相关论文: Probabilistic Count Matrix Factorization for Singl…

The Principal Component Analysis (PCA) is a data dimensionality reduction technique well-suited for processing data from sensor networks. It can be applied to tasks like compression, event detection, and event recognition. This technique is…

Researchers often have datasets measuring features $x_{ij}$ of samples, such as test scores of students. In factor analysis and PCA, these features are thought to be influenced by unobserved factors, such as skills. Can we determine how…

Principal Component Analysis (PCA) is a well known procedure to reduce intrinsic complexity of a dataset, essentially through simplifying the covariance structure or the correlation structure. We introduce a novel algebraic, model-based…

Matrix factorization methods are linear models, with limited capability to model complex relations. In our work, we use tropical semiring to introduce non-linearity into matrix factorization models. We propose a method called Sparse…

In this work, we are trying to extent the existing photometric redshift regression models from modeling pure photometric data back to the spectra themselves. To that end, we developed a PCA that is capable of describing the input…

Principal Component Analysis (PCA) is the workhorse tool for dimensionality reduction in this era of big data. While often overlooked, the purpose of PCA is not only to reduce data dimensionality, but also to yield features that are…

We perform differential expression analysis of high-throughput sequencing count data under a Bayesian nonparametric framework, removing sophisticated ad-hoc pre-processing steps commonly required in existing algorithms. We propose to use…

Classical methods such as Principal Component Analysis (PCA) and Canonical Correlation Analysis (CCA) are ubiquitous in statistics. However, these techniques are only able to reveal linear relationships in data. Although nonlinear variants…

The idea of representation has been used in various fields of study from data analysis to political science. In this paper, we define representativeness and describe a method to isolate data points that can represent the entire data set.…

The ability to represent complex high dimensional probability distributions in a compact form is one of the key insights in the field of graphical models. Factored representations are ubiquitous in machine learning and lead to major…

Nonnegative matrix factorization (NMF) has an established reputation as a useful data analysis technique in numerous applications. However, its usage in practical situations is undergoing challenges in recent years. The fundamental factor…

Principal component analysis (PCA) is a fundamental tool in multivariate statistics, yet its sensitivity to outliers and limitations in distributed environments restrict its effectiveness in modern large-scale applications. To address these…

Understanding how stochastic gene expression is regulated in biological systems using snapshots of single-cell transcripts requires state-of-the-art methods of computational analysis and statistical inference. A Bayesian approach to…

PCA is often used to visualize data when the rows and the columns are both of interest. In such a setting there is a lack of inferential methods on the PCA output. We study the asymptotic variance of a fixed-effects model for PCA, and…

Count data is becoming more and more ubiquitous in a wide range of applications, with datasets growing both in size and in dimension. In this context, an increasing amount of work is dedicated to the construction of statistical models…

Healthcare decision-making requires not only accurate predictions but also insights into how factors influence patient outcomes. While traditional Machine Learning (ML) models excel at predicting outcomes, such as identifying high risk…

While single-cell RNA sequencing provides an understanding of the transcriptome of individual cells, its high sparsity, often termed dropout, hampers the capture of significant cell-cell relationships. Here, we propose scFP (single-cell…

Connectivity estimation is challenging in the context of high-dimensional data. A useful preprocessing step is to group variables into clusters, however, it is not always clear how to do so from the perspective of connectivity estimation.…

Compact Genetic Algorithms (cGAs) are condensed variants of classical Genetic Algorithms (GAs) that use a probability vector representation of the population instead of the complete population. cGAs have been shown to significantly reduce…

In probabilistic principal component analysis (PPCA), an observed vector is modeled as a linear transformation of a low-dimensional Gaussian factor plus isotropic noise. We generalize PPCA to tensors by constraining the loading operator to…