Related papers: Non-Gaussian Component Analysis via Lattice Basis …
Non-gaussian component analysis (NGCA) introduced in offered a method for high dimensional data analysis allowing for identifying a low-dimensional non-Gaussian component of the whole distribution in an iterative and structure adaptive way.…
The problem of Non-Gaussian Component Analysis (NGCA) is about finding a maximal low-dimensional subspace $E$ in $\mathbb{R}^n$ so that data points projected onto $E$ follow a non-gaussian distribution. Although this is an appropriate model…
Non-Gaussian component analysis (NGCA) is a problem in multidimensional data analysis which, since its formulation in 2006, has attracted considerable attention in statistics and machine learning. In this problem, we have a random variable…
Non-Gaussian Component Analysis (NGCA) is the statistical task of finding a non-Gaussian direction in a high-dimensional dataset. Specifically, given i.i.d.\ samples from a distribution $P^A_{v}$ on $\mathbb{R}^n$ that behaves like a known…
Non-Gaussian component analysis (NGCA) is aimed at identifying a linear subspace such that the projected data follows a non-Gaussian distribution. In this paper, we propose a novel NGCA algorithm based on log-density gradient estimation.…
Non-Gaussian component analysis (NGCA) is an unsupervised linear dimension reduction method that extracts low-dimensional non-Gaussian "signals" from high-dimensional data contaminated with Gaussian noise. NGCA can be regarded as a…
Independent component analysis (ICA) decomposes multivariate data into mutually independent components (ICs). The ICA model is subject to a constraint that at most one of these components is Gaussian, which is required for model…
We study the complexity of Non-Gaussian Component Analysis (NGCA) in the Statistical Query (SQ) model. Prior work developed a general methodology to prove SQ lower bounds for this task that have been applicable to a wide range of contexts.…
Probabilistic Component Latent Analysis (PLCA) is a statistical modeling method for feature extraction from non-negative data. It has been fruitfully applied to various research fields of information retrieval. However, the EM-solved…
Sparse non-Gaussian component analysis (SNGCA) is an unsupervised method of extracting a linear structure from a high dimensional data based on estimating a low-dimensional non-Gaussian data component. In this paper we discuss a new…
Independent component analysis (ICA) is popular in many applications, including cognitive neuroscience and signal processing. Due to computational constraints, principal component analysis is used for dimension reduction prior to ICA…
Nonlinear independent component analysis (nICA) aims at recovering statistically independent latent components that are mixed by unknown nonlinear functions. Central to nICA is the identifiability of the latent components, which had been…
This work studies information-computation gaps for statistical problems. A common approach for providing evidence of such gaps is to show sample complexity lower bounds (that are stronger than the information-theoretic optimum) against…
The statistical dependencies which independent component analysis (ICA) cannot remove often provide rich information beyond the linear independent components. It would thus be very useful to estimate the dependency structure from data.…
Dimensionality reduction is critical across various domains of science including neuroscience. Probabilistic Principal Component Analysis (PPCA) is a prominent dimensionality reduction method that provides a probabilistic approach unlike…
Distributed Principal Component Analysis (PCA) has been studied to deal with the case when data are stored across multiple machines and communication cost or privacy concerns prohibit the computation of PCA in a central location. However,…
Dimensionality reduction is a crucial step for pattern recognition and data mining tasks to overcome the curse of dimensionality. Principal component analysis (PCA) is a traditional technique for unsupervised dimensionality reduction, which…
Given a single observation from a Gaussian distribution with unknown mean $\theta$, we design computationally efficient procedures that can approximately generate an observation from a different target distribution $Q_{\theta}$ uniformly…
Sparse canonical correlation analysis (CCA) is a useful statistical tool to detect latent information with sparse structures. However, sparse CCA works only for two datasets, i.e., there are only two views or two distinct objects. To…
We consider linear non-Gaussian structural equation models that involve latent confounding. In this setting, the causal structure is identifiable, but, in general, it is not possible to identify the specific causal effects. Instead, a…