Zhe Liu

Z Liu, J Lou, W Bao et al.

Fine-tuning on task-specific datasets is a widely-embraced paradigm of harnessing the powerful capability of pretrained LLMs for various downstream tasks. Due to the popularity of LLMs fine-tuning and its accompanying privacy concerns, differentially private (DP) fine-tuning of pretrained LLMs has been widely used to safeguarding the privacy of task-specific datasets. Lying at the design core of DP LLM fine-tuning methods is the satisfactory tradeoff among privacy, utility, and scalability. Most existing methods build upon the seminal work of DP-SGD. Despite pushing the scalability of DP-SGD to its limit, DP-SGD-based fine-tuning methods are unfortunately limited by the inherent inefficiency of SGD. In this paper, we investigate the potential of DP zeroth-order methods for LLM pretraining, which avoids the scalability bottleneck of SGD by approximating the gradient with the more efficient zeroth-order gradient. Rather than treating the zeroth-order method as a drop-in replacement for SGD, this paper presents a comprehensive study both theoretically and empirically. First, we propose the stagewise DP zeroth-order method (DP-ZOSO) that dynamically schedules key hyperparameters. This design is grounded on the synergy between DP random perturbation and the gradient approximation error of the zeroth-order method, and its effect on fine-tuning trajectory. We provide theoretical analysis for both proposed methods. We conduct extensive empirical analysis on both encoder-only masked language model and decoder-only autoregressive language model, achieving impressive results in terms of scalability and utility regardless of the class of tasks (compared with DPZero, DP-ZOPO improves $4.5\%$ on SST-5, $5.5\%$ on MNLI with RoBERTa-Large and 9.2\% on CB, 3.9\% on BoolQ with OPT-2.7b when $ε=4$, demonstrates more significant enhancement in performance on more complicated tasks).

Yuancheng Zhu, Zhe Liu, Siqi Sun

We present a framework for incorporating prior information into nonparametric estimation of graphical models. To avoid distributional assumptions, we restrict the graph to be a forest and build on the work of forest density estimation (FDE). We reformulate the FDE approach from a Bayesian perspective, and introduce prior distributions on the graphs. As two concrete examples, we apply this framework to estimating scale-free graphs and learning multiple graphs with similar structures. The resulting algorithms are equivalent to finding a maximum spanning tree of a weighted graph with a penalty term on the connectivity pattern of the graph. We solve the optimization problem via a minorize-maximization procedure with Kruskal's algorithm. Simulations show that the proposed methods outperform competing parametric methods, and are robust to the true data distribution. They also lead to improvement in predictive power and interpretability in two real data sets.

Zhe Liu

$L_1$ regularized logistic regression has now become a workhorse of data mining and bioinformatics: it is widely used for many classification problems, particularly ones with many features. However, $L_1$ regularization typically selects too many features and that so-called false positives are unavoidable. In this paper, we demonstrate and analyze an aggregation method for sparse logistic regression in high dimensions. This approach linearly combines the estimators from a suitable set of logistic models with different underlying sparsity patterns and can balance the predictive ability and model interpretability. Numerical performance of our proposed aggregation method is then investigated using simulation studies. We also analyze a published genome-wide case-control dataset to further evaluate the usefulness of the aggregation method in multilocus association mapping.