Monday, Aug 5: 8:30 AM - 10:20 AM
5036
Contributed Papers
Oregon Convention Center
Room: CC-C125
This session will explore aspects of parametric modelling from various viewpoints including robust estimation, machine learning and a nonparametric view.
Main Sponsor
International Statistical Institute
Co Sponsors
International Statistical Institute
Presentations
Prediction performance in practical settings often relies on a single, complex model, which may sacrifice interpretability. The concept of the Rashomon set challenges this paradigm by advocating for a set of equally-performing models rather than a singular one. We introduce the Sparse Wrapper Algorithm (SWAG), a novel multi-model selection method that employs a greedy algorithm combining screening and wrapper approaches. SWAG produces a set of low-dimensional models with high predictive power, offering practitioners the flexibility to choose models aligned with their needs or domain expertise without compromising accuracy. SWAG works in a forward step manner; the user selects a learning mechanism and the SWAG begins by evaluating low-dimensional models. It then systematically builds larger models based on the best-performing ones from previous steps. It results with a set of models called "SWAG models." SWAG's modeling flexibility empowers decision-makers in diverse fields such as genomics, engineering, and neurology. Its adaptability allows it to construct a network revealing the intensity and direction of attribute interactions, providing a more insightful perspective.
Keywords
Prediction accuracy
multi-model selection
SWAG
Interpretability
Feature importance
When independent errors in a linear model have non-identity covariance, the ordinary least squares estimate of the model coefficients is less efficient than the weighted least squares estimate. However, the practical application of weighted least squares is challenging due to its reliance on the unknown error covariance matrix. Although feasible weighted least squares estimates, which use an approximation of this matrix, often outperform the ordinary least squares estimate in terms of efficiency, this is not always the case. In some situations, feasible weighted least squares can be less efficient than ordinary least squares. The comparison between these two estimates has significant implications for the application of regression analysis in varied fields, yet such a comparison remains an unresolved challenge despite its seemingly straightforward nature. In this study, we directly address this challenge by identifying the conditions under which feasible weighted least squares estimates using fixed weights demonstrate greater efficiency than the ordinary least squares estimate. These conditions provide guidance for the design of feasible estimates using random weights. They also shed light on how certain robust regression estimates behave with respect to the linear model with normal errors of unequal variance.
Keywords
heteroscedasticity
M-estimation
linear regression
quasi-convexity
Co-Author
Didong Li
First Author
Jordan Bryan, University of North Carolina at Chapel Hill
Presenting Author
Jordan Bryan, University of North Carolina at Chapel Hill
The conventional statistical models assume the availability of covariates without associated costs, yet real-world scenarios often involve acquisition costs and budget constraints imposed on these variables. Scientists must navigate a trade-off between model accuracy and expenditure within these constraints. In this paper, we introduce fast cost-constrained regression (FCR), designed to tackle such problems with computational and statistical efficiency. Specifically, we develop fast and efficient algorithms to solve cost-constrained problems with the loss function satisfying a quadratic majorization condition. We theoretically establish nonasymptotic error bounds for the algorithm's solution, considering both estimation and selection accuracy. We apply FCR to extensive numerical simulations and four datasets from the National Health and Nutrition Examination Survey. Our method outperforms the latest approaches in various performance measures, while requiring fewer iterations and a shorter runtime.
Keywords
budget constraints
cost
high dimensional regression
non-convex optimiztion
Agent-based and microsimulation models can quickly become structurally and computationally complex, and require substantial efforts to build, parameterize, calibrate and validate. Simpler "back of the envelope" models can provide ballpark estimates in a much shorter time but with lower accuracy. We discuss compensations for complex networks and non-linearities in simpler models with practical applications to policy and epidemiology. We show from the examples of policy evaluation studies how simple models could provide the upper and lower boundaries of the estimates and discuss the utility of population averaged (conditional probabilities), microsimulation, and agent-based models and the tradeoffs of accuracy, cost, and complexity.
Keywords
Agent-based models
Microsimulation models
Model simplification
Population averaged model
Forecasting
Epidemic model
For estimating the average treatment effect in randomized trials, covariate adjustment improves the efficiency of an estimator with minimal impact on bias and type 1 error. However, there have been insufficient comparisons between parametric models and machine learning-based causal inference methods in randomized settings, specifically considering the trade-offs between a specified model's correctness and its parametric constraints. This study aims to compare the efficiency among the following methods: 1) linear regression models, 2) meta-learners (machine learning-based S-, T-, X-, and DR-learners), and 3) augmented inverse probability weighted estimators (semiparametric or nonparametric machine learning-based specification). In simulation study, the efficiency is improved by meta-learners to the same extent as or more than parametric model, regardless of the correctness of the specification of parametric model. However, some methods have issues such as bias to the null for S-learner. Considering both efficiency and bias, we conclude that DR-learner is a viable potion in modest-sized trials.
Keywords
randomized controlled trials
covariate adjustment
machine learning
asymptotic efficiency
model misspecification
semiparametric efficient estimators
Coevolving Latent Space Networks with Attractors (CLSNA), introduced by Zhu et al. (2023; JRSS-A), model dynamic networks where nodes in a latent space represent social actors, and edges indicate their interactions. Attractors are added at the latent level to capture the notion of attractive and repulsive forces between nodes, borrowing ideas from dynamical systems theory. The reliance of previous work on MCMC and the requirement for nodes to be present throughout the study period make scaling difficult. We address these issues by (i) introducing an SGD-based parameter estimation method, (ii) developing a novel approach for uncertainty quantification using SGD, and (iii) extending the model to allow nodes to join and leave. Simulation results suggest that our approach results in little loss of accuracy compared to MCMC, but can scale to much larger networks. We revisit Zhu et al.'s analysis of longitudinal social networks for the US Congress from social media X and reinvestigate positive and negative forces among political elites. We now overcome an important selection bias in the previous study and reveal a negative force at play within the Republican Party.
Keywords
Longitudinal social networks
Attractors
Partisan polarization
Dynamic networks analysis
Co-evolving network model
One argument against statistical tests, which have come under intense criticism recently, is that the null hypothesis is never true ("all models are wrong but some are useful"), and therefore it is not informative to reject it.
Given a (parametric) test, a general nonparametric space of distributions can be split up into distributions for which the rejection probability is either (a) smaller (or equal) or (b) larger than the nominal test level. These constitute the "effective null hypothesis" and "effective alternative" of the test. When tests are applied, normally there is an informal research hypothesis, which would be translated into a set of statistical models. This set can be called the "interpretative null hypothesis" (or "interpretative alternative" depending on how the test problem is formulated). Understanding whether a statistical test is appropriate in such a situation amounts to understanding how the effective hypotheses relate to the interpretative hypotheses. This is essentially different from the question whether the test's model assumptions hold, which is not required to apply it.
Keywords
Foundations of statistics
Frequentism
Statistical tests