Multivariate Online Linear Regression for Hierarchical Forecasting

• URL: http://arxiv.org/abs/2402.14578v1
• Date: Thu, 22 Feb 2024 14:33:54 GMT
• Title: Multivariate Online Linear Regression for Hierarchical Forecasting
• Authors: Massil Hihat, Guillaume Garrigos, Adeline Fermanian, Simon Bussy
• Abstract summary: We introduce MultiVAW, a method that extends the well-known Vovk-Azoury-Warmuth algorithm to the multivariate setting. We apply our results to the online hierarchical forecasting problem and recover an algorithm from this literature as a special case.
• Score: 1.5361702135159843
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: In this paper, we consider a deterministic online linear regression model where we allow the responses to be multivariate. To address this problem, we introduce MultiVAW, a method that extends the well-known Vovk-Azoury-Warmuth algorithm to the multivariate setting, and show that it also enjoys logarithmic regret in time. We apply our results to the online hierarchical forecasting problem and recover an algorithm from this literature as a special case, allowing us to relax the hypotheses usually made for its analysis.

Related papers

• A Simplified Analysis of SGD for Linear Regression with Weight Averaging [64.2393952273612]
  Recent work bycitetzou 2021benign provides sharp rates for SGD optimization in linear regression using constant learning rate.<n>We provide a simplified analysis recovering the same bias and variance bounds provided incitepzou 2021benign based on simple linear algebra tools.<n>We believe our work makes the analysis of gradient descent on linear regression very accessible and will be helpful in further analyzing mini-batching and learning rate scheduling.
  arXiv  Detail & Related papers  (2025-06-18T15:10:38Z)
• Solving Linear Inverse Problems Provably via Posterior Sampling with Latent Diffusion Models [98.95988351420334]
  We present the first framework to solve linear inverse problems leveraging pre-trained latent diffusion models. We theoretically analyze our algorithm showing provable sample recovery in a linear model setting.
  arXiv  Detail & Related papers  (2023-07-02T17:21:30Z)
• Robust Regularized Low-Rank Matrix Models for Regression and Classification [14.698622796774634]
  We propose a framework for matrix variate regression models based on a rank constraint, vector regularization (e.g., sparsity), and a general loss function. We show that the algorithm is guaranteed to converge, all accumulation points of the algorithm have estimation errors in the order of $O(sqrtn)$ally and substantially attaining the minimax rate.
  arXiv  Detail & Related papers  (2022-05-14T18:03:48Z)
• Machine Learning for Multi-Output Regression: When should a holistic multivariate approach be preferred over separate univariate ones? [62.997667081978825]
  Tree-based ensembles such as the Random Forest are modern classics among statistical learning methods. We compare these methods in extensive simulations to help in answering the primary question when to use multivariate ensemble techniques.
  arXiv  Detail & Related papers  (2022-01-14T08:44:25Z)
• Time varying regression with hidden linear dynamics [74.9914602730208]
  We revisit a model for time-varying linear regression that assumes the unknown parameters evolve according to a linear dynamical system. Counterintuitively, we show that when the underlying dynamics are stable the parameters of this model can be estimated from data by combining just two ordinary least squares estimates.
  arXiv  Detail & Related papers  (2021-12-29T23:37:06Z)
• A Variational Inference Approach to Inverse Problems with Gamma Hyperpriors [60.489902135153415]
  This paper introduces a variational iterative alternating scheme for hierarchical inverse problems with gamma hyperpriors. The proposed variational inference approach yields accurate reconstruction, provides meaningful uncertainty quantification, and is easy to implement.
  arXiv  Detail & Related papers  (2021-11-26T06:33:29Z)
• Stochastic Online Linear Regression: the Forward Algorithm to Replace Ridge [24.880035784304834]
  We derive high probability regret bounds for online ridge regression and the forward algorithm. This enables us to compare online regression algorithms more accurately and eliminate assumptions of bounded observations and predictions.
  arXiv  Detail & Related papers  (2021-11-02T13:57:53Z)
• Benign Overfitting of Constant-Stepsize SGD for Linear Regression [122.70478935214128]
  inductive biases are central in preventing overfitting empirically. This work considers this issue in arguably the most basic setting: constant-stepsize SGD for linear regression. We reflect on a number of notable differences between the algorithmic regularization afforded by (unregularized) SGD in comparison to ordinary least squares.
  arXiv  Detail & Related papers  (2021-03-23T17:15:53Z)
• Online Orthogonal Matching Pursuit [6.6389732792316005]
  We present a novel online algorithm: Online Orthogonal Matching Pursuit (OOMP) for online support recovery in the random design setting of sparse linear regression. Our procedure selects features sequentially, alternating between allocation of samples only as needed to candidate features, and optimization over the selected set of variables to estimate the regression coefficients.
  arXiv  Detail & Related papers  (2020-11-22T21:59:05Z)
• A spectral algorithm for robust regression with subgaussian rates [0.0]
  We study a new linear up to quadratic time algorithm for linear regression in the absence of strong assumptions on the underlying distributions of samples. The goal is to design a procedure which attains the optimal sub-gaussian error bound even though the data have only finite moments.
  arXiv  Detail & Related papers  (2020-07-12T19:33:50Z)
• Sparse Methods for Automatic Relevance Determination [0.0]
  We first review automatic relevance determination (ARD) and analytically demonstrate the need to additional regularization or thresholding to achieve sparse models. We then discuss two classes of methods, regularization based and thresholding based, which build on ARD to learn parsimonious solutions to linear problems.
  arXiv  Detail & Related papers  (2020-05-18T14:08:49Z)
• Multiscale Non-stationary Stochastic Bandits [83.48992319018147]
  We propose a novel multiscale changepoint detection method for the non-stationary linear bandit problems, called Multiscale-LinUCB. Experimental results show that our proposed Multiscale-LinUCB algorithm outperforms other state-of-the-art algorithms in non-stationary contextual environments.
  arXiv  Detail & Related papers  (2020-02-13T00:24:17Z)

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.