11 citations · 19 across the 9 of their papers we have counts for
10 papers
Lipschitzian SLLNs for random functions
Lai Tian, Johannes O. Royset
We prove strong laws of large numbers for random functions in the Lipschitz pseudometric. Our results hold under either a topological or a model-theoretic condition, with the latte…
Failure of uniform laws of large numbers for subdifferentials and beyond
Lai Tian, Johannes O. Royset
We provide counterexamples showing that uniform laws of large numbers do not hold for subdifferentials under natural assumptions. Our constructions are univariate random Lipschitz…
Approximating Rockafellians Mitigate Distributional Perturbations: Discontinuous Integrands and Chance-Constrained Applications
Lai Tian, Johannes O. Royset
In this paper, we show how approximating Rockafellians serve as a principled and effective alternative for improving the stability of stochastic programs under distributional chang…
Testing Approximate Stationarity Concepts for Piecewise Affine Functions
Lai Tian, Anthony Man-Cho So
We study the basic computational problem of detecting approximate stationary points for continuous piecewise affine (PA) functions. Our contributions span multiple aspects, includi…
Testing Stationarity Concepts for ReLU Networks: Hardness, Regularity, and Robust Algorithms
Lai Tian, Anthony Man-Cho So
We study the computational problem of the stationarity test for the empirical loss of neural networks with ReLU activation functions. Our contributions are: Hardness: We show that…
No Dimension-Free Deterministic Algorithm Computes Approximate Stationarities of Lipschitzians
Lai Tian, Anthony Man-Cho So
We consider the computation of an approximately stationary point for a Lipschitz and semialgebraic function with a local oracle. If is smooth, simple deterministic methods…
On the Finite-Time Complexity and Practical Computation of Approximate Stationarity Concepts of Lipschitz Functions
Lai Tian, Kaiwen Zhou, Anthony Man-Cho So
We report a practical finite-time algorithmic scheme to compute approximately stationary points for nonconvex nonsmooth Lipschitz functions. In particular, we are interested in two…
Practical Schemes for Finding Near-Stationary Points of Convex Finite-Sums
Kaiwen Zhou, Lai Tian, Anthony Man-Cho So +1
In convex optimization, the problem of finding near-stationary points has not been adequately studied yet, unlike other optimality measures such as the function value. Even in the…
Learning Feature Sparse Principal Components
Lai Tian, Feiping Nie, Xuelong Li
This paper presents new algorithms to solve the feature-sparsity constrained PCA problem (FSPCA), which performs feature selection and PCA simultaneously. Existing optimization met…
Non-Greedy L21-Norm Maximization for Principal Component Analysis
Feiping Nie, Heng Huang
Principal Component Analysis (PCA) is one of the most important unsupervised methods to handle high-dimensional data. However, due to the high computational complexity of its eigen…