Probabilistic Low-Rank Matrix Completion from Quantized Measurements
Authors: Sonia A. Bhaskar
JMLR 2016 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In this section, we test our methods on synthetic and real data, and also compare our methods with that of Keshavan et al. (2009, 2010) (Opt Space), Cai et al. (2010) (SVT), Cai and Zhou (2013) and Davenport et al. (2014). |
| Researcher Affiliation | Academia | Sonia A. Bhaskar EMAIL Department of Electrical Engineering Stanford University Stanford, CA 94305, USA |
| Pseudocode | Yes | Algorithm 3 Block-Coordinate Descent Method for Solving (9) Input: Set of observed entries Yij for (i, j) Ω, initialization U0 Rm k, V 0 Rm k, ω0 1, ω0 2, , ω0 K 1 R, ω0 1 < ω0 2 < < ω0 K 1, parameters α, λ Output: Solution X = U V , ω 1: for ℓ= 1, 2, , until convergence, do Lℓ, Rℓ arg min U,V FΩ,Y (UV , ωℓ 1 1 , , ωℓ 1 K 1) subject to UV α. Solve using approximate projected gradient method (27) initialized with Uℓ 1, V ℓ 1. Uℓ, V ℓ arg min U,V FΩ,Y (UV , ωℓ 1 1 , , ωℓ 1 K 1). Solve using log-barrier gradient method (31) initialized with Lℓ, Rℓ. 4: for i = 1, 2, , K 1, do 5: ωℓ i arg min ωi FΩ,Y (UℓV ℓ , ωℓ 1, , ωℓ i 1, ωi, ωℓ 1 i+1, , ωℓ 1 K 1) subject to ωℓ i 1+δ0 ωi ωℓ 1 i+1 δ0 for some small δ0 > 0 . Solve using a gradient descent method initialized with ωi = ωℓ 1 i . 8: return X = U V , ω |
| Open Source Code | No | Explanation: The paper refers to code for other methods (Opt Space and SVT) that was made available by their respective authors, not the methodology described in this paper. There is no explicit statement from the author about releasing their own code or providing a link to it. |
| Open Datasets | Yes | Now we consider the Movie Lens 1M dataset (available from http://www.grouplens.org) consisting of 1,000,000 movie ratings on a scale from 1 to 5, from 6040 users on 3952 movies (95.8% missing entries). |
| Dataset Splits | Yes | We consider 20 independent realizations of 80%/20% training/test splits of the 1 million revealed entries. |
| Hardware Specification | No | Explanation: The paper does not specify any hardware details like CPU, GPU, or memory used for conducting the experiments. |
| Software Dependencies | No | Explanation: The paper does not specify any software versions for libraries, frameworks, or programming languages used in the implementation. |
| Experiment Setup | Yes | For Algorithm 1 we used α = 1, rank(M) = 7, the logistic model with σ = 1/16, and considered fixed bin boundaries ω0 1 = 0.6, ω0 2 = 0.2, ω0 3 = 0.2 and ω0 4 = 0.6 spaced (arbitrarily) uniformly over [ α, α] to get equal width bins. ... For Algorithm 3, based on additional optimization w.r.t. ω, we used α = 1, rank(M) = 7, initialization ω0 1 = 0.6, ω0 2 = 0.2, ω0 3 = 0.2 and ω0 4 = 0.6, and either the logistic model with σ = 1/16, or the probit model with σ = 1/13. |