Mixture Matrix Completion

Authors: Daniel Pimentel-Alarcon

NeurIPS 2018 | Conference PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Experimental We first present a series of synthetic experiments to study the performance of AMMC (Algorithm 1). In our simulations we first generate matrices Uk Rd r and Θk Rr n with i.i.d. N(0, 1) entries to use as bases and coefficients of the low-rank matrices in the mixture, i.e., Xk = UkΘk Rd n. Here d = n = 100, r = 5 and K = 2. With probability (1 p), the (i, j)th entry of XΩwill be missing, and with probability p/K it will be equal to the corresponding entry in Xk. Recall that similar to EM and other alternating approaches, AMMC depends on initialization. Hence, we study the performance of AMMC as a function of both p and the distance δ [0, 1] between {Uk} and their initial estimates (measured as the normalized Frobenius norm of the difference between their projection operators). We measure accuracy using the normalized Frobenius norm of the difference between each Xk and its completion. We considered a success if this quantity was below 10 8. The results of 100 trials are summarized in Figure 2.
Researcher Affiliation Academia Daniel Pimentel-Alarcón Department of Computer Science Georgia State University Atlanta, GA, 30303 pimentel@gsu.edu
Pseudocode Yes The entire procedure is summarized in Algorithm 1, in Appendix D, where we also discuss initialization, generalizations to noise and outliers, and other simple extensions to improve performance.
Open Source Code No The paper does not provide any concrete access information (link, explicit statement of release) to the source code for the described methodology.
Open Datasets Yes To this end, we use the Yale B dataset [64], containing 2432 photos of 38 subjects (64 photos per subject), each photo of size 48 42.
Dataset Splits No The paper mentions running "100 trials" and varying a "sampling rate (p)" but does not explicitly define training, validation, or testing splits with percentages or counts.
Hardware Specification No The paper does not provide specific details about the hardware used for running the experiments (e.g., specific GPU/CPU models).
Software Dependencies No The paper does not provide specific version numbers for any software components used in the experiments.
Experiment Setup Yes In our simulations we first generate matrices Uk Rd r and Θk Rr n with i.i.d. N(0, 1) entries to use as bases and coefficients of the low-rank matrices in the mixture, i.e., Xk = UkΘk Rd n. Here d = n = 100, r = 5 and K = 2. With probability (1 p), the (i, j)th entry of XΩwill be missing, and with probability p/K it will be equal to the corresponding entry in Xk. Recall that similar to EM and other alternating approaches, AMMC depends on initialization. Hence, we study the performance of AMMC as a function of both p and the distance δ [0, 1] between {Uk} and their initial estimates (measured as the normalized Frobenius norm of the difference between their projection operators).