A Nonconvex Framework for Structured Dynamic Covariance Recovery
Authors: Katherine Tsai, Mladen Kolar, Oluwasanmi Koyejo
JMLR 2022 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Empirical results using simulated data and brain imaging data illustrate that our approach outperforms existing baselines. Keywords: dynamic covariance, structured factor model, alternating projected gradient descent, time series data, functional connectivity |
| Researcher Affiliation | Academia | Katherine Tsai EMAIL Department of Electrical and Computer Engineering University of Illinois at Urbana-Champaign Urbana, IL 61801, USA Mladen Kolar EMAIL University of Chicago Booth School of Business Chicago, IL 60637, USA Oluwasanmi Koyejo EMAIL Department of Computer Science, Beckman Institute for Advanced Science and Technology, and Statistics University of Illinois at Urbana-Champaign Urbana, IL 61801, USA |
| Pseudocode | Yes | Algorithm 1 summarizes our initialization procedure. Here, the eigendecomposition of {SN,j}j [J] is performed to obtain initial estimates of V and A . ... Algorithm 1: Spectral initialization After initialization, we iteratively refine the estimates of V and A using an alternating projected gradient descent. In each iteration, the iterates V and A are updated using the gradient of f N, where η denotes the step size. Note that we scale down the step size for the V update by J to balance the magnitude of the gradient. After a gradient update, we project the iterates onto the constraint sets CV and CA to enforce sparsity in V and smoothness in A. Details are given in Algorithm 2. ... Algorithm 2: Dynamic covariance estimation |
| Open Source Code | Yes | The code to implement our procedure is available at: https://github.com/koyejo-lab/dynamicCov.git. |
| Open Datasets | Yes | We use motor task data from the Human Connectome Project functional magnetic resonance imaging (f MRI) data (Van Essen et al., 2013). Data are preprocessed using the existing pipeline (Van Essen et al., 2013), and an additional high-pass filter with a cutofffrequency 0.015Hz to remove physiological noise as recommended by Smith et al. (1999). The data consist of five motor tasks: tapping the right hand, tapping the left foot, wagging the tongue, tapping the right foot, and tapping the left hand. |
| Dataset Splits | Yes | We partition 103 subjects in the Human Connectome Project motor task data set (Van Essen et al., 2013) randomly into a training and testing set. The duration of each task is identical, 27 time points for each activation, and 2 activations in each session. Since each task partially overlaps with others (see Figure 4), we predict the task based on activation blocks rather than on a single time point. We group the estimated covariances {Σj}j [J] and the test data based on the task activation map and perform a nearest-neighbor search. Clustered covariances are denoted as Σtask,i, where task {tapping the right hand, tapping the left foot, wagging the tongue, tapping the right foot, tapping the left hand} and i [54]. The task score for each test data block is defined as ... We repeat the experiment 10 times. In each run, we randomly split the data into a training and testing set. We select the number of training subjects to be N {10, 20, 30, 40, 50} and set the remaining subjects as test sets. |
| Hardware Specification | No | The paper does not explicitly state the hardware specifications (e.g., specific GPU/CPU models, memory details, or cloud resources) used for running the experiments. |
| Software Dependencies | No | The paper mentions 'Python' in Algorithm 6's pseudocode but does not provide specific version numbers for Python or any libraries, frameworks, or solvers used in their implementation. |
| Experiment Setup | Yes | The parameters of the proposed model include the sparsity level s, the rank K, the kernel length scale l, the smoothness coefficient γ, the truncation level δA, and the upper bound c for the constraint. ... In experiments, we find that δA = 10 5 is a good empirical choice and satisfies the sufficient conditions. In the first stage, we perform a grid search on s, K, γ, l and find the configuration that minimizes the Bayesian information criterion bic = log N PK k=1 vk 0 2b LN, where b LN is the maximized Gaussian log-likelihood function. ... Figure 1: Covariance recovery with K = 4, P = 20, J = 50 and σ = 0. ... For M1, we set the window length as W = 20. ... For the model interpretation experiment, we select N = 20 subjects. For each subject, the preprocessed time series of length J = 284 were extracted from P = 375 cortical and subcortical parcels... |