Lei You (Ph.D.)
Assistant Professor in Applied Mathematics
AI, Mathematics and Software
Department of Engineering Technology
Technical University of Denmark
I received my Ph.D. in Computer Science (specialized in Mathematical Optimization) from the Department of Information Technology at Uppsala University in 2019. During the PhD, I interned in The Boston Consulting Group (BCG) Gamma as a visiting data scientist. After the PhD, I had been working as a data scientist in Bolt and Wolt (Doordash) in the domain of on-demand logistics optimization. My previous research was focused on the application of information theory to optimize resource allocation for data throughput and network reliability in advanced communication systems.
Optimal Model Refinement is my current research interest, centered around leveraging mathematical optimization to enhance the interpretability and efficiency of machine learning models. I explore strategies to streamline complex models without performance loss, as well as to unravel the intricate mechanisms of decision-making models. Central to this pursuit is understanding the synergy between model simplification and explainability: Reducing a model's complexity aids in elucidating its functions, and concurrently, and explainability drives the efficient compression of the model for learning.
Counterfactual Explanations (CE) is the de facto method for providing insight and interpretability in black-box decision-making models by identifying alternative input instances that lead to different outcomes. This paper extends the concept of CEs to a distributional context, broadening the scope from individual data points to entire input and output distributions, named Distributional Counterfactual Explanation (DCE). In DCE, our focus shifts to analyzing the distributional properties of the factual and counterfactual, drawing parallels to the classical approach of assessing individual instances and their resulting decisions. We leverage Optimal Transport (OT) to frame a chance-constrained optimization problem, aiming to derive a counterfactual distribution that closely aligns with its factual counterpart, substantiated by statistical confidence. Our proposed optimization method, DISCOUNT, strategically balances this confidence across both input and output distributions. This algorithm is accompanied by an analysis of its convergence rate. The efficacy of our proposed method is substantiated through a series of illustrative case studies, highlighting its potential in providing deep insights into decision-making models.
This study tackles the issue of neural network pruning that inaccurate gradients exist when computing the empirical Fisher Information Matrix (FIM). We introduce SWAP, an Entropic Wasserstein regression (EWR) network pruning formulation, capitalizing on the geometric attributes of the optimal transport (OT) problem. The “swap” of a commonly used standard linear regression (LR) with the EWR in optimization is analytically showcased to excel in noise mitigation by adopting neighborhood interpolation across data points, yet incurs marginal extra computational cost. The unique strength of SWAP is its intrinsic ability to strike a balance between noise reduction and covariance information preservation. Extensive experiments performed on various networks show comparable performance of SWAP with state-of-the-art (SoTA) network pruning algorithms. Our proposed method outperforms the SoTA when the network size or the target sparsity is large, the gain is even larger with the existence of noisy gradients, possibly from noisy data, analog memory, or adversarial attacks. Notably, our proposed method achieves a gain of 6% improvement in accuracy and 8% improvement in testing loss for MobileNetV1 with less than one-fourth of the network parameters remaining.
The paper investigates the weighted sum-rate maximization (WSRM) problem with latent interfering sources outside the known network, whose power allocation policy is hidden from and uncontrollable to optimization. The paper extends the famous alternate optimization algorithm weighted minimum mean square error (WMMSE) under a causal inference framework to tackle with WSRM. Specifically, with the possibility of power policy shifting in the hidden network, computing an iterating direction based only on the observed interference inherently implies that counterfactual is ignored in decision making. A method called synthetic control (SC) is used to estimate the counterfactual. For any link in the known network, SC constructs a convex combination of the interference on other links and uses it as an estimate for the counterfactual. Power iteration in the proposed SC-WMMSE is performed taking into account both the observed interference and its counterfactual. SC-WMMSE requires no more information than the original WMMSE in the optimization stage. To our best knowledge, this is the first paper explores the potential of SC in assisting mathematical optimization in addressing classic wireless optimization problems. Numerical results suggest the superiority of the SC-WMMSE over the original in both convergence and objective.
In a cloud radio access network (C-RAN), distributed remote radio heads (RRHs) are coordinated by baseband units (BBUs) in the cloud. The centralization of signal processing provides flexibility for coordinated multi-point transmission (CoMP) of RRHs to cooperatively serve user equipments (UEs). We target enhancing UEs' capacity performance, by jointly optimizing the selection of RRHs for serving UEs, i.e., resource allocation (and CoMP selection). We analyze the computational complexity of the problem. Next, we prove that under fixed CoMP selection, the optimal resource allocation amounts to solving a so-called iterated function. Towards user-centric network optimization, we propose an algorithm for the joint optimization problem, aiming at maximumly scaling up the capacity for any target UE group of interest. The proposed algorithm enables network-level performance evaluation for quality of experience.