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Low-rank multivariate regression (LRMR) is an important statistical learningmodel that combines highly correlated tasks as a multiresponse regressionproblem with low-rank priori on the coefficient matrix. In this paper, we studyquantized LRMR, a practical setting where the responses and/or the covariatesare discretized to finite precision. We focus on the estimation of theunderlying coefficient matrix. To make consistent estimator that could achievearbitrarily small error possible, we employ uniform quantization with randomdithering, i.e., we add appropriate random noise to the data beforequantization. Specifically, uniform dither and triangular dither are used forresponses and covariates, respectively. Based on the quantized data, we proposethe constrained Lasso and regularized Lasso estimators, and derive thenon-asymptotic error bounds. With the aid of dithering, the estimators achieveminimax optimal rate, while quantization only slightly worsens themultiplicative factor in the error rate. Moreover, we extend our results to alow-rank regression model with matrix responses. We corroborate and demonstrateour theoretical results via simulations on synthetic data or image restoration.

Quantized Low-Rank Multivariate Regression with Random Dithering