LIT-LVM: Structured Regularization for Interaction Terms in Linear Predictors using Latent Variable Models

• URL: http://arxiv.org/abs/2506.15492v1
• Date: Wed, 18 Jun 2025 14:30:04 GMT
• Title: LIT-LVM: Structured Regularization for Interaction Terms in Linear Predictors using Latent Variable Models
• Authors: Mohammadreza Nemati, Zhipeng Huang, Kevin S. Xu,
• Abstract summary: We consider the problem of accurately estimating coefficients for interaction terms in linear predictors.<n>We demonstrate that our approach, called LIT-LVM, achieves superior prediction accuracy compared to elastic net and factorization machines.
• Score: 2.4084733805040153
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Some of the simplest, yet most frequently used predictors in statistics and machine learning use weighted linear combinations of features. Such linear predictors can model non-linear relationships between features by adding interaction terms corresponding to the products of all pairs of features. We consider the problem of accurately estimating coefficients for interaction terms in linear predictors. We hypothesize that the coefficients for different interaction terms have an approximate low-dimensional structure and represent each feature by a latent vector in a low-dimensional space. This low-dimensional representation can be viewed as a structured regularization approach that further mitigates overfitting in high-dimensional settings beyond standard regularizers such as the lasso and elastic net. We demonstrate that our approach, called LIT-LVM, achieves superior prediction accuracy compared to elastic net and factorization machines on a wide variety of simulated and real data, particularly when the number of interaction terms is high compared to the number of samples. LIT-LVM also provides low-dimensional latent representations for features that are useful for visualizing and analyzing their relationships.

Related papers

• Detecting and Pruning Prominent but Detrimental Neurons in Large Language Models [68.57424628540907]
  Large language models (LLMs) often develop learned mechanisms specialized to specific datasets.<n>We introduce a fine-tuning approach designed to enhance generalization by identifying and pruning neurons associated with dataset-specific mechanisms.<n>Our method employs Integrated Gradients to quantify each neuron's influence on high-confidence predictions, pinpointing those that disproportionately contribute to dataset-specific performance.
  arXiv  Detail & Related papers  (2025-07-12T08:10:10Z)
• Random Matrix Theory for Deep Learning: Beyond Eigenvalues of Linear Models [51.85815025140659]
  Modern Machine Learning (ML) and Deep Neural Networks (DNNs) often operate on high-dimensional data.<n>In particular, the proportional regime where the data dimension, sample size, and number of model parameters are all large gives rise to novel and sometimes counterintuitive behaviors.<n>This paper extends traditional Random Matrix Theory (RMT) beyond eigenvalue-based analysis of linear models to address the challenges posed by nonlinear ML models.
  arXiv  Detail & Related papers  (2025-06-16T06:54:08Z)
• Sequential-Parallel Duality in Prefix Scannable Models [68.39855814099997]
  Recent developments have given rise to various models, such as Gated Linear Attention (GLA) and Mamba.<n>This raises a natural question: can we characterize the full class of neural sequence models that support near-constant-time parallel evaluation and linear-time, constant-space sequential inference?
  arXiv  Detail & Related papers  (2025-06-12T17:32:02Z)
• Efficient Interpretable Nonlinear Modeling for Multiple Time Series [5.448070998907116]
  This paper proposes an efficient nonlinear modeling approach for multiple time series. It incorporates nonlinear interactions among different time-series variables. Experimental results show that the proposed algorithm improves the identification of the support of the VAR coefficients in a parsimonious manner.
  arXiv  Detail & Related papers  (2023-09-29T11:42:59Z)
• On LASSO for High Dimensional Predictive Regression [0.0]
  This paper examines LASSO, a widely-used $L_1$-penalized regression method, in high dimensional linear predictive regressions. The consistency of LASSO is contingent upon two key components: the deviation bound of the cross product of the regressors and the error term. Using machine learning and macroeconomic domain expertise, LASSO demonstrates strong performance in forecasting the unemployment rate.
  arXiv  Detail & Related papers  (2022-12-14T06:14:58Z)
• Factorized Fusion Shrinkage for Dynamic Relational Data [16.531262817315696]
  We consider a factorized fusion shrinkage model in which all decomposed factors are dynamically shrunk towards group-wise fusion structures. The proposed priors enjoy many favorable properties in comparison and clustering of the estimated dynamic latent factors. We present a structured mean-field variational inference framework that balances optimal posterior inference with computational scalability.
  arXiv  Detail & Related papers  (2022-09-30T21:03:40Z)
• Post-mortem on a deep learning contest: a Simpson's paradox and the complementary roles of scale metrics versus shape metrics [61.49826776409194]
  We analyze a corpus of models made publicly-available for a contest to predict the generalization accuracy of neural network (NN) models. We identify what amounts to a Simpson's paradox: where "scale" metrics perform well overall but perform poorly on sub partitions of the data. We present two novel shape metrics, one data-independent, and the other data-dependent, which can predict trends in the test accuracy of a series of NNs.
  arXiv  Detail & Related papers  (2021-06-01T19:19:49Z)
• The Predictive Normalized Maximum Likelihood for Over-parameterized Linear Regression with Norm Constraint: Regret and Double Descent [12.929639356256928]
  We show that modern machine learning models do not obey a trade-off between the complexity of a prediction rule and its ability to generalize. We use the recently proposed predictive normalized maximum likelihood (pNML) which is the min-max regret solution for individual data. We demonstrate the use of the pNML regret as a point-wise learnability measure on synthetic data and that it can successfully predict the double-decent phenomenon.
  arXiv  Detail & Related papers  (2021-02-14T15:49:04Z)
• Generalized Matrix Factorization: efficient algorithms for fitting generalized linear latent variable models to large data arrays [62.997667081978825]
  Generalized Linear Latent Variable models (GLLVMs) generalize such factor models to non-Gaussian responses. Current algorithms for estimating model parameters in GLLVMs require intensive computation and do not scale to large datasets. We propose a new approach for fitting GLLVMs to high-dimensional datasets, based on approximating the model using penalized quasi-likelihood.
  arXiv  Detail & Related papers  (2020-10-06T04:28:19Z)
• Provably Efficient Neural Estimation of Structural Equation Model: An Adversarial Approach [144.21892195917758]
  We study estimation in a class of generalized Structural equation models (SEMs) We formulate the linear operator equation as a min-max game, where both players are parameterized by neural networks (NNs), and learn the parameters of these neural networks using a gradient descent. For the first time we provide a tractable estimation procedure for SEMs based on NNs with provable convergence and without the need for sample splitting.
  arXiv  Detail & Related papers  (2020-07-02T17:55:47Z)
• Controlling for sparsity in sparse factor analysis models: adaptive latent feature sharing for piecewise linear dimensionality reduction [2.896192909215469]
  We propose a simple and tractable parametric feature allocation model which can address key limitations of current latent feature decomposition techniques. We derive a novel adaptive Factor analysis (aFA), as well as, an adaptive probabilistic principle component analysis (aPPCA) capable of flexible structure discovery and dimensionality reduction. We show that aPPCA and aFA can infer interpretable high level features both when applied on raw MNIST and when applied for interpreting autoencoder features.
  arXiv  Detail & Related papers  (2020-06-22T16:09:11Z)
• Asymptotic Analysis of an Ensemble of Randomly Projected Linear Discriminants [94.46276668068327]
  In [1], an ensemble of randomly projected linear discriminants is used to classify datasets. We develop a consistent estimator of the misclassification probability as an alternative to the computationally-costly cross-validation estimator. We also demonstrate the use of our estimator for tuning the projection dimension on both real and synthetic data.
  arXiv  Detail & Related papers  (2020-04-17T12:47:04Z)

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.