Yang Zhou

Jiayin Jin, Zeru Zhang, Yang Zhou et al.

Only recently, researchers attempt to provide classification algorithms with provable group fairness guarantees. Most of these algorithms suffer from harassment caused by the requirement that the training and deployment data follow the same distribution. This paper proposes an input-agnostic certified group fairness algorithm, FairSmooth, for improving the fairness of classification models while maintaining the remarkable prediction accuracy. A Gaussian parameter smoothing method is developed to transform base classifiers into their smooth versions. An optimal individual smooth classifier is learnt for each group with only the data regarding the group and an overall smooth classifier for all groups is generated by averaging the parameters of all the individual smooth ones. By leveraging the theory of nonlinear functional analysis, the smooth classifiers are reformulated as output functions of a Nemytskii operator. Theoretical analysis is conducted to derive that the Nemytskii operator is smooth and induces a Frechet differentiable smooth manifold. We theoretically demonstrate that the smooth manifold has a global Lipschitz constant that is independent of the domain of the input data, which derives the input-agnostic certified group fairness.

Shuxian Niu, Qian Liu, Yang Zhou et al.

In this paper, we apply a Threshold-Decreasing Algorithm to maximize $k$-submodular functions under a matroid constraint, which reduces the query complexity of the algorithm compared to the greedy algorithm with little loss in approximation ratio. We give a $(\frac{1}{2} - ε)$-approximation algorithm for monotone $k$-submodular function maximization, and a $(\frac{1}{3} - ε)$-approximation algorithm for non-monotone case, with complexity $O(\frac{n(k\cdot EO + IO)}ε \log \frac{r}ε)$, where $r$ denotes the rank of the matroid, and $IO, EO$ denote the number of oracles to evaluate whether a subset is an independent set and to compute the function value of $f$, respectively. Since the constraint of total size can be looked as a special matroid, called uniform matroid, then we present the fast algorithm for maximizing $k$-submodular functions subject to a total size constraint as corollaries. corollaries.

Yang Zhou, Xiaojun Chen

A spherical $t$-design is a set of points on the sphere that are nodes of a positive equal weight quadrature rule having algebraic accuracy $t$ for all spherical polynomials with degrees $\le t$. Spherical $t$-designs have many distinguished properties in approximations on the sphere and receive remarkable attention. Although the existence of a spherical $t$-design is known for any $t\ge 0$, a spherical design is only known in a set of interval enclosures on the sphere \cite{chen2011computational} for $t\le 100$. It is unknown how to choose a set of points from the set of interval enclosures to obtain a spherical $t$-design. In this paper we investigate a new concept of point sets on the sphere named spherical $t_ε$-design ($0<ε<1$), which are nodes of a positive weight quadrature rule with algebraic accuracy $t$. The sum of the weights is equal to the area of the sphere and the mean value of the weights is equal to the weight of the quadrature rule defined by the spherical $t$-design. A spherical $t_ε$-design is a spherical $t$-design when $ε=0,$ and a spherical $t$-design is a spherical $t_ε$-design for any $0<ε<1$. We show that any point set chosen from the set of interval enclosures \cite{chen2011computational} is a spherical $t_ε$-design. We then study the worst-case errors of quadrature rules using spherical $t_ε$-designs in a Sobolev space, and investigate a model of polynomial approximation with the $l_1$-regularization using spherical $t_ε$-designs. Numerical results illustrate good performance of spherical $t_ε$-designs for numerical integration and function approximation on the sphere.

Zhou Yang, Shunyan Luo, Jiazhen Zhu et al.

Deep neural networks (DNNs) have made significant strides in Natural Language Processing (NLP), yet their interpretability remains elusive, particularly when evaluating their intricate decision-making processes. Traditional methods often rely on post-hoc interpretations, such as saliency maps or feature visualization, which might not be directly applicable to the discrete nature of word data in NLP. Addressing this, we introduce the Model-agnostic Saliency Estimation (MASE) framework. MASE offers local explanations for text-based predictive models without necessitating in-depth knowledge of a model's internal architecture. By leveraging Normalized Linear Gaussian Perturbations (NLGP) on the embedding layer instead of raw word inputs, MASE efficiently estimates input saliency. Our results indicate MASE's superiority over other model-agnostic interpretation methods, especially in terms of Delta Accuracy, positioning it as a promising tool for elucidating the operations of text-based models in NLP.