Convergence of an Alternating Maximization Procedure
Authors: Andreas Andresen, Vladimir Spokoiny
JMLR 2016 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | We derive two convergence results for a sequential alternating maximization procedure to approximate the maximizer of random functionals such as the realized log likelihood in MLE estimation. We manage to show that the sequence attains the same deviation properties as shown for the profile M-estimator by Andresen and Spokoiny (2013), that means a finite sample Wilks and Fisher theorem. Further under slightly stronger smoothness constraints on the random functional we can show nearly linear convergence to the global maximizer if the starting point for the procedure is well chosen. Keywords: alternating maximization, alternating minimization, profile maximum likelihood, EM-algorithm, M-estimation, local linear approximation, local concentration, semiparametric. |
| Researcher Affiliation | Academia | Andreas Andresen EMAIL Weierstrass-Institute, Mohrenstr. 39, 10117 Berlin, Germany. Vladimir Spokoiny EMAIL Weierstrass-Institute and Humboldt University Berlin, Higher School of Economics, IITP RAN, MIPT Moscow, Mohrenstr. 39, 10117 Berlin, Germany. All listed institutions are academic or public research institutes. |
| Pseudocode | No | The paper describes mathematical procedures and proofs but does not contain explicitly labeled pseudocode or algorithm blocks. The iterative procedure for alternating maximization is described in prose and mathematical notation in Section 1. |
| Open Source Code | No | The paper does not contain any statements about releasing code or links to source code repositories. |
| Open Datasets | No | The paper discusses theoretical properties of an alternating maximization procedure applied to statistical estimation problems, often referring to 'observed random data' or 'i.i.d. models' and parameters within 'semiparametric models'. It illustrates results with a 'Single Index Model' but does not specify or provide access information for any particular public dataset used for empirical experiments. |
| Dataset Splits | No | The paper is theoretical and does not conduct experiments with specific datasets, therefore, there is no mention of training/test/validation dataset splits. |
| Hardware Specification | No | The paper focuses on theoretical mathematical results and does not describe any experimental hardware specifications. |
| Software Dependencies | No | The paper is theoretical and does not describe specific software dependencies with version numbers for experimental replication. |
| Experiment Setup | No | The paper focuses on theoretical mathematical results and does not provide details of an experimental setup, hyperparameters, or training configurations. |