Calculating Optimistic Likelihoods Using (Geodesically) Convex Optimization
Authors: Viet Anh Nguyen, Soroosh Shafieezadeh Abadeh, Man-Chung Yue, Daniel Kuhn, Wolfram Wiesemann
NeurIPS 2019 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We showcase the advantages of working with optimistic likelihoods on a classification problem using synthetic as well as empirical data. We test our theoretical findings in the context of a classification problem, and we report on numerical experiments in Section 4. |
| Researcher Affiliation | Academia | Viet Anh Nguyen Soroosh Shafieezadeh-Abadeh École Polytechnique Fédérale de Lausanne, Switzerland {viet-anh.nguyen, soroosh.shafiee}@epfl.ch Man-Chung Yue The Hong Kong Polytechnic University, Hong Kong manchung.yue@polyu.edu.hk Daniel Kuhn École Polytechnique Fédérale de Lausanne, Switzerland daniel.kuhn@epfl.ch Wolfram Wiesemann Imperial College Business School, United Kingdom ww@imperial.ac.uk |
| Pseudocode | Yes | Algorithm 1 Projected Geodesic Gradient Descent Algorithm |
| Open Source Code | Yes | Our algorithm and all tests are implemented in Python, and the source code is available from https: //github.com/sorooshafiee/Optimistic_Likelihoods. |
| Open Datasets | Yes | We compare the performance of our flexible discriminant rules with standard QDA implementations from the literature on datasets from the UCI repository [4]. [4] K. Bache and M. Lichman. UCI machine learning repository, 2013. Available from http: //archive.ics.uci.edu/ml. |
| Dataset Splits | Yes | In each trial, we randomly select 75% of the data for training and the remaining 25% for testing. The size of the ambiguity set and the regularization parameter are selected using stratified 5-fold cross validation. |
| Hardware Specification | No | No specific hardware details (e.g., GPU/CPU models, memory) used for running experiments are mentioned in the paper. |
| Software Dependencies | No | Our algorithm and all tests are implemented in Python, and the source code is available from https: //github.com/sorooshafiee/Optimistic_Likelihoods. No specific version numbers for Python or any libraries are provided. |
| Experiment Setup | Yes | To study the empirical convergence behavior of Algorithm 1, for n {10, 20, . . . , 100} we generate 100 covariance matrices ˆΣ according to the following procedure. We (i) draw a standard normal random matrix B Rn n and compute A = B + B ; we (ii) conduct an eigenvalue decomposition A = RDRT ; we (iii) replace D with a random diagonal matrix ˆD whose diagonal elements are sampled uniformly from [1, 10]n; and we (iv) set ˆΣ = R ˆDR . For each of these covariance matrices, we set ˆµ = 0, M = 1, x M 1 x for a standard normal random vector x Rn and calculate the optimistic likelihood (6) for ρ = n/100. This choice of ρ ensures that the radius of the ambiguity set scales with n in the same way as the Frobenius norm. ... The size of the ambiguity set and the regularization parameter are selected using stratified 5-fold cross validation. |