arXiv subjects

Wooseok Ha

Publications and source records attributed to Wooseok Ha.

14 recordsLinked to original sources

arXiv2026

Distributionally Robust Classification for Multi-source Unsupervised Domain Adaptation

Unsupervised domain adaptation (UDA) is a statistical learning problem when the distribution of training (source) data is different from that of test (target) data. In this setting, one has access to labeled data only from the source domain and unlabeled data from the target domain. The central objective is to leverage the source data and the unlabeled target data to build models that generalize to the target domain. Despite its potential, existing UDA approaches often struggle in practice, particularly in scenarios where the target domain offers only limited unlabeled data or spurious correlations dominate the source domain. To address these challenges, we propose a novel distributionally robust learning framework that models uncertainty in both the covariate distribution and the conditional label distribution. Our approach is motivated by the multi-source domain adaptation setting but is also directly applicable to the single-source scenario, making it versatile in practice. We develop an efficient learning algorithm that can be seamlessly integrated with existing UDA methods. Extensive experiments under various distribution shift scenarios show that our method consistently outperforms strong baselines, especially when target data are extremely scarce.

cs.LG↗

arXiv2025

When few labeled target data suffice: a theory of semi-supervised domain adaptation via fine-tuning from multiple adaptive starts

Semi-supervised domain adaptation (SSDA) seeks to achieve accurate predictions in a target domain with limited labeled target data by exploiting abundant source and unlabeled target data. We study this problem under structural causal models (SCMs), which provide a statistical framework to describe distribution shifts between source and target domains as interventions in the data-generating process rather than ad hoc changes in model parameters. The central phenomenon is that, under low-dimensional interventions, source and unlabeled target data can help identify the high-dimensional shared structure, leaving only a low-dimensional target-specific correction to be learned from limited labeled target data. We formalize this principle for three canonical intervention models and propose the corresponding SSDA methods FT-DIP, FT-OLS-Src and FT-CIP. Under each intervention model, we demonstrate how extending an unsupervised domain adaptation (UDA) method to SSDA can achieve minimax-optimal target performance with limited target labels, with the labeled-target sample complexity scaling with the intervention dimension rather than the ambient dimension. When the distribution shift is underspecified, we propose the Multi-Adaptive-Start Fine-Tuning (MASFT) algorithm, which fine-tunes from multiple adaptive starts and selects among them using a small target validation set, incurring only logarithmic overhead in the number of starts. We validate the effectiveness of our proposed methods through simulated and real data experiments.

stat.ML↗

arXiv2024

Variance-reduced Zeroth-Order Methods for Fine-Tuning Language Models

Fine-tuning language models (LMs) has demonstrated success in a wide array of downstream tasks. However, as LMs are scaled up, the memory requirements for backpropagation become prohibitively high. Zeroth-order (ZO) optimization methods can leverage memory-efficient forward passes to estimate gradients. More recently, MeZO, an adaptation of ZO-SGD, has been shown to consistently outperform zero-shot and in-context learning when combined with suitable task prompts. In this work, we couple ZO methods with variance reduction techniques to enhance stability and convergence for inference-based LM fine-tuning. We introduce Memory-Efficient Zeroth-Order Stochastic Variance-Reduced Gradient (MeZO-SVRG) and demonstrate its efficacy across multiple LM fine-tuning tasks, eliminating the reliance on task-specific prompts. Evaluated across a range of both masked and autoregressive LMs on benchmark GLUE tasks, MeZO-SVRG outperforms MeZO with up to 20% increase in test accuracies in both full- and partial-parameter fine-tuning settings. MeZO-SVRG benefits from reduced computation time as it often surpasses MeZO's peak test accuracy with a $2\times$ reduction in GPU-hours. MeZO-SVRG significantly reduces the required memory footprint compared to first-order SGD, i.e. by $2\times$ for autoregressive models. Our experiments highlight that MeZO-SVRG's memory savings progressively improve compared to SGD with larger batch sizes.

cs.LG↗

arXiv2023

Prominent Roles of Conditionally Invariant Components in Domain Adaptation: Theory and Algorithms

Domain adaptation (DA) is a statistical learning problem that arises when the distribution of the source data used to train a model differs from that of the target data used to evaluate the model. While many DA algorithms have demonstrated considerable empirical success, blindly applying these algorithms can often lead to worse performance on new datasets. To address this, it is crucial to clarify the assumptions under which a DA algorithm has good target performance. In this work, we focus on the assumption of the presence of conditionally invariant components (CICs), which are relevant for prediction and remain conditionally invariant across the source and target data. We demonstrate that CICs, which can be estimated through conditional invariant penalty (CIP), play three prominent roles in providing target risk guarantees in DA. First, we propose a new algorithm based on CICs, importance-weighted conditional invariant penalty (IW-CIP), which has target risk guarantees beyond simple settings such as covariate shift and label shift. Second, we show that CICs help identify large discrepancies between source and target risks of other DA algorithms. Finally, we demonstrate that incorporating CICs into the domain invariant projection (DIP) algorithm can address its failure scenario caused by label-flipping features. We support our new algorithms and theoretical findings via numerical experiments on synthetic data, MNIST, CelebA, Camelyon17, and DomainNet datasets.

stat.ML↗

arXiv2023

The Effect of SGD Batch Size on Autoencoder Learning: Sparsity, Sharpness, and Feature Learning

In this work, we investigate the dynamics of stochastic gradient descent (SGD) when training a single-neuron autoencoder with linear or ReLU activation on orthogonal data. We show that for this non-convex problem, randomly initialized SGD with a constant step size successfully finds a global minimum for any batch size choice. However, the particular global minimum found depends upon the batch size. In the full-batch setting, we show that the solution is dense (i.e., not sparse) and is highly aligned with its initialized direction, showing that relatively little feature learning occurs. On the other hand, for any batch size strictly smaller than the number of samples, SGD finds a global minimum which is sparse and nearly orthogonal to its initialization, showing that the randomness of stochastic gradients induces a qualitatively different type of "feature selection" in this setting. Moreover, if we measure the sharpness of the minimum by the trace of the Hessian, the minima found with full batch gradient descent are flatter than those found with strictly smaller batch sizes, in contrast to previous works which suggest that large batches lead to sharper minima. To prove convergence of SGD with a constant step size, we introduce a powerful tool from the theory of non-homogeneous random walks which may be of independent interest.

stat.ML↗

arXiv2021

Adaptive wavelet distillation from neural networks through interpretations

Recent deep-learning models have achieved impressive prediction performance, but often sacrifice interpretability and computational efficiency. Interpretability is crucial in many disciplines, such as science and medicine, where models must be carefully vetted or where interpretation is the goal itself. Moreover, interpretable models are concise and often yield computational efficiency. Here, we propose adaptive wavelet distillation (AWD), a method which aims to distill information from a trained neural network into a wavelet transform. Specifically, AWD penalizes feature attributions of a neural network in the wavelet domain to learn an effective multi-resolution wavelet transform. The resulting model is highly predictive, concise, computationally efficient, and has properties (such as a multi-scale structure) which make it easy to interpret. In close collaboration with domain experts, we showcase how AWD addresses challenges in two real-world settings: cosmological parameter inference and molecular-partner prediction. In both cases, AWD yields a scientifically interpretable and concise model which gives predictive performance better than state-of-the-art neural networks. Moreover, AWD identifies predictive features that are scientifically meaningful in the context of respective domains. All code and models are released in a full-fledged package available on Github (https://github.com/Yu-Group/adaptive-wavelets).

stat.ML↗

arXiv2021

Interpreting and improving deep-learning models with reality checks

Recent deep-learning models have achieved impressive predictive performance by learning complex functions of many variables, often at the cost of interpretability. This chapter covers recent work aiming to interpret models by attributing importance to features and feature groups for a single prediction. Importantly, the proposed attributions assign importance to interactions between features, in addition to features in isolation. These attributions are shown to yield insights across real-world domains, including bio-imaging, cosmology image and natural-language processing. We then show how these attributions can be used to directly improve the generalization of a neural network or to distill it into a simple model. Throughout the chapter, we emphasize the use of reality checks to scrutinize the proposed interpretation techniques.

stat.ML↗

arXiv2021

Transformation Importance with Applications to Cosmology

Machine learning lies at the heart of new possibilities for scientific discovery, knowledge generation, and artificial intelligence. Its potential benefits to these fields requires going beyond predictive accuracy and focusing on interpretability. In particular, many scientific problems require interpretations in a domain-specific interpretable feature space (e.g. the frequency domain) whereas attributions to the raw features (e.g. the pixel space) may be unintelligible or even misleading. To address this challenge, we propose TRIM (TRansformation IMportance), a novel approach which attributes importances to features in a transformed space and can be applied post-hoc to a fully trained model. TRIM is motivated by a cosmological parameter estimation problem using deep neural networks (DNNs) on simulated data, but it is generally applicable across domains/models and can be combined with any local interpretation method. In our cosmology example, combining TRIM with contextual decomposition shows promising results for identifying which frequencies a DNN uses, helping cosmologists to understand and validate that the model learns appropriate physical features rather than simulation artifacts.

stat.ML↗

arXiv2020

An equivalence between critical points for rank constraints versus low-rank factorizations

Two common approaches in low-rank optimization problems are either working directly with a rank constraint on the matrix variable, or optimizing over a low-rank factorization so that the rank constraint is implicitly ensured. In this paper, we study the natural connection between the rank-constrained and factorized approaches. We show that all second-order stationary points of the factorized objective function correspond to fixed points of projected gradient descent run on the original problem (where the projection step enforces the rank constraint). This result allows us to unify many existing optimization guarantees that have been proved specifically in either the rank-constrained or the factorized setting, and leads to new results for certain settings of the problem. We demonstrate application of our results to several concrete low-rank optimization problems arising in matrix inverse problems.

math.OC↗

arXiv2020

Statistical guarantees for local graph clustering

Local graph clustering methods aim to find small clusters in very large graphs. These methods take as input a graph and a seed node, and they return as output a good cluster in a running time that depends on the size of the output cluster but that is independent of the size of the input graph. In this paper, we adopt a statistical perspective on local graph clustering, and we analyze the performance of the l1-regularized PageRank method~(Fountoulakis et. al.) for the recovery of a single target cluster, given a seed node inside the cluster. Assuming the target cluster has been generated by a random model, we present two results. In the first, we show that the optimal support of l1-regularized PageRank recovers the full target cluster, with bounded false positives. In the second, we show that if the seed node is connected solely to the target cluster then the optimal support of l1-regularized PageRank recovers exactly the target cluster. We also show empirically that l1-regularized PageRank has a state-of-the-art performance on many real graphs, demonstrating the superiority of the method. From a computational perspective, we show that the solution path of l1-regularized PageRank is monotonic. This allows for the application of the forward stagewise algorithm, which approximates the solution path in running time that does not depend on the size of the whole graph. Finally, we show that l1-regularized PageRank and approximate personalized PageRank (APPR), another very popular method for local graph clustering, are equivalent in the sense that we can lower and upper bound the output of one with the output of the other. Based on this relation, we establish for APPR similar results to those we establish for l1-regularized PageRank.

cs.LG↗

arXiv2019

Alternating minimization and alternating descent over nonconvex sets

We analyze the performance of alternating minimization for loss functions optimized over two variables, where each variable may be restricted to lie in some potentially nonconvex constraint set. This type of setting arises naturally in high-dimensional statistics and signal processing, where the variables often reflect different structures or components within the signals being considered. Our analysis relies on the notion of local concavity coefficients, which has been proposed in Barber and Ha to measure and quantify the concavity of a general nonconvex set. Our results further reveal important distinctions between alternating and non-alternating methods. Since computing the alternating minimization steps may not be tractable for some problems, we also consider an inexact version of the algorithm and provide a set of sufficient conditions to ensure fast convergence of the inexact algorithms. We demonstrate our framework on several examples, including low rank + sparse decomposition and multitask regression, and provide numerical experiments to validate our theoretical results.

math.OC↗

arXiv2018

Estimating the spectrum in computed tomography via Kullback-Leibler divergence constrained optimization

We study the problem of spectrum estimation from transmission data of a known phantom. The goal is to reconstruct an x-ray spectrum that can accurately model the x-ray transmission curves and reflects a realistic shape of the typical energy spectra of the CT system. To this end, spectrum estimation is posed as an optimization problem with x-ray spectrum as unknown variables, and a Kullback-Leibler (KL) divergence constraint is employed to incorporate prior knowledge of the spectrum and enhance numerical stability of the estimation process. The formulated constrained optimization problem is convex and can be solved efficiently by use of the exponentiated-gradient (EG) algorithm. We demonstrate the effectiveness of the proposed approach on the simulated and experimental data. The comparison to the expectation-maximization (EM) method is also discussed. In simulations, the proposed algorithm is seen to yield x-ray spectra that closely match the ground truth and represent the attenuation process of x-ray photons in materials, both included and not included in the estimation process. In experiments, the calculated transmission curve is in good agreement with the measured transmission curve, and the estimated spectra exhibits physically realistic looking shapes. The results further show the comparable performance between the proposed optimization-based approach and EM. In conclusion, our formulation of a constrained optimization provides an interpretable and flexible framework for spectrum estimation. Moreover, a KL-divergence constraint can include a prior spectrum and appears to capture important features of x-ray spectrum, allowing accurate and robust estimation of x-ray spectrum in CT imaging.

physics.med-ph↗

arXiv2017

Gradient descent with nonconvex constraints: local concavity determines convergence

Many problems in high-dimensional statistics and optimization involve minimization over nonconvex constraints-for instance, a rank constraint for a matrix estimation problem-but little is known about the theoretical properties of such optimization problems for a general nonconvex constraint set. In this paper we study the interplay between the geometric properties of the constraint set and the convergence behavior of gradient descent for minimization over this set. We develop the notion of local concavity coefficients of the constraint set, measuring the extent to which convexity is violated, which govern the behavior of projected gradient descent over this set. We demonstrate the versatility of these concavity coefficients by computing them for a range of problems in low-rank estimation, sparse estimation, and other examples. Through our understanding of the role of these geometric properties in optimization, we then provide a convergence analysis when projections are calculated only approximately, leading to a more efficient method for projected gradient descent in low-rank estimation problems.

math.OC↗

arXiv2016

Trimmed Conformal Prediction for High-Dimensional Models

In regression, conformal prediction is a general methodology to construct prediction intervals in a distribution-free manner. Although conformal prediction guarantees strong statistical property for predictive inference, its inherent computational challenge has attracted the attention of researchers in the community. In this paper, we propose a new framework, called Trimmed Conformal Prediction (TCP), based on two stage procedure, a trimming step and a prediction step. The idea is to use a preliminary trimming step to substantially reduce the range of possible values for the prediction interval, and then applying conformal prediction becomes far more efficient. As is the case of conformal prediction, TCP can be applied to any regression method, and further offers both statistical accuracy and computational gains. For a specific example, we also show how TCP can be implemented in the sparse regression setting. The experiments on both synthetic and real data validate the empirical performance of TCP.

math.ST↗