arXiv subjects

Weijie J. Su

Publications and source records attributed to Weijie J. Su.

At least 55 records · Page 3Linked to original sources

arXiv2023

DP-HyPO: An Adaptive Private Hyperparameter Optimization Framework

Hyperparameter optimization, also known as hyperparameter tuning, is a widely recognized technique for improving model performance. Regrettably, when training private ML models, many practitioners often overlook the privacy risks associated with hyperparameter optimization, which could potentially expose sensitive information about the underlying dataset. Currently, the sole existing approach to allow privacy-preserving hyperparameter optimization is to uniformly and randomly select hyperparameters for a number of runs, subsequently reporting the best-performing hyperparameter. In contrast, in non-private settings, practitioners commonly utilize ``adaptive'' hyperparameter optimization methods such as Gaussian process-based optimization, which select the next candidate based on information gathered from previous outputs. This substantial contrast between private and non-private hyperparameter optimization underscores a critical concern. In our paper, we introduce DP-HyPO, a pioneering framework for ``adaptive'' private hyperparameter optimization, aiming to bridge the gap between private and non-private hyperparameter optimization. To accomplish this, we provide a comprehensive differential privacy analysis of our framework. Furthermore, we empirically demonstrate the effectiveness of DP-HyPO on a diverse set of real-world datasets.

cs.LG↗

arXiv2023

Unified Enhancement of Privacy Bounds for Mixture Mechanisms via $f$-Differential Privacy

Differentially private (DP) machine learning algorithms incur many sources of randomness, such as random initialization, random batch subsampling, and shuffling. However, such randomness is difficult to take into account when proving differential privacy bounds because it induces mixture distributions for the algorithm's output that are difficult to analyze. This paper focuses on improving privacy bounds for shuffling models and one-iteration differentially private gradient descent (DP-GD) with random initializations using $f$-DP. We derive a closed-form expression of the trade-off function for shuffling models that outperforms the most up-to-date results based on $(ε,δ)$-DP. Moreover, we investigate the effects of random initialization on the privacy of one-iteration DP-GD. Our numerical computations of the trade-off function indicate that random initialization can enhance the privacy of DP-GD. Our analysis of $f$-DP guarantees for these mixture mechanisms relies on an inequality for trade-off functions introduced in this paper. This inequality implies the joint convexity of $F$-divergences. Finally, we study an $f$-DP analog of the advanced joint convexity of the hockey-stick divergence related to $(ε,δ)$-DP and apply it to analyze the privacy of mixture mechanisms.

stat.ML↗

arXiv2023

A Law of Data Separation in Deep Learning

While deep learning has enabled significant advances in many areas of science, its black-box nature hinders architecture design for future artificial intelligence applications and interpretation for high-stakes decision makings. We addressed this issue by studying the fundamental question of how deep neural networks process data in the intermediate layers. Our finding is a simple and quantitative law that governs how deep neural networks separate data according to class membership throughout all layers for classification. This law shows that each layer improves data separation at a constant geometric rate, and its emergence is observed in a collection of network architectures and datasets during training. This law offers practical guidelines for designing architectures, improving model robustness and out-of-sample performance, as well as interpreting the predictions.

cs.LG↗

arXiv2023

What Should Data Science Education Do with Large Language Models?

The rapid advances of large language models (LLMs), such as ChatGPT, are revolutionizing data science and statistics. These state-of-the-art tools can streamline complex processes. As a result, it reshapes the role of data scientists. We argue that LLMs are transforming the responsibilities of data scientists, shifting their focus from hands-on coding, data-wrangling and conducting standard analyses to assessing and managing analyses performed by these automated AIs. This evolution of roles is reminiscent of the transition from a software engineer to a product manager. We illustrate this transition with concrete data science case studies using LLMs in this paper. These developments necessitate a meaningful evolution in data science education. Pedagogy must now place greater emphasis on cultivating diverse skillsets among students, such as LLM-informed creativity, critical thinking, AI-guided programming. LLMs can also play a significant role in the classroom as interactive teaching and learning tools, contributing to personalized education. This paper discusses the opportunities, resources and open challenges for each of these directions. As with any transformative technology, integrating LLMs into education calls for careful consideration. While LLMs can perform repetitive tasks efficiently, it's crucial to remember that their role is to supplement human intelligence and creativity, not to replace it. Therefore, the new era of data science education should balance the benefits of LLMs while fostering complementary human expertise and innovations. In conclusion, the rise of LLMs heralds a transformative period for data science and its education. This paper seeks to shed light on the emerging trends, potential opportunities, and challenges accompanying this paradigm shift, hoping to spark further discourse and investigation into this exciting, uncharted territory.

cs.CY↗

arXiv2023

The Implicit Regularization of Dynamical Stability in Stochastic Gradient Descent

In this paper, we study the implicit regularization of stochastic gradient descent (SGD) through the lens of {\em dynamical stability} (Wu et al., 2018). We start by revising existing stability analyses of SGD, showing how the Frobenius norm and trace of Hessian relate to different notions of stability. Notably, if a global minimum is linearly stable for SGD, then the trace of Hessian must be less than or equal to $2/η$, where $η$ denotes the learning rate. By contrast, for gradient descent (GD), the stability imposes a similar constraint but only on the largest eigenvalue of Hessian. We then turn to analyze the generalization properties of these stable minima, focusing specifically on two-layer ReLU networks and diagonal linear networks. Notably, we establish the {\em equivalence} between these metrics of sharpness and certain parameter norms for the two models, which allows us to show that the stable minima of SGD provably generalize well. By contrast, the stability-induced regularization of GD is provably too weak to ensure satisfactory generalization. This discrepancy provides an explanation of why SGD often generalizes better than GD. Note that the learning rate (LR) plays a pivotal role in the strength of stability-induced regularization. As the LR increases, the regularization effect becomes more pronounced, elucidating why SGD with a larger LR consistently demonstrates superior generalization capabilities. Additionally, numerical experiments are provided to support our theoretical findings.

stat.ML↗

arXiv2023

On Quantum Speedups for Nonconvex Optimization via Quantum Tunneling Walks

Classical algorithms are often not effective for solving nonconvex optimization problems where local minima are separated by high barriers. In this paper, we explore possible quantum speedups for nonconvex optimization by leveraging the global effect of quantum tunneling. Specifically, we introduce a quantum algorithm termed the quantum tunneling walk (QTW) and apply it to nonconvex problems where local minima are approximately global minima. We show that QTW achieves quantum speedup over classical stochastic gradient descents (SGD) when the barriers between different local minima are high but thin and the minima are flat. Based on this observation, we construct a specific double-well landscape, where classical algorithms cannot efficiently hit one target well knowing the other well but QTW can when given proper initial states near the known well. Finally, we corroborate our findings with numerical experiments.

quant-ph↗

arXiv2022

You Are the Best Reviewer of Your Own Papers: An Owner-Assisted Scoring Mechanism

I consider a setting where reviewers offer very noisy scores for several items for the selection of high-quality ones (e.g., peer review of large conference proceedings), whereas the owner of these items knows the true underlying scores but prefers not to provide this information. To address this withholding of information, in this paper, I introduce the Isotonic Mechanism, a simple and efficient approach to improving imprecise raw scores by leveraging certain information that the owner is incentivized to provide. This mechanism takes the ranking of the items from best to worst provided by the owner as input, in addition to the raw scores provided by the reviewers. It reports the adjusted scores for the items by solving a convex optimization problem. Under certain conditions, I show that the owner's optimal strategy is to honestly report the true ranking of the items to her best knowledge in order to maximize the expected utility. Moreover, I prove that the adjusted scores provided by this owner-assisted mechanism are significantly more accurate than the raw scores provided by the reviewers. This paper concludes with several extensions of the Isotonic Mechanism and some refinements of the mechanism for practical consideration.

cs.LG↗

arXiv2022

ROCK: Causal Inference Principles for Reasoning about Commonsense Causality

Commonsense causality reasoning (CCR) aims at identifying plausible causes and effects in natural language descriptions that are deemed reasonable by an average person. Although being of great academic and practical interest, this problem is still shadowed by the lack of a well-posed theoretical framework; existing work usually relies on deep language models wholeheartedly, and is potentially susceptible to confounding co-occurrences. Motivated by classical causal principles, we articulate the central question of CCR and draw parallels between human subjects in observational studies and natural languages to adopt CCR to the potential-outcomes framework, which is the first such attempt for commonsense tasks. We propose a novel framework, ROCK, to Reason O(A)bout Commonsense K(C)ausality, which utilizes temporal signals as incidental supervision, and balances confounding effects using temporal propensities that are analogous to propensity scores. The ROCK implementation is modular and zero-shot, and demonstrates good CCR capabilities.

cs.CL↗

arXiv2022

FIFA: Making Fairness More Generalizable in Classifiers Trained on Imbalanced Data

Algorithmic fairness plays an important role in machine learning and imposing fairness constraints during learning is a common approach. However, many datasets are imbalanced in certain label classes (e.g. "healthy") and sensitive subgroups (e.g. "older patients"). Empirically, this imbalance leads to a lack of generalizability not only of classification, but also of fairness properties, especially in over-parameterized models. For example, fairness-aware training may ensure equalized odds (EO) on the training data, but EO is far from being satisfied on new users. In this paper, we propose a theoretically-principled, yet Flexible approach that is Imbalance-Fairness-Aware (FIFA). Specifically, FIFA encourages both classification and fairness generalization and can be flexibly combined with many existing fair learning methods with logits-based losses. While our main focus is on EO, FIFA can be directly applied to achieve equalized opportunity (EqOpt); and under certain conditions, it can also be applied to other fairness notions. We demonstrate the power of FIFA by combining it with a popular fair classification algorithm, and the resulting algorithm achieves significantly better fairness generalization on several real-world datasets.

cs.LG↗

arXiv2022

Characterizing the SLOPE Trade-off: A Variational Perspective and the Donoho-Tanner Limit

Sorted l1 regularization has been incorporated into many methods for solving high-dimensional statistical estimation problems, including the SLOPE estimator in linear regression. In this paper, we study how this relatively new regularization technique improves variable selection by characterizing the optimal SLOPE trade-off between the false discovery proportion (FDP) and true positive proportion (TPP) or, equivalently, between measures of type I error and power. Assuming a regime of linear sparsity and working under Gaussian random designs, we obtain an upper bound on the optimal trade-off for SLOPE, showing its capability of breaking the Donoho-Tanner power limit. To put it into perspective, this limit is the highest possible power that the Lasso, which is perhaps the most popular l1-based method, can achieve even with arbitrarily strong effect sizes. Next, we derive a tight lower bound that delineates the fundamental limit of sorted l1 regularization in optimally trading the FDP off for the TPP. Finally, we show that on any problem instance, SLOPE with a certain regularization sequence outperforms the Lasso, in the sense of having a smaller FDP, larger TPP and smaller l2 estimation risk simultaneously. Our proofs are based on a novel technique that reduces a calculus of variations problem to a class of infinite-dimensional convex optimization problems and a very recent result from approximate message passing theory.

math.ST↗

arXiv2022

A Power Analysis for Model-X Knockoffs with $\ell_{p}$-Regularized Statistics

Variable selection properties of procedures utilizing penalized-likelihood estimates is a central topic in the study of high dimensional linear regression problems. Existing literature emphasizes the quality of ranking of the variables by such procedures as reflected in the receiver operating characteristic curve or in prediction performance. Specifically, recent works have harnessed modern theory of approximate message-passing (AMP) to obtain, in a particular setting, exact asymptotic predictions of the type I-type II error tradeoff for selection procedures that rely on $\ell_{p}$-regularized estimators. In practice, effective ranking by itself is often not sufficient because some calibration for Type I error is required. In this work we study theoretically the power of selection procedures that similarly rank the features by the size of an $\ell_{p}$-regularized estimator, but further use Model-X knockoffs to control the false discovery rate in the realistic situation where no prior information about the signal is available. In analyzing the power of the resulting procedure, we extend existing results in AMP theory to handle the pairing between original variables and their knockoffs. This is used to derive exact asymptotic predictions for power. We apply the general results to compare the power of the knockoffs versions of Lasso and thresholded-Lasso selection, and demonstrate that in the i.i.d. covariate setting under consideration, tuning by cross-validation on the augmented design matrix is nearly optimal. We further demonstrate how the techniques allow to analyze also the Type S error, and a corresponding notion of power, when selections are supplemented with a decision on the sign of the coefficient.

math.ST↗

arXiv2022

An Unconstrained Layer-Peeled Perspective on Neural Collapse

Neural collapse is a highly symmetric geometric pattern of neural networks that emerges during the terminal phase of training, with profound implications on the generalization performance and robustness of the trained networks. To understand how the last-layer features and classifiers exhibit this recently discovered implicit bias, in this paper, we introduce a surrogate model called the unconstrained layer-peeled model (ULPM). We prove that gradient flow on this model converges to critical points of a minimum-norm separation problem exhibiting neural collapse in its global minimizer. Moreover, we show that the ULPM with the cross-entropy loss has a benign global landscape for its loss function, which allows us to prove that all the critical points are strict saddle points except the global minimizers that exhibit the neural collapse phenomenon. Empirically, we show that our results also hold during the training of neural networks in real-world tasks when explicit regularization or weight decay is not used.

cs.LG↗

arXiv2022

The Price of Competition: Effect Size Heterogeneity Matters in High Dimensions

In high-dimensional sparse regression, would increasing the signal-to-noise ratio while fixing the sparsity level always lead to better model selection? For high-dimensional sparse regression problems, surprisingly, in this paper we answer this question in the negative in the regime of linear sparsity for the Lasso method, relying on a new concept we term effect size heterogeneity. Roughly speaking, a regression coefficient vector has high effect size heterogeneity if its nonzero entries have significantly different magnitudes. From the viewpoint of this new measure, we prove that the false and true positive rates achieve the optimal trade-off uniformly along the Lasso path when this measure is maximal in a certain sense, and the worst trade-off is achieved when it is minimal in the sense that all nonzero effect sizes are roughly equal. Moreover, we demonstrate that the first false selection occurs much earlier when effect size heterogeneity is minimal than when it is maximal. The underlying cause of these two phenomena is, metaphorically speaking, the ``competition'' among variables with effect sizes of the same magnitude in entering the model. Taken together, our findings suggest that effect size heterogeneity shall serve as an important complementary measure to the sparsity of regression coefficients in the analysis of high-dimensional regression problems. Our proofs use techniques from approximate message passing theory as well as a novel technique for estimating the rank of the first false variable.

math.ST↗

arXiv2022

Weighted Training for Cross-Task Learning

In this paper, we introduce Target-Aware Weighted Training (TAWT), a weighted training algorithm for cross-task learning based on minimizing a representation-based task distance between the source and target tasks. We show that TAWT is easy to implement, is computationally efficient, requires little hyperparameter tuning, and enjoys non-asymptotic learning-theoretic guarantees. The effectiveness of TAWT is corroborated through extensive experiments with BERT on four sequence tagging tasks in natural language processing (NLP), including part-of-speech (PoS) tagging, chunking, predicate detection, and named entity recognition (NER). As a byproduct, the proposed representation-based task distance allows one to reason in a theoretically principled way about several critical aspects of cross-task learning, such as the choice of the source data and the impact of fine-tuning.

cs.LG↗

arXiv2021

Detecting Multiple Replicating Signals using Adaptive Filtering Procedures

Replicability is a fundamental quality of scientific discoveries: we are interested in those signals that are detectable in different laboratories, study populations, across time etc. Unlike meta-analysis which accounts for experimental variability but does not guarantee replicability, testing a partial conjunction (PC) null aims specifically to identify the signals that are discovered in multiple studies. In many contemporary applications, e.g., comparing multiple high-throughput genetic experiments, a large number $M$ of PC nulls need to be tested simultaneously, calling for a multiple comparisons correction. However, standard multiple testing adjustments on the $M$ PC $p$-values can be severely conservative, especially when $M$ is large and the signals are sparse. We introduce AdaFilter, a new multiple testing procedure that increases power by adaptively filtering out unlikely candidates of PC nulls. We prove that AdaFilter can control FWER and FDR as long as data across studies are independent, and has much higher power than other existing methods. We illustrate the application of AdaFilter with three examples: microarray studies of Duchenne muscular dystrophy, single-cell RNA sequencing of T cells in lung cancer tumors and GWAS for metabolomics.

stat.ME↗

arXiv2021

Imitating Deep Learning Dynamics via Locally Elastic Stochastic Differential Equations

Understanding the training dynamics of deep learning models is perhaps a necessary step toward demystifying the effectiveness of these models. In particular, how do data from different classes gradually become separable in their feature spaces when training neural networks using stochastic gradient descent? In this study, we model the evolution of features during deep learning training using a set of stochastic differential equations (SDEs) that each corresponds to a training sample. As a crucial ingredient in our modeling strategy, each SDE contains a drift term that reflects the impact of backpropagation at an input on the features of all samples. Our main finding uncovers a sharp phase transition phenomenon regarding the {intra-class impact: if the SDEs are locally elastic in the sense that the impact is more significant on samples from the same class as the input, the features of the training data become linearly separable, meaning vanishing training loss; otherwise, the features are not separable, regardless of how long the training time is. Moreover, in the presence of local elasticity, an analysis of our SDEs shows that the emergence of a simple geometric structure called the neural collapse of the features. Taken together, our results shed light on the decisive role of local elasticity in the training dynamics of neural networks. We corroborate our theoretical analysis with experiments on a synthesized dataset of geometric shapes and CIFAR-10.

cs.LG↗

arXiv2021

Exploring Deep Neural Networks via Layer-Peeled Model: Minority Collapse in Imbalanced Training

In this paper, we introduce the \textit{Layer-Peeled Model}, a nonconvex yet analytically tractable optimization program, in a quest to better understand deep neural networks that are trained for a sufficiently long time. As the name suggests, this new model is derived by isolating the topmost layer from the remainder of the neural network, followed by imposing certain constraints separately on the two parts of the network. We demonstrate that the Layer-Peeled Model, albeit simple, inherits many characteristics of well-trained neural networks, thereby offering an effective tool for explaining and predicting common empirical patterns of deep learning training. First, when working on class-balanced datasets, we prove that any solution to this model forms a simplex equiangular tight frame, which in part explains the recently discovered phenomenon of neural collapse \cite{papyan2020prevalence}. More importantly, when moving to the imbalanced case, our analysis of the Layer-Peeled Model reveals a hitherto unknown phenomenon that we term \textit{Minority Collapse}, which fundamentally limits the performance of deep learning models on the minority classes. In addition, we use the Layer-Peeled Model to gain insights into how to mitigate Minority Collapse. Interestingly, this phenomenon is first predicted by the Layer-Peeled Model before being confirmed by our computational experiments.

cs.LG↗

arXiv2021

Toward Better Generalization Bounds with Locally Elastic Stability

Algorithmic stability is a key characteristic to ensure the generalization ability of a learning algorithm. Among different notions of stability, \emph{uniform stability} is arguably the most popular one, which yields exponential generalization bounds. However, uniform stability only considers the worst-case loss change (or so-called sensitivity) by removing a single data point, which is distribution-independent and therefore undesirable. There are many cases that the worst-case sensitivity of the loss is much larger than the average sensitivity taken over the single data point that is removed, especially in some advanced models such as random feature models or neural networks. Many previous works try to mitigate the distribution independent issue by proposing weaker notions of stability, however, they either only yield polynomial bounds or the bounds derived do not vanish as sample size goes to infinity. Given that, we propose \emph{locally elastic stability} as a weaker and distribution-dependent stability notion, which still yields exponential generalization bounds. We further demonstrate that locally elastic stability implies tighter generalization bounds than those derived based on uniform stability in many situations by revisiting the examples of bounded support vector machines, regularized least square regressions, and stochastic gradient descent.

cs.LG↗