SOFARI: High-Dimensional Manifold-Based Inference

• URL: http://arxiv.org/abs/2309.15032v1
• Date: Tue, 26 Sep 2023 16:01:54 GMT
• Title: SOFARI: High-Dimensional Manifold-Based Inference
• Authors: Zemin Zheng, Xin Zhou, Yingying Fan, Jinchi Lv
• Abstract summary: We introduce two SOFARI variants to handle strongly and weakly latent factors, where the latter covers a broader range of applications. We show that SOFARI provides bias-corrected estimators for both latent left factor vectors and singular values, for which we show to enjoy the mean-zero normal distributions with sparse estimable variances. We illustrate the effectiveness of SOFARI and justify our theoretical results through simulation examples and a real data application in economic forecasting.
• Score: 8.860162863559163
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Multi-task learning is a widely used technique for harnessing information from various tasks. Recently, the sparse orthogonal factor regression (SOFAR) framework, based on the sparse singular value decomposition (SVD) within the coefficient matrix, was introduced for interpretable multi-task learning, enabling the discovery of meaningful latent feature-response association networks across different layers. However, conducting precise inference on the latent factor matrices has remained challenging due to orthogonality constraints inherited from the sparse SVD constraint. In this paper, we suggest a novel approach called high-dimensional manifold-based SOFAR inference (SOFARI), drawing on the Neyman near-orthogonality inference while incorporating the Stiefel manifold structure imposed by the SVD constraints. By leveraging the underlying Stiefel manifold structure, SOFARI provides bias-corrected estimators for both latent left factor vectors and singular values, for which we show to enjoy the asymptotic mean-zero normal distributions with estimable variances. We introduce two SOFARI variants to handle strongly and weakly orthogonal latent factors, where the latter covers a broader range of applications. We illustrate the effectiveness of SOFARI and justify our theoretical results through simulation examples and a real data application in economic forecasting.

Related papers

• Learning Controlled Stochastic Differential Equations [61.82896036131116]
  This work proposes a novel method for estimating both drift and diffusion coefficients of continuous, multidimensional, nonlinear controlled differential equations with non-uniform diffusion. We provide strong theoretical guarantees, including finite-sample bounds for (L2), (Linfty), and risk metrics, with learning rates adaptive to coefficients' regularity. Our method is available as an open-source Python library.
  arXiv  Detail & Related papers  (2024-11-04T11:09:58Z)
• Distributionally Robust Optimization as a Scalable Framework to Characterize Extreme Value Distributions [22.765095010254118]
  The goal of this paper is to develop distributionally robust optimization (DRO) estimators, specifically for multidimensional Extreme Value Theory (EVT) statistics. In order to mitigate over-conservative estimates while enhancing out-of-sample performance, we study DRO estimators informed by semi-parametric max-stable constraints in the space of point processes. Both approaches are validated using synthetically generated data, recovering prescribed characteristics, and verifying the efficacy of the proposed techniques.
  arXiv  Detail & Related papers  (2024-07-31T19:45:27Z)
• Synergistic eigenanalysis of covariance and Hessian matrices for enhanced binary classification [72.77513633290056]
  We present a novel approach that combines the eigenanalysis of a covariance matrix evaluated on a training set with a Hessian matrix evaluated on a deep learning model. Our method captures intricate patterns and relationships, enhancing classification performance.
  arXiv  Detail & Related papers  (2024-02-14T16:10:42Z)
• Distribution-Dependent Rates for Multi-Distribution Learning [26.38831409926518]
  Recent multi-distribution learning framework tackles this objective in a dynamic interaction with the environment. We provide distribution-dependent guarantees in the MDL regime, that scale with suboptimality gaps and result in superior dependence on the sample size. We devise an adaptive optimistic algorithm, LCB-DR, that showcases enhanced dependence on the gaps, mirroring the contrast between uniform and optimistic allocation in the multi-armed bandit literature.
  arXiv  Detail & Related papers  (2023-12-20T15:50:16Z)
• Implicit Variational Inference for High-Dimensional Posteriors [7.924706533725115]
  In variational inference, the benefits of Bayesian models rely on accurately capturing the true posterior distribution. We propose using neural samplers that specify implicit distributions, which are well-suited for approximating complex multimodal and correlated posteriors. Our approach introduces novel bounds for approximate inference using implicit distributions by locally linearising the neural sampler.
  arXiv  Detail & Related papers  (2023-10-10T14:06:56Z)
• Synergies between Disentanglement and Sparsity: Generalization and Identifiability in Multi-Task Learning [79.83792914684985]
  We prove a new identifiability result that provides conditions under which maximally sparse base-predictors yield disentangled representations. Motivated by this theoretical result, we propose a practical approach to learn disentangled representations based on a sparsity-promoting bi-level optimization problem.
  arXiv  Detail & Related papers  (2022-11-26T21:02:09Z)
• Alpha-divergence Variational Inference Meets Importance Weighted Auto-Encoders: Methodology and Asymptotics [21.51266421854127]
  We formalize and study the VR-IWAE bound, a generalization of the Importance Weighted Auto-Encoder (IWAE) bound. We show that the VR-IWAE bound enjoys several desirable properties and notably leads to the same gradient descent procedure as the VR bound. We then provide two complementary theoretical analyses of the VR-IWAE bound and thus of the standard IWAE bound.
  arXiv  Detail & Related papers  (2022-10-12T14:15:39Z)
• MULTIPAR: Supervised Irregular Tensor Factorization with Multi-task Learning [19.67636717572317]
  PARAFAC2 has been successfully applied on EHRs for extracting meaningful medical concepts (phenotypes) We propose MULTIPAR: a supervised irregular tensor factorization with multi-task learning.
  arXiv  Detail & Related papers  (2022-08-01T17:07:23Z)
• Efficient CDF Approximations for Normalizing Flows [64.60846767084877]
  We build upon the diffeomorphic properties of normalizing flows to estimate the cumulative distribution function (CDF) over a closed region. Our experiments on popular flow architectures and UCI datasets show a marked improvement in sample efficiency as compared to traditional estimators.
  arXiv  Detail & Related papers  (2022-02-23T06:11:49Z)
• Regularizing Variational Autoencoder with Diversity and Uncertainty Awareness [61.827054365139645]
  Variational Autoencoder (VAE) approximates the posterior of latent variables based on amortized variational inference. We propose an alternative model, DU-VAE, for learning a more Diverse and less Uncertain latent space.
  arXiv  Detail & Related papers  (2021-10-24T07:58:13Z)
• Stochastic-Sign SGD for Federated Learning with Theoretical Guarantees [49.91477656517431]
  Quantization-based solvers have been widely adopted in Federated Learning (FL) No existing methods enjoy all the aforementioned properties. We propose an intuitively-simple yet theoretically-simple method based on SIGNSGD to bridge the gap.
  arXiv  Detail & Related papers  (2020-02-25T15:12:15Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.