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Multiresolution Matrix Factorization (MMF) was recently introduced as an alternative to the dominant low-rank paradigm in order to capture structure in matrices at multiple different scales. Using ideas from multiresolution analysis (MRA),…
Matrix factorization is a well-studied task in machine learning for compactly representing large, noisy data. In our approach, instead of using the traditional concept of matrix rank, we define a new notion of link-rank based on a…
A multivariate quantile regression model with a factor structure is proposed to study data with many responses of interest. The factor structure is allowed to vary with the quantile levels, which makes our framework more flexible than the…
Collaborative filtering (CF) has achieved great success in the field of recommender systems. In recent years, many novel CF models, particularly those based on deep learning or graph techniques, have been proposed for a variety of…
In real-world federated learning scenarios, participants could have their own personalized labels which are incompatible with those from other clients, due to using different label permutations or tackling completely different tasks or…
Co-clustering is a data mining technique used to extract the underlying block structure between the rows and columns of a data matrix. Many approaches have been studied and have shown their capacity to extract such structures in continuous,…
Large datasets with interactions between objects are common to numerous scientific fields (i.e. social science, internet, biology...). The interactions naturally define a graph and a common way to explore or summarize such dataset is graph…
Matrix Factorization (MF) has found numerous applications in Machine Learning and Data Mining, including collaborative filtering recommendation systems, dimensionality reduction, data visualization, and community detection. Motivated by the…
Spectral clustering is popular among practitioners and theoreticians alike. While performance guarantees for spectral clustering are well understood, recent studies have focused on enforcing ``fairness'' in clusters, requiring them to be…
Dimensionality reduction techniques play an essential role in data analytics, signal processing and machine learning. Dimensionality reduction is usually performed in a preprocessing stage that is separate from subsequent data analysis,…
The imminent need to interpret the output of a Machine Learning model with counterfactual (CF) explanations - via small perturbations to the input - has been notable in the research community. Although the variety of CF examples is…
Constrained low-rank matrix approximations have been known for decades as powerful linear dimensionality reduction techniques to be able to extract the information contained in large data sets in a relevant way. However, such low-rank…
Low-rank matrix factorizations are a class of linear models widely used in various fields such as machine learning, signal processing, and data analysis. These models approximate a matrix as the product of two smaller matrices, where the…
Data fusion models based on Coupled Matrix and Tensor Factorizations (CMTF) have been effective tools for joint analysis of data from multiple sources. While the vast majority of CMTF models are based on the strictly multilinear…
We consider the problem of spectral clustering under group fairness constraints, where samples from each sensitive group are approximately proportionally represented in each cluster. Traditional fair spectral clustering (FSC) methods…
My dissertation revolves around Bayesian approaches towards constrained statistical inference in the factor analysis (FA) model. Two interconnected types of restricted-model selection are considered. These types have a natural connection to…
Feature selection is a core area of data mining with a recent innovation of graph-driven unsupervised feature selection for linked data. In this setting we have a dataset $\mathbf{Y}$ consisting of $n$ instances each with $m$ features and a…
Factorization machines (FMs) are machine learning predictive models based on second-order feature interactions and FMs with sparse regularization are called sparse FMs. Such regularizations enable feature selection, which selects the most…
We tackle the challenge of estimating grouping structures and factor loadings in asset pricing models, where traditional regressions struggle due to sparse data and high noise. Existing approaches, such as those using fused penalties and…
Many clustering schemes are defined by optimizing an objective function defined on the partitions of the underlying set of a finite metric space. In this paper, we construct a framework for studying what happens when we instead impose…