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Tianxi Li

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6 papers

2 author rows

JMLR Journal 2024 Journal Article

The Non-Overlapping Statistical Approximation to Overlapping Group Lasso

Mingyu Qi
Tianxi Li

The group lasso penalty is widely used to introduce structured sparsity in statistical learning, characterized by its ability to eliminate predefined groups of parameters automatically. However, when the groups overlap, solving the group lasso problem can be time-consuming in high-dimensional settings due to groups’ non-separability. This computational challenge has limited the applicability of the overlapping group lasso penalty in cutting-edge areas, such as gene pathway selection and graphical model estimation. This paper introduces a non-overlapping and separable penalty designed to efficiently approximate the overlapping group lasso penalty. The approximation substantially enhances the computational efficiency in optimization, especially for large-scale and high-dimensional problems. We show that the proposed penalty is the tightest separable relaxation of the overlapping group lasso norm within the family of $\ell_{q_1}/\ell_{q_2}$ norms. Moreover, the estimators derived from our proposed norm are statistically equivalent to those derived from the overlapping group lasso penalty in terms of estimation error, support recovery, and minimax rate under the squared loss. The effectiveness of our method is demonstrated through extensive simulation examples and a predictive task of cancer tumors. [abs] [ pdf ][ bib ] [ code ] &copy JMLR 2024. ( edit, beta )

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JMLR Journal 2023 Journal Article

Community models for networks observed through edge nominations

Tianxi Li
Elizaveta Levina
Ji Zhu

Communities are a common and widely studied structure in networks, typically assuming that the network is fully and correctly observed. In practice, network data are often collected by querying nodes about their connections. In some settings, all edges of a sampled node will be recorded, and in others, a node may be asked to name its connections. These sampling mechanisms introduce noise and bias, which can obscure the community structure and invalidate assumptions underlying standard community detection methods. We propose a general model for a class of network sampling mechanisms based on recording edges via querying nodes, designed to improve community detection for network data collected in this fashion. We model edge sampling probabilities as a function of both individual preferences and community parameters, and show community detection can be performed by spectral clustering under this general class of models. We also propose, as a special case of the general framework, a parametric model for directed networks we call the nomination stochastic block model, which allows for meaningful parameter interpretations and can be fitted by the method of moments. In this case, spectral clustering and the method of moments are computationally efficient and come with theoretical guarantees of consistency. We evaluate the proposed model in simulation studies on unweighted and weighted networks and under misspecified models. The method is applied to a faculty hiring dataset, discovering a meaningful hierarchy of communities among US business schools. [abs] [ pdf ][ bib ] [ code ] &copy JMLR 2023. ( edit, beta )

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NeurIPS Conference 2022 Conference Paper

Incrementality Bidding via Reinforcement Learning under Mixed and Delayed Rewards

Ashwinkumar Badanidiyuru Varadaraja
Zhe Feng
Tianxi Li
Haifeng Xu

Incrementality, which measures the causal effect of showing an ad to a potential customer (e. g. a user in an internet platform) versus not, is a central object for advertisers in online advertising platforms. This paper investigates the problem of how an advertiser can learn to optimize the bidding sequence in an online manner \emph{without} knowing the incrementality parameters in advance. We formulate the offline version of this problem as a specially structured episodic Markov Decision Process (MDP) and then, for its online learning counterpart, propose a novel reinforcement learning (RL) algorithm with regret at most $\widetilde{O}(H^2\sqrt{T})$, which depends on the number of rounds $H$ and number of episodes $T$, but does not depend on the number of actions (i. e. , possible bids). A fundamental difference between our learning problem from standard RL problems is that the realized reward feedback from conversion incrementality is \emph{mixed} and \emph{delayed}. To handle this difficulty we propose and analyze a novel pairwise moment-matching algorithm to learn the conversion incrementality, which we believe is of independent interest.

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ICML Conference 2021 Conference Paper

Diffusion Source Identification on Networks with Statistical Confidence

Quinlan Dawkins
Tianxi Li
Haifeng Xu

Diffusion source identification on networks is a problem of fundamental importance in a broad class of applications, including controlling the spreading of rumors on social media, identifying a computer virus over cyber networks, or identifying the disease center during epidemiology. Though this problem has received significant recent attention, most known approaches are well-studied in only very restrictive settings and lack theoretical guarantees for more realistic networks. We introduce a statistical framework for the study of this problem and develop a confidence set inference approach inspired by hypothesis testing. Our method efficiently produces a small subset of nodes, which provably covers the source node with any pre-specified confidence level without restrictive assumptions on network structures. To our knowledge, this is the first diffusion source identification method with a practically useful theoretical guarantee on general networks. We demonstrate our approach via extensive synthetic experiments on well-known random network models, a large data set of real-world networks as well as a mobility network between cities concerning the COVID-19 spreading in January 2020.

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JMLR Journal 2020 Journal Article

High-dimensional Gaussian graphical models on network-linked data

Tianxi Li
Cheng Qian
Elizaveta Levina
Ji Zhu

Graphical models are commonly used to represent conditional dependence relationships between variables. There are multiple methods available for exploring them from high-dimensional data, but almost all of them rely on the assumption that the observations are independent and identically distributed. At the same time, observations connected by a network are becoming increasingly common, and tend to violate these assumptions. Here we develop a Gaussian graphical model for observations connected by a network with potentially different mean vectors, varying smoothly over the network. We propose an efficient estimation algorithm and demonstrate its effectiveness on both simulated and real data, obtaining meaningful and interpretable results on a statistics coauthorship network. We also prove that our method estimates both the inverse covariance matrix and the corresponding graph structure correctly under the assumption of network “cohesion”, which refers to the empirically observed phenomenon of network neighbors sharing similar traits. [abs] [ pdf ][ bib ] [ code ] &copy JMLR 2020. ( edit, beta )

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NeurIPS Conference 2017 Conference Paper

Probabilistic Rule Realization and Selection

Haizi Yu
Tianxi Li
Lav Varshney

Abstraction and realization are bilateral processes that are key in deriving intelligence and creativity. In many domains, the two processes are approached through \emph{rules}: high-level principles that reveal invariances within similar yet diverse examples. Under a probabilistic setting for discrete input spaces, we focus on the rule realization problem which generates input sample distributions that follow the given rules. More ambitiously, we go beyond a mechanical realization that takes whatever is given, but instead ask for proactively selecting reasonable rules to realize. This goal is demanding in practice, since the initial rule set may not always be consistent and thus intelligent compromises are needed. We formulate both rule realization and selection as two strongly connected components within a single and symmetric bi-convex problem, and derive an efficient algorithm that works at large scale. Taking music compositional rules as the main example throughout the paper, we demonstrate our model's efficiency in not only music realization (composition) but also music interpretation and understanding (analysis).

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