相关论文: When are the most informative components for infer…

We analyse the matrix factorization problem. Given a noisy measurement of a product of two matrices, the problem is to estimate back the original matrices. It arises in many applications such as dictionary learning, blind matrix…

We consider the problem of identifying the sparse principal component of a rank-deficient matrix. We introduce auxiliary spherical variables and prove that there exists a set of candidate index-sets (that is, sets of indices to the nonzero…

Data collection often results in records that have missing values or variables. This investigation compares 3 different data imputation models and identifies their merits by using accuracy measures. Autoencoder Neural Networks, Principal…

High-dimensional, higher-order tensor data are gaining prominence in a variety of fields, including but not limited to computer vision and network analysis. Tensor factor models, induced from noisy versions of tensor decompositions or…

Dictionary learning and component analysis are part of one of the most well-studied and active research fields, at the intersection of signal and image processing, computer vision, and statistical machine learning. In dictionary learning,…

In this paper, we develop new statistical theory for probabilistic principal component analysis models in high dimensions. The focus is the estimation of the noise variance, which is an important and unresolved issue when the number of…

Factorization of matrices where the rank of the two factors diverges linearly with their sizes has many applications in diverse areas such as unsupervised representation learning, dictionary learning or sparse coding. We consider a setting…

This work proposes a component based model for the raw ultrasound signals acquired by the transducer elements. Based on this approach, before undergoing the standard digital processing chain, every sampled raw signal is first decomposed…

With the growing adoption of deep learning models in different real-world domains, including computational biology, it is often necessary to understand which data features are essential for the model's decision. Despite extensive recent…

We introduce a new framework for unsupervised learning of representations based on a novel hierarchical decomposition of information. Intuitively, data is passed through a series of progressively fine-grained sieves. Each layer of the sieve…

Neural speech models build deeply entangled internal representations, which capture a variety of features (e.g., fundamental frequency, loudness, syntactic category, or semantic content of a word) in a distributed encoding. This complexity…

Prior-Fitted Networks (PFNs) amortize Bayesian prediction by meta-learning over a synthetic task prior, but their standard output is a posterior predictive distribution over noisy observations. For sequential decision-making, such as active…

In this paper, we study the problem of principal component analysis with generative modeling assumptions, adopting a general model for the observed matrix that encompasses notable special cases, including spiked matrix recovery and phase…

The Manual labeling of data is and will remain a costly endeavor. For this reason, semi-supervised learning remains a topic of practical importance. The recently proposed Ladder Network is one such approach that has proven to be very…

The low-complexity assumption in linear systems can often be expressed as rank deficiency in data matrices with generalized Hankel structure. This makes it possible to denoise the data by estimating the underlying structured low-rank…

Understanding and quantifying node importance is a fundamental problem in network science and engineering, underpinning a wide range of applications such as influence maximization, social recommendation, and network dismantling. Prior…

This article considers a novel and widely applicable approach to modeling high-dimensional dependent data when a large number of explanatory variables are available and the signal-to-noise ratio is low. We postulate that a $p$-dimensional…

Decision-making in complex systems often relies on machine learning models, yet highly accurate models such as XGBoost and neural networks can obscure the reasoning behind their predictions. In operations research applications,…

This paper investigates the signal detection problem in colored Gaussian noise with an unknown covariance matrix. To be specific, we consider a sample deficient scenario in which the number of signal bearing samples ($n$) is strictly…

Let $A$ be an $m \times n$ matrix with rank $r$ and spectral decomposition $A = \sum_{i=1}^r \sigma_i u_i v_i^\top,$ where $\sigma_i$ are its singular values, ordered decreasingly, and $u_i, v_i$ are the corresponding left and right…