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Boolean matrix factorization and Boolean matrix completion from noisy observations are desirable unsupervised data-analysis methods due to their interpretability, but hard to perform due to their NP-hardness. We treat these problems as…

We present a general framework for designing efficient algorithms for unsupervised learning problems, such as mixtures of Gaussians and subspace clustering. Our framework is based on a meta algorithm that learns arithmetic circuits in the…

Principal component analysis (PCA) algorithms use neural networks to extract the eigenvectors of the correlation matrix from the data. However, if the process is non-Gaussian, PCA algorithms or their higher order generalisations provide…

Modern technologies are producing datasets with complex intrinsic structures, and they can be naturally represented as matrices instead of vectors. To preserve the latent data structures during processing, modern regression approaches…

The noisy-or and its generalization noisy-max have been utilized to reduce the complexity of knowledge acquisition. In this paper, we present a new representation of noisy-max that allows for efficient inference in general Bayesian…

We tackle the problem of learning linear classifiers from noisy datasets in a multiclass setting. The two-class version of this problem was studied a few years ago by, e.g. Bylander (1994) and Blum et al. (1996): in these contributions, the…

The behavior of the leading singular values and vectors of noisy low-rank matrices is fundamental to many statistical and scientific problems. Theoretical understanding currently derives from asymptotic analysis under one of two regimes:…

Recently years, the attempts on distilling mobile data into useful knowledge has been led to the deployment of machine learning algorithms at the network edge. Principal component analysis (PCA) is a classic technique for extracting the…

We study the high-dimensional inference of a rank-one signal corrupted by sparse noise. The noise is modelled as the adjacency matrix of a weighted undirected graph with finite average connectivity in the large size limit. Using the replica…

The learning with privileged information setting has recently attracted a lot of attention within the machine learning community, as it allows the integration of additional knowledge into the training process of a classifier, even when this…

Quantum protocols on hardware are subject to noise that prohibits performance. Protocols for addressing errors, such as error correction or error mitigation, may fail to combat errors in quantum computation if noise violates critical…

Principal component analysis (PCA) is a classical and ubiquitous method for reducing data dimensionality, but it is suboptimal for heterogeneous data that are increasingly common in modern applications. PCA treats all samples uniformly so…

Subset selection is a fundamental problem in combinatorial optimization, which has a wide range of applications such as influence maximization and sparse regression. The goal is to select a subset of limited size from a ground set in order…

Low-rank matrix completion has been studied extensively under various type of categories. The problem could be categorized as noisy completion or exact completion, also active or passive completion algorithms. In this paper we focus on…

We consider the problem of noisy matrix completion, in which the goal is to reconstruct a structured matrix whose entries are partially observed in noise. Standard approaches to this underdetermined inverse problem are based on assuming…

Differentially private learning algorithms inject noise into the learning process. While the most common private learning algorithm, DP-SGD, adds independent Gaussian noise in each iteration, recent work on matrix factorization mechanisms…

Noisy linear problems have been studied in various science and engineering disciplines. A class of "hard" noisy linear problems can be formulated as follows: Given a matrix $\hat{A}$ and a vector $\mathbf{b}$ constructed using a finite set…

Principal component analysis (PCA) is a well-known tool in multivariate statistics. One significant challenge in using PCA is the choice of the number of components. In order to address this challenge, we propose an exact distribution-based…

The matrix profile (MP) is a data structure computed from a time series which encodes the data required to locate motifs and discords, corresponding to recurring patterns and outliers respectively. When the time series contains noisy data…

Principal component analysis (PCA) is a widely employed statistical tool used primarily for dimensionality reduction. However, it is known to be adversely affected by the presence of outlying observations in the sample, which is quite…