Sparse PCA via Covariance Thresholding
Authors: Yash Deshpande, Andrea Montanari
NeurIPS 2014 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Figure 1 presents simulations on synthetic data under the strictly sparse model, and the Covariance Thresholding algorithm of Table 1, used in the proof of Theorem 2. The objective is to check whether the log p factor has an impact at moderate p. We compare this with Diagonal Thresholding. We plot the empirical success probability as a function of k/ n for several values of p, with p = n. |
| Researcher Affiliation | Academia | Yash Deshpande Electrical Engineering Stanford University yashd@stanford.edu Andrea Montanari Electrical Engineering and Statistics Stanford University montanari@stanford.edu |
| Pseudocode | Yes | Algorithm 1 Covariance Thresholding |
| Open Source Code | No | The paper does not provide any explicit statements about making its source code publicly available or providing links to a code repository. |
| Open Datasets | No | Figure 1 presents simulations on synthetic data under the strictly sparse model... We plot the empirical success probability as a function of k/ n for several values of p, with p = n. Assume the following model, for i [n] βquq,ivq + σzi. The paper generates its own data and does not provide public access information for it. |
| Dataset Splits | Yes | For notational convenience, we shall assume hereafter that 2n sample vectors are given (instead of n): {xi}1 i 2n. These are distributed according to the model (1). The number of spikes r will be treated as a known parameter in the problem. We start by splitting the data into two halves: (xi)1 i n and (xi)n<i 2n and compute the respective sample covariance matrices G and G respectively. |
| Hardware Specification | No | The paper does not provide any specific hardware details such as GPU/CPU models, memory, or cloud instances used for running experiments. |
| Software Dependencies | No | The paper does not specify any software dependencies with version numbers used for its implementation or experiments. |
| Experiment Setup | Yes | In simulations, a choice 3 ν 4 appears to work well. We use β = 1.4, p = 4096, and the rows correspond to sample sizes n = 1024, 1625, 2580, 4096 respectively. Parameters for Covariance Thresholding are chosen as in Section 3, with ν = 4.5. |