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迁移学习中最小范数插值器的泛化误差AI 解读

This paper establishes the generalization error of pooled min-$\ell_2$-norm interpolation in transfer learning, where data from diverse distributions are available. Min-norm interpolators arise naturally as implicit regularized limits of modern machine learning algorithms. Prior work has characterized their out-of-distribution risk when samples from the test distribution are unavailable during training. In many applications, however, limited test samples may be available at…

张量网络依赖下的高维逻辑回归推断AI 解读

We investigate the problem of statistical inference for logistic regression with high-dimensional covariates in settings where dependence among individuals is induced by an underlying Markov random field. Going beyond the pairwise interaction models such as the Ising model, we consider a framework to accommodate more general tensor structures that capture higher-order dependencies. We develop a two-step procedure for low-dimensional linear and quadratic functionals. The…

过参数化下的模型坍缩防范：插值学习与岭回归的最优混合比例AI 解读

Model collapse occurs when generative models degrade after repeatedly training on their own synthetic outputs. We study this effect in overparameterized linear regression in a setting where each iteration mixes fresh real labels with synthetic labels drawn from the model fitted in the previous iteration. We derive precise generalization error formulae for minimum-$\ell_2$-norm interpolation and ridge regression under this iterative scheme. Our analysis reveals intriguing…

干扰下的因果推断：计算障碍与算法解决方案AI 解读

We study causal effect estimation under interference from network data. We work under the chain-graph formulation pioneered in Tchetgen Tchetgen et. al (2021). Our first result shows that polynomial time evaluation of treatment effects is computationally hard in this framework without additional assumptions on the underlying chain graph. Subsequently, we assume that the interactions among the study units are governed either by (i) a dense graph or (ii) an i.i.d. Gaussian…

含干扰参数的半参数推断：后期融合多任务学习AI 解读

In the age of large and heterogeneous datasets, the integration of information from diverse sources is essential to improve parameter estimation. Multi-task learning offers a powerful approach by enabling simultaneous learning across related tasks. In this work, we introduce a late fusion framework for multi-task learning with semiparametric models that involve infinite-dimensional nuisance parameters, focusing on applications such as heterogeneous treatment effect…

利用平均场方法估计网络干扰下的因果效应AI 解读

We study causal effect estimation from observational data under interference. The interference pattern is captured by an observed network. We adopt the chain graph framework of Tchetgen Tchetgen et. al. (2021), which allows (i) interaction among the outcomes of distinct study units connected along the graph and (ii) long range interference, whereby the outcome of an unit may depend on the treatments assigned to distant units connected along the interference network. For…

具有成对依赖的马尔可夫随机场中的伪关联AI 解读

Yule (1926) identified the issue of "nonsense correlations" in time series data, where dependence within each of two random vectors causes overdispersion -- i.e. variance inflation -- for measures of dependence between the two. During the near century since then, much has been written about nonsense correlations -- but nearly all of it confined to the time series literature. In this paper we provide the first, to our knowledge, rigorous study of this phenomenon for more…

混合成员模型中混合概率与排序的推断AI 解读

Network data is prevalent in numerous big data applications including economics and health networks where it is of prime importance to understand the latent structure of network. In this paper, we model the network using the Degree-Corrected Mixed Membership (DCMM) model. In DCMM model, for each node $i$, there exists a membership vector $\boldsymbolπ_ i = (\boldsymbolπ_i(1), \boldsymbolπ_i(2),\ldots, \boldsymbolπ_i(K))$, where $\boldsymbolπ_i(k)$ denotes the weight that…

维度增长下非参数交互模型的深度神经网络估计AI 解读

Deep neural networks have achieved tremendous success due to their representation power and adaptation to low-dimensional structures. Their potential for estimating structured regression functions has been recently established in the literature. However, most of the studies require the input dimension to be fixed and consequently ignore the effect of dimension on the rate of convergence and hamper their applications to modern big data with high dimensionality. In this paper,…