Instability, Computational Efficiency and Statistical Accuracy
Authors: Nhat Ho, Koulik Khamaru, Raaz Dwivedi, Martin J. Wainwright, Michael I. Jordan, Bin Yu
JMLR 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We begin in Section 2.1 with simulations that illustrate the phenomena to be investigated in this paper. We then introduce some definitions and discuss different properties of the sample and population operators. Section 3 is devoted to statements of our general computational and statistical guarantees with detailed proofs presented in Appendix A. In Section 4, we apply our general results to demonstrate the trade-offbetween stable and unstable methods for several examples. We conclude with a discussion of potential future work in Section 5. Proofs of supporting lemmas and technical results are provided in the appendices. Figure 1 provides some plots that summarize some results from these simulations. |
| Researcher Affiliation | Academia | Nhat Ho EMAIL Department of Statistics and Data Sciences University of Texas, Austin Koulik Khamaru EMAIL Department of Statistics Rutgers University Raaz Dwivedi EMAIL Department of Operations Research & Information Engineering Cornell Martin J. Wainwright EMAIL Department of EECS, Department of Mathematics Massachusetts Institute of Technology Michael I. Jordan EMAIL Department of EECS, Department of Statistics University of California, Berkeley INRIA, Paris Bin Yu EMAIL Department of EECS, Department of Statistics University of California, Berkeley |
| Pseudocode | No | The paper describes iterative algorithms (gradient descent, Newton's method, EM algorithm) using mathematical update equations and textual descriptions of their steps, but it does not include any explicitly labeled 'Pseudocode' or 'Algorithm' blocks, nor structured, code-like formatted procedures. |
| Open Source Code | No | License: CC-BY 4.0, see https://creativecommons.org/licenses/by/4.0/. Attribution requirements are provided at http://jmlr.org/papers/v26/22-0300.html. The paper provides licensing and attribution information for the publication itself but does not explicitly state that source code for the methodology described in the paper is released or provide a link to a code repository. |
| Open Datasets | No | We first consider a certain class of statistical estimation problems in which there are interesting differences between algorithms. Here we keep the discussion very brief; see Section 4.3 for a more detailed discussion. We consider a simple type of non-linear regression model, one based on a function f : Rd -> R that can be written in the form f(x) = g ( x, θ ) for some parameter vector θ Rd, and some univariate function g : R -> R. In the simplest setting considered here, the univariate function g is known, and we have a parametric family of functions as θ ranges over Rd; when g is unknown, we have a semi-parametric family. Now suppose that we are given a collection of pairs {(Xi, Yi)}n i=1, generated from a noisy regression model of the form Yi = g ( Xi, θ ) + ξi, for i = 1, . . . , n. (2) The paper uses synthetic data generated from described statistical models (e.g., noisy regression models, standard normal distribution for Gaussian mixtures, or specific distributions for non-response models) for its simulations rather than referring to publicly available datasets or providing access information for any external datasets. |
| Dataset Splits | No | The paper uses synthetic data generated from statistical models. For example, in Section 2.1, it describes data generated from a 'noisy regression model'. In Section 4.2, it refers to 'n i.i.d. draws from the standard normal distribution'. Since the data is generated for simulation purposes rather than using a fixed external dataset, there are no traditional train/test/validation splits described. |
| Hardware Specification | No | The paper includes simulations and computational studies but does not provide any specific details about the hardware (e.g., CPU, GPU models, memory) used to run these experiments or simulations. |
| Software Dependencies | No | The paper describes various algorithms (e.g., gradient descent, Newton's method, EM algorithm) and their theoretical properties and empirical behavior. However, it does not specify any software names with version numbers (e.g., programming languages, libraries, or frameworks) used for implementation or analysis. |
| Experiment Setup | No | The paper discusses algorithmic properties and convergence rates, and presents simulation results. It specifies general parameters like a 'step-size η' for gradient descent (e.g., 'η (0, 8/3)' or 'η (0, 1 / ((4p-1)!!(2p)))') and initialization conditions like 'θ0 B(θ , ρ/2)'. However, it does not provide specific hyperparameter values (e.g., exact numerical values for η, batch sizes, number of epochs) or system-level training configurations used to generate the plots in Figures 1, 2, 4, or 6. |