Jungeum Kim

Jungeum Kim, Xiao Wang

The idea of robustness is central and critical to modern statistical analysis. However, despite the recent advances of deep neural networks (DNNs), many studies have shown that DNNs are vulnerable to adversarial attacks. Making imperceptible changes to an image can cause DNN models to make the wrong classification with high confidence, such as classifying a benign mole as a malignant tumor and a stop sign as a speed limit sign. The trade-off between robustness and standard accuracy is common for DNN models. In this paper, we introduce sensible adversarial learning and demonstrate the synergistic effect between pursuits of standard natural accuracy and robustness. Specifically, we define a sensible adversary which is useful for learning a robust model while keeping high natural accuracy. We theoretically establish that the Bayes classifier is the most robust multi-class classifier with the 0-1 loss under sensible adversarial learning. We propose a novel and efficient algorithm that trains a robust model using implicit loss truncation. We apply sensible adversarial learning for large-scale image classification to a handwritten digital image dataset called MNIST and an object recognition colored image dataset called CIFAR10. We have performed an extensive comparative study to compare our method with other competitive methods. Our experiments empirically demonstrate that our method is not sensitive to its hyperparameter and does not collapse even with a small model capacity while promoting robustness against various attacks and keeping high natural accuracy.

Brandon R. Feng, Brian J. Reich, Daniel Beaglehole et al.

The recent developments of complex deep learning models have led to unprecedented ability to accurately predict across multiple data representation types. Conformal prediction for uncertainty quantification of these models has risen in popularity, providing adaptive, statistically-valid prediction sets. For classification tasks, conformal methods have typically focused on utilizing logit scores. For pre-trained models, however, this can result in inefficient, overly conservative set sizes when not calibrated towards the target task. We propose DANCE, a doubly locally adaptive nearest-neighbor based conformal algorithm combining two novel nonconformity scores directly using the data's embedded representation. DANCE first fits a task-adaptive kernel regression model from the embedding layer before using the learned kernel space to produce the final prediction sets for uncertainty quantification. We test against state-of-the-art local, task-adapted and zero-shot conformal baselines, demonstrating DANCE's superior blend of set size efficiency and robustness across various datasets.

Jungeum Kim, Sean O'Hagan, Veronika Rockova

This work is concerned with conformal prediction in contemporary applications (including generative AI) where a black-box model has been trained on data that are not accessible to the user. Mirroring split-conformal inference, we design a wrapper around a black-box algorithm which calibrates conformity scores. This calibration is local and proceeds in two stages by first adaptively partitioning the predictor space into groups and then calibrating sectionally group by group. Adaptive partitioning (self-grouping) is achieved by fitting a robust regression tree to the conformity scores on the calibration set. This new tree variant is designed in such a way that adding a single new observation does not change the tree fit with overwhelmingly large probability. This add-one-in robustness property allows us to conclude a finite sample group-conditional coverage guarantee, a refinement of the marginal guarantee. In addition, unlike traditional split-conformal inference, adaptive splitting and within-group calibration yields adaptive bands which can stretch and shrink locally. We demonstrate benefits of local tightening on several simulated as well as real examples using non-parametric regression. Finally, we consider two contemporary classification applications for obtaining uncertainty quantification around GPT-4o predictions. We conformalize skin disease diagnoses based on self-reported symptoms as well as predicted states of U.S. legislators based on summaries of their ideology. We demonstrate substantial local tightening of the uncertainty sets while attaining similar marginal coverage.

Sean O'Hagan, Jungeum Kim, Veronika Rockova

In generative models with obscured likelihood, Approximate Bayesian Computation (ABC) is often the tool of last resort for inference. However, ABC demands many prior parameter trials to keep only a small fraction that passes an acceptance test. To accelerate ABC rejection sampling, this paper develops a self-aware framework that learns from past trials and errors. We apply recursive partitioning classifiers on the ABC lookup table to sequentially refine high-likelihood regions into boxes. Each box is regarded as an arm in a binary bandit problem treating ABC acceptance as a reward. Each arm has a proclivity for being chosen for the next ABC evaluation, depending on the prior distribution and past rejections. The method places more splits in those areas where the likelihood resides, shying away from low-probability regions destined for ABC rejections. We provide two versions: (1) ABC-Tree for posterior sampling, and (2) ABC-MAP for maximum a posteriori estimation. We demonstrate accurate ABC approximability at much lower simulation cost. We justify the use of our tree-based bandit algorithms with nearly optimal regret bounds. Finally, we successfully apply our approach to the problem of masked image classification using deep generative models.

Jungeum Kim, Xiao Wang

Nonlinear dimensional reduction with the manifold assumption, often called manifold learning, has proven its usefulness in a wide range of high-dimensional data analysis. The significant impact of t-SNE and UMAP has catalyzed intense research interest, seeking further innovations toward visualizing not only the local but also the global structure information of the data. Moreover, there have been consistent efforts toward generalizable dimensional reduction that handles unseen data. In this paper, we first propose GLoMAP, a novel manifold learning method for dimensional reduction and high-dimensional data visualization. GLoMAP preserves locally and globally meaningful distance estimates and displays a progression from global to local formation during the course of optimization. Furthermore, we extend GLoMAP to its inductive version, iGLoMAP, which utilizes a deep neural network to map data to its lower-dimensional representation. This allows iGLoMAP to provide lower-dimensional embeddings for unseen points without needing to re-train the algorithm. iGLoMAP is also well-suited for mini-batch learning, enabling large-scale, accelerated gradient calculations. We have successfully applied both GLoMAP and iGLoMAP to the simulated and real-data settings, with competitive experiments against the state-of-the-art methods.