High-Dimensional Covariance Decomposition into Sparse Markov and Independence Models
Authors: Majid Janzamin, Animashree Anandkumar
JMLR 2014 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | 7. Experiments In this section, we provide synthetic and real experimental results for the proposed algorithm. We term our proposed optimization program as ℓ1 +ℓ method and compare it with the well-known ℓ1 method which is a special case of the proposed algorithm when λ = . |
| Researcher Affiliation | Academia | Majid Janzamin EMAIL Animashree Anandkumar EMAIL Department of Electrical Engineering and Computer Science University of California Irvine, CA 92697, USA |
| Pseudocode | No | The paper describes methods using mathematical formulations and theoretical analysis, such as optimization programs (e.g., (4), (6), (7), (19)) and proofs (Appendix A, B, C, D, E, F), but does not present these methods in a structured pseudocode or algorithm block format. |
| Open Source Code | No | The paper states: "The primal optimization program (19) is implemented via the ADMM (Alternating Direction Method of Multipliers) technique proposed in Mohan (2013)." This refers to the use of a third-party implementation, not a release of the authors' own code for the methodology described in this paper. |
| Open Datasets | Yes | The data set includes monthly exchange rates of 19 countries currency with respect to US dollars from October 1983 to January 2012. Thus, the data set has 340 samples of 19 variables. We apply the optimization program (7) with a slight modification... Data set available at http://research.stlouisfed.org/fred2/categories/15/downloaddata. |
| Dataset Splits | No | The paper mentions using "n i.i.d. samples" from a Gaussian model and discusses "sample complexity" in the theoretical analysis. For the experiments, it describes using synthetic data generated based on a model and real-world datasets ("foreign exchange rate data set," "monthly stock returns data") with a certain number of samples (e.g., "340 samples of 19 variables"). However, there is no explicit mention of how these samples are divided into training, validation, or test sets, nor any specific percentages or counts for such splits. |
| Hardware Specification | No | The paper does not provide specific details regarding the hardware (e.g., CPU, GPU models, memory) used to conduct the experiments. It only mentions general computational aspects such as implementing the optimization program via the ADMM technique. |
| Software Dependencies | No | The paper states: "The primal optimization program (19) is implemented via the ADMM (Alternating Direction Method of Multipliers) technique proposed in Mohan (2013)." While it references a specific algorithm and a related arXiv paper, it does not list any specific software packages, libraries, or programming languages with their version numbers that were used for implementation. |
| Experiment Setup | Yes | In section 7.2.1, it states: "The parameter σmin is set to 0.001 in this experiment. The resulting edges of Markov and residual matrices for some moderate choice of regularization parameters γ = 20 and λ = 0.004 are plotted in Figure 8." Section 7.2.2 mentions: "The resulting edges for Markov and residual matrices are plotted in Figure 9 for regularization parameters γ = 2.2e 03 and λ = 1e 04." Additionally, section 7.1.2 discusses specific values for the regularization parameter cγ: "Here, we fix the regularization parameter10 λ = 0.2 and change the regularization parameter γ = cγ p log p/n where cγ {1, 1.3, 2.08, 2.5, 3}." These are specific hyperparameters used in the experimental setup. |