Generalized multi-view model: Adaptive density estimation under low-rank constraints

Authors: Julien Chhor, Olga Klopp, Alexandre B. Tsybakov

JMLR 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Experimental We present the results of numerical experiments on synthetic data. We have performed simulations with different values of parameters d, n and the number of components K. For the experiments, we use the Python implementation of our algorithm. Figures 1 and 2 present numerical experiments with discrete distributions. ... Finally, we provide simulations for the problem of density estimation (Figures 5 and 6).
Researcher Affiliation Academia Julien Chhor EMAIL Toulouse School of Economics, University of Toulouse Capitole, Toulouse, France Olga Klopp EMAIL ESSEC Business School Cergy-Pontoise, France Alexandre B. Tsybakov EMAIL CREST, ENSAE Institut Polytechnique de Paris, France Palaiseau, France
Pseudocode Yes Algorithm 1: Estimation procedure Algorithm 2: Two-dimensional density estimator Algorithm 3: Two-dimensional density estimator Algorithm 4: One-dimensional density estimator
Open Source Code Yes We provide a package for computation available at https://github.com/hi-paris/Lowrankdensity. 1. The code of Lowrankdensity algorithm is available at https://github.com/hi-paris/Lowrankdensity
Open Datasets No We present the results of numerical experiments on synthetic data. We have performed simulations with different values of parameters d, n and the number of components K.
Dataset Splits Yes We use sample splitting to define H(1) Rd1 d2 and H(2) Rd1 d2 as the matrices of empirical frequencies (the histograms) corresponding to the sub-samples (X1, . . . , Xn) and (Xn+1, . . . , X2n) respectively. ... We divide the data into two subsamples of equal size. ... Dividing the second subsample in two equal parts
Hardware Specification No The paper describes numerical experiments and simulations on synthetic data but does not mention any specific hardware used (e.g., GPU/CPU models, memory specifications) for these computations.
Software Dependencies No For the experiments, we use the Python implementation of our algorithm. The paper mentions Python as the implementation language but does not specify any version numbers for Python itself or any required libraries/packages.
Experiment Setup Yes For the experiments, we use the Python implementation of our algorithm. Figures 1 and 2 present numerical experiments with discrete distributions. ... In Figure 1, we fix K = 1 and n = 105, and apply the two estimators on square matrices of size ranging from d = 10 to d = 1600. ... Figure 3 presents the dependence of the total variation error on the rank K for fixed dimension d = 100 and fixed number of observations n = 105. ... We compare the standard histogram density estimator with bin width n 1/4 and our estimator defined by Algorithm 3 with β = 1, K = 1. We let n vary from 1000 to 106.