

Lifelong learning (LL) aims to improve a predictive model as the data source evolves continuously. Most work in this learning paradigm has focused on resolving the problem of 'catastrophic forgetting,' which refers to a notorious dilemma between improving model accuracy over new data and retaining accuracy over previous data. Yet, it is also known that machine learning (ML) models can be vulnerable in the sense that tiny, adversarial input perturbations can deceive the models into producing erroneous predictions. This motivates the research objective of this paper - specification of a new LL framework that can salvage model robustness (against adversarial attacks) from catastrophic forgetting. Specifically, we propose a new memory-replay LL strategy that leverages modern bi-level optimization techniques to determine the 'coreset' of the current data (i.e., a small amount of data to be memorized) for ease of preserving adversarial robustness over time. We term the resulting LL framework 'Data-Efficient Robustness-Preserving LL' (DERPLL). The effectiveness of DERPLL is evaluated for class-incremental image classification using ResNet-18 over the CIFAR-10 dataset. Experimental results show that DERPLL outperforms the conventional coreset-guided LL baseline and achieves a substantial improvement in both standard accuracy and robust accuracy.

Incorporating Polar Field Data for Improved Solar Flare Prediction

In this paper, we consider incorporating data associated with the sun's north and south polar field strengths to improve solar flare prediction performance using machine learning models. When used to supplement local data from active regions on the photospheric magnetic field of the sun, the polar field data provides global information to the predictor. While such global features have been previously proposed for predicting the next solar cycle's intensity, in this paper we propose using them to help classify individual solar flares. We conduct experiments using HMI data employing four different machine learning algorithms that can exploit polar field information. Additionally, we propose a novel probabilistic mixture of experts model that can simply and effectively incorporate polar field data and provide on-par prediction performance with state-of-the-art solar flare prediction algorithms such as the Recurrent Neural Network (RNN). Our experimental results indicate the usefulness of the polar field data for solar flare prediction, which can improve Heidke Skill Score (HSS2) by as much as 10.1%.

A Graphical Model for Fusing Diverse Microbiome Data

This paper develops a Bayesian graphical model for fusing disparate types of count data. The motivating application is the study of bacterial communities from diverse high dimensional features, in this case transcripts, collected from different treatments. In such datasets, there are no explicit correspondences between the communities and each correspond to different factors, making data fusion challenging. We introduce a flexible multinomial-Gaussian generative model for jointly modeling such count data. This latent variable model jointly characterizes the observed data through a common multivariate Gaussian latent space that parameterizes the set of multinomial probabilities of the transcriptome counts. The covariance matrix of the latent variables induces a covariance matrix of co-dependencies between all the transcripts, effectively fusing multiple data sources. We present a computationally scalable variational Expectation-Maximization (EM) algorithm for inferring the latent variables and the parameters of the model. The inferred latent variables provide a common dimensionality reduction for visualizing the data and the inferred parameters provide a predictive posterior distribution. In addition to simulation studies that demonstrate the variational EM procedure, we apply our model to a bacterial microbiome dataset.

Resolution Limits of Non-Adaptive 20 Questions Search for a Moving Target

Using the 20 questions estimation framework with query-dependent noise, we study non-adaptive search strategies for a moving target over the unit cube with unknown initial location and velocities under a piecewise constant velocity model. In this search problem, there is an oracle who knows the instantaneous location of the target at any time. Our task is to query the oracle as few times as possible to accurately estimate the location of the target at any specified time. We first study the case where the oracle's answer to each query is corrupted by discrete noise and then generalize our results to the case of additive white Gaussian noise. In our formulation, the performance criterion is the resolution, which is defined as the maximal $L_\infty$ distance between the true locations and estimated locations. We characterize the minimal resolution of an optimal non-adaptive query procedure with a finite number of queries by deriving non-asymptotic and asymptotic bounds. Our bounds are tight in the first-order asymptotic sense when the number of queries satisfies a certain condition and our bounds are tight in the stronger second-order asymptotic sense when the target moves with a constant velocity. To prove our results, we relate the current problem to channel coding, borrow ideas from finite blocklength information theory and construct bounds on the number of possible quantized target trajectories.

Predicting Solar Flares Using CNN and LSTM on Two Solar Cycles of Active Region Data

We consider the flare prediction problem that distinguishes flare-imminent active regions that produce an M- or X-class flare in the future 24 hours, from quiet active regions that do not produce any flare within $\pm 24$ hours. Using line-of-sight magnetograms and parameters of active regions in two data products covering Solar Cycle 23 and 24, we train and evaluate two deep learning algorithms -- CNN and LSTM -- and their stacking ensembles. The decisions of CNN are explained using visual attribution methods. We have the following three main findings. (1) LSTM trained on data from two solar cycles achieves significantly higher True Skill Scores (TSS) than that trained on data from a single solar cycle with a confidence level of at least 0.95. (2) On data from Solar Cycle 23, a stacking ensemble that combines predictions from LSTM and CNN using the TSS criterion achieves significantly higher TSS than the "select-best" strategy with a confidence level of at least 0.95. (3) A visual attribution method called Integrated Gradients is able to attribute the CNN's predictions of flares to the emerging magnetic flux in the active region. It also reveals a limitation of CNN as a flare prediction method using line-of-sight magnetograms: it treats the polarity artifact of line-of-sight magnetograms as positive evidence of flares.

Asymptotics for Outlier Hypothesis Testing

We revisit the outlier hypothesis testing framework of Li \emph{et al.} (TIT 2014) and derive fundamental limits for the optimal test. In outlier hypothesis testing, one is given multiple observed sequences, where most sequences are generated i.i.d. from a nominal distribution. The task is to discern the set of outlying sequences that are generated according to anomalous distributions. The nominal and anomalous distributions are \emph{unknown}. We consider the case of multiple outliers where the number of outliers is unknown and each outlier can follow a different anomalous distribution. Under this setting, we study the tradeoff among the probabilities of misclassification error, false alarm and false reject. Specifically, we propose a threshold-based test that ensures exponential decay of misclassification error and false alarm probabilities. We study two constraints on the false reject probability, with one constraint being that it is a non-vanishing constant and the other being that it has an exponential decay rate. For both cases, we characterize bounds on the false reject probability, as a function of the threshold, for each tuple of nominal and anomalous distributions. Finally, we demonstrate the asymptotic optimality of our test under the generalized Neyman-Pearson criterion.

Multiway Ensemble Kalman Filter

In this work, we study the emergence of sparsity and multiway structures in second-order statistical characterizations of dynamical processes governed by partial differential equations (PDEs). We consider several state-of-the-art multiway covariance and inverse covariance (precision) matrix estimators and examine their pros and cons in terms of accuracy and interpretability in the context of physics-driven forecasting when incorporated into the ensemble Kalman filter (EnKF). In particular, we show that multiway data generated from the Poisson and the convection-diffusion types of PDEs can be accurately tracked via EnKF when integrated with appropriate covariance and precision matrix estimators.