Inference in latent factor regression with clusterable features

Regression models, in which the observed features X∈Rp and response Y∈R depend, jointly, on a lower dimensional, unobserved, latent vector Z∈RK, with K≪p, are popular large array of applications, mainly used for predicting from correlated features. In contrast, methodology theory inference regression coefficient β∈RK relating Y to Z scarce, since typically un-observable factor is hard interpret. Furthermore, determination asymptotic variance an estimator β long-standing problem, solutions known only few particular cases. To address some these outstanding questions, we develop inferential tools class models signed mixtures factors. The model specifications both practically desirable, render interpretability components Z, sufficient parameter identifiability. Without assuming that number factors K or structure mixture advance, construct computationally efficient estimators β, along other important parameters. We benchmark rate convergence by first establishing its ℓ2-norm minimax bound, show our proposed βˆ minimax-rate adaptive. Our main contribution provision unified analysis component-wise Gaussian distribution and, especially, derivation closed form expression variance, together consistent estimators. resulting can be when p independent sample size n, also both, either, vary while allowing p>n. This complements normality results obtained case under consideration, regime K=O(1) p→∞, but without estimate. As application, provide, within specifications, statistical platform cluster centers, thereby increasing scope theoretical results. newly developed recently collected data set study effectiveness new SIV vaccine. enables top antibody-centric mechanisms associated vaccine response.