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Privacy preservation has become a critical concern in high-dimensional data analysis due to the growing prevalence of data-driven applications. Since its proposal, sliced inverse regression has emerged as a widely utilized statistical…
We consider whether algorithmic choices in over-parameterized linear matrix factorization introduce implicit regularization. We focus on noiseless matrix sensing over rank-$r$ positive semi-definite (PSD) matrices in $\mathbb{R}^{n \times…
Matrix-variate time series data are increasingly popular in economics, statistics, and environmental studies, among other fields. This paper develops regularized estimation methods for analyzing high-dimensional matrix-variate time series…
Matrix factorization is a popular approach to solving matrix estimation problems based on partial observations. Existing matrix factorization is based on least squares and aims to yield a low-rank matrix to interpret the conditional sample…
We propose a method that meta-learns a knowledge on matrix factorization from various matrices, and uses the knowledge for factorizing unseen matrices. The proposed method uses a neural network that takes a matrix as input, and generates…
Compression has emerged as one of the essential deep learning research topics, especially for the edge devices that have limited computation power and storage capacity. Among the main compression techniques, low-rank compression via matrix…
Despite their promise, fair machine learning methods often yield Pareto-inefficient models, in which the performance of certain groups can be improved without degrading that of others. This issue arises frequently in traditional…
Matrix square roots and their inverses arise frequently in machine learning, e.g., when sampling from high-dimensional Gaussians $\mathcal{N}(\mathbf 0, \mathbf K)$ or whitening a vector $\mathbf b$ against covariance matrix $\mathbf K$.…
Optimization of machine learning models is commonly performed through stochastic gradient updates on randomly ordered training examples. This practice means that sub-epochs comprise of independent random samples of the training data that…
We investigate the problem of maximizing the sum-rate performance of a beyond-diagonal reconfigurable intelligent surface (BD-RIS)-aided multi-user (MU)-multiple-input single-output (MISO) system using fractional programming (FP)…
Sharpe Ratio (SR) is a critical parameter in characterizing financial time series as it jointly considers the reward and the volatility of any stock/portfolio through its variance. Deriving online algorithms for optimizing the SR is…
Mixed-integer programming (MIP) has emerged as a powerful framework for learning optimal decision trees. Yet, existing MIP approaches for regression tasks are either limited to purely binary features or become computationally intractable…
Sliced Inverse Regression (SIR) is an effective method for dimension reduction in high-dimensional regression problems. The original method, however, requires the inversion of the predictors covariance matrix. In case of collinearity…
Binary matrix factorisation is an essential tool for identifying discrete patterns in binary data. In this paper we consider the rank-k binary matrix factorisation problem (k-BMF) under Boolean arithmetic: we are given an n x m binary…
Matrix factorization is a very common machine learning technique in recommender systems. Bayesian Matrix Factorization (BMF) algorithms would be attractive because of their ability to quantify uncertainty in their predictions and avoid…
We study the multivariate square-root lasso, a method for fitting the multivariate response linear regression model with dependent errors. This estimator minimizes the nuclear norm of the residual matrix plus a convex penalty. Unlike…
In this paper, we address the challenge of differential privacy in the context of graph cuts, specifically focusing on the multiway cut and the minimum $k$-cut. We introduce edge-differentially private algorithms that achieve nearly optimal…
Multiple rotation averaging plays a crucial role in computer vision and robotics domains. The conventional optimization-based methods optimize a nonlinear cost function based on certain noise assumptions, while most previous learning-based…
Sparse regularization techniques are well-established in machine learning, yet their application in neural networks remains challenging due to the non-differentiability of penalties like the $L_1$ norm, which is incompatible with stochastic…
Gradient descent for matrix factorization exhibits an implicit bias toward approximately low-rank solutions. While existing theories often assume the boundedness of iterates, empirically the bias persists even with unbounded sequences. This…