We propose the Factor Augmented (sparse linear) Regression Model (FARM) that not only admits both the latent factor regression and sparse linear regression as special cases but also bridges dimension reduction and sparse regression together. We provide theoretical guarantees for the estimation of our model under the existence of sub-Gaussian and heavy-tailed noises (with bounded $(1+\vartheta )$-th moment, for all $\vartheta >0$) respectively. In addition, the existing works on supervised learning often assume the latent factor regression or sparse linear regression is the true underlying model without justifying its adequacy. To fill in such an important gap on high-dimensional inference, we also leverage our model as the alternative model to test the sufficiency of the latent factor regression and the sparse linear regression models. To accomplish these goals, we propose the Factor-Adjusted deBiased Test (FabTest) and a two-stage ANOVA type test respectively. We also conduct large-scale numerical experiments including both synthetic and FRED macroeconomics data to corroborate the theoretical properties of our methods. Numerical results illustrate the robustness and effectiveness of our model against latent factor regression and sparse linear regression models.

In this paper, we study the contextual dynamic pricing problem where the market value of a product is linear in its observed features plus some market noise. Products are sold one at a time, and only a binary response indicating success or failure of a sale is observed. Our model setting is similar to Javanmard and Nazerzadeh (2019) except that we expand the demand curve to a semiparametric model and learn dynamically both parametric and nonparametric components. We propose a dynamic statistical learning and decision making policy that minimizes regret (maximizes revenue) by combining semiparametric estimation for a generalized linear model with unknown link and online decision making. Under mild conditions, for a market noise c.d.f. $F(·)$ with m-th order derivative ( $m\ge 2$), our policy achieves a regret upper bound of ${\tilde{\mathcal{O}}}_d(T^{\frac{2m+1}{4m-1}})$, where T is the time horizon and ${\tilde{\mathcal{O}}}_d$ is the order hiding logarithmic terms and the feature dimension d. The upper bound is further reduced to ${\tilde{\mathcal{O}}}_d(\sqrt{T})$ if F is super smooth. These upper bounds are close to $\Omega (\sqrt{T})$, the lower bound where F belongs to a parametric class. We further generalize these results to the case with dynamic dependent product features under the strong mixing condition.

1 With the astonishing empirical success in various application domains such as computer vision (Voulodimos et al. 2018), natural language processing (Otter, Medina, and Kalita 2020; Torfi et al. 2...

Ranking Inferences for General Multiway Comparisons Ranking inference underpins critical decision-making across diverse domains including e.g. university ranking, journal ranking, academic paper review, voting, online recommendation and tournament competition. Beyond generating point estimates of ranks, these applications also demand confidence intervals for ranks through robust uncertainty quantification, in order to ensure reliable and informed decisions. However, existing approaches predominantly rely on classical models such as Bradley-Terry-Luce and Plackett-Luce, which assume homogeneous comparison structures and prove inadequate for complex real-world scenarios. This paper presents a unified spectral ranking methodology for heterogeneous multiway comparisons, which simultaneously achieves statistical efficiency under minimal structural assumptions and computational scalability. The authors establish comprehensive ranking inference tools, grounded in the asymptotic normality theory and bootstrapping techniques, facilitating top-K selection, rank confidence interval construction, and hypothesis testing for cross-population or cross-period ranking consistency.

Quantifying the uncertainty of predictions is a core problem in modern statistics. Methods for predictive inference have been developed under a variety of assumptions, often—for instance, in standard conformal prediction—relying on the invariance of the distribution of the data under special groups of transformations such as permutation groups. Moreover, many existing methods for predictive inference aim to predict unobserved outcomes in sequences of feature-outcome observations. Meanwhile, there is interest in predictive inference under more general observation models (e.g. for partially observed features) and for data satisfying more general distributional symmetries (e.g. rotationally invariant observations in physics). Here, we propose SymmPI, a methodology for predictive inference when data distributions have general group symmetries in arbitrary observation models. Our methods leverage the novel notion of distributionally equivariant transformations, which process the data while preserving their distributional invariances. We show that SymmPI has valid coverage under distributional invariance and characterize its performance under distribution shift, recovering recent results as special cases. We apply SymmPI to predict unobserved values associated with vertices in a network, where the distribution is unchanged under relabellings that keep the network structure unchanged. In several simulations in a two-layer hierarchical model, and in an empirical data analysis example, SymmPI performs favourably compared with existing methods.