Related papers: A generalized information criterion for high-dimen…
Regularized models have been applied in lots of areas, with high-dimensional data sets being popular. Because tuning parameter decides the theoretical performance and computational efficiency of the regularized models, tuning parameter…
Principal component analysis (PCA) is one of the most commonly used statistical procedures with a wide range of applications. This paper considers both minimax and adaptive estimation of the principal subspace in the high dimensional…
A popular model selection approach for generalized linear mixed-effects models is the Akaike information criterion, or AIC. Among others, \cite{vaida05} pointed out the distinction between the marginal and conditional inference depending on…
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…
A general framework for principal component analysis (PCA) in the presence of heteroskedastic noise is introduced. We propose an algorithm called HeteroPCA, which involves iteratively imputing the diagonal entries of the sample covariance…
Principal Component analysis (PCA) is a useful statistical technique that is commonly used for multivariate analysis of correlated variables. It is usually applied as a dimension reduction method: the top principal components (PCs)…
Principal component analysis (PCA) defines a reduced space described by PC axes for a given multidimensional-data sequence to capture the variations of the data. In practice, we need multiple data sequences that accurately obey individual…
The Akaike information criterion (AIC) is a model selection criterion widely used in practical applications. The AIC is an estimator of the log-likelihood expected value, and measures the discrepancy between the true model and the estimated…
Covariances from categorical variables are defined using a regular simplex expression for categories. The method follows the variance definition by Gini, and it gives the covariance as a solution of simultaneous equations. The calculated…
We develop an algorithm for model selection which allows for the consideration of a combinatorially large number of candidate models governing a dynamical system. The innovation circumvents a disadvantage of standard model selection which…
Principal component analysis (PCA) is very popular to perform dimension reduction. The selection of the number of significant components is essential but often based on some practical heuristics depending on the application. Only few works…
Model selection is the problem of distinguishing competing models, perhaps featuring different numbers of parameters. The statistics literature contains two distinct sets of tools, those based on information theory such as the Akaike…
Selecting the number of regimes in Hidden Markov models is an important problem. There are many criteria that are used to select this number, such as Akaike information criterion (AIC), Bayesian information criterion (BIC), integrated…
Principal component analysis (PCA) is a well-established method commonly used to explore and visualise data. A classical PCA model is the fixed effect model where data are generated as a fixed structure of low rank corrupted by noise. Under…
Probabilistic principal component analysis (PPCA) seeks a low dimensional representation of a data set in the presence of independent spherical Gaussian noise, Sigma = (sigma^2)*I. The maximum likelihood solution for the model is an…
In many CAD-based applications, complex geometries are defined by a high number of design parameters. This leads to high-dimensional design spaces that are challenging for downstream engineering processes like simulations, optimization, and…
Model selection is indispensable to high-dimensional sparse modeling in selecting the best set of covariates among a sequence of candidate models. Most existing work assumes implicitly that the model is correctly specified or of fixed…
A system with many degrees of freedom can be characterized by a covariance matrix; principal components analysis (PCA) focuses on the eigenvalues of this matrix, hoping to find a lower dimensional description. But when the spectrum is…
Principal component analysis (PCA) has been widely applied to dimensionality reduction and data pre-processing for different applications in engineering, biology and social science. Classical PCA and its variants seek for linear projections…
Data integration, or the strategic analysis of multiple sources of data simultaneously, can often lead to discoveries that may be hidden in individualistic analyses of a single data source. We develop a new unsupervised data integration…