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Principal component analysis (PCA) is one of the most widely used dimension reduction and multivariate statistical techniques. From a probabilistic perspective, PCA seeks a low-dimensional representation of data in the presence of…
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…
We study parameter estimation in Nonlinear Factor Analysis (NFA) where the generative model is parameterized by a deep neural network. Recent work has focused on learning such models using inference (or recognition) networks; we identify a…
Sparse feature selection is necessary when we fit statistical models, we have access to a large group of features, don't know which are relevant, but assume that most are not. Alternatively, when the number of features is larger than the…
In this article, we derive a Bayesian model to learning the sparse and low rank PARAFAC decomposition for the observed tensor with missing values via the elastic net, with property to find the true rank and sparse factor matrix which is…
The sparse pseudo-input Gaussian process (SPGP) is a new approximation method for speeding up GP regression in the case of a large number of data points N. The approximation is controlled by the gradient optimization of a small set of M…
In sparse principal component analysis we are given noisy observations of a low-rank matrix of dimension $n\times p$ and seek to reconstruct it under additional sparsity assumptions. In particular, we assume here each of the principal…
Slow feature analysis (SFA) is a method for extracting slowly varying features from a quickly varying multidimensional signal. An open source Matlab-implementation sfa-tk makes SFA easily useable. We show here that under certain…
In the study of the brain, there is a hypothesis that sparse coding is realized in information representation of external stimuli, which is experimentally confirmed for visual stimulus recently. However, unlike the specific functional…
We consider learning a sparse pairwise Markov Random Field (MRF) with continuous-valued variables from i.i.d samples. We adapt the algorithm of Vuffray et al. (2019) to this setting and provide finite-sample analysis revealing sample…
Motivation: Modelling methods that find structure in data are necessary with the current large volumes of genomic data, and there have been various efforts to find subsets of genes exhibiting consistent patterns over subsets of treatments.…
In recent years, there is a growing need for processing methods aimed at extracting useful information from large datasets. In many cases the challenge is to discover a low-dimensional structure in the data, often concealed by the existence…
Random feature methods have been successful in various machine learning tasks, are easy to compute, and come with theoretical accuracy bounds. They serve as an alternative approach to standard neural networks since they can represent…
Due to advances in sensors, growing large and complex medical image data have the ability to visualize the pathological change in the cellular or even the molecular level or anatomical changes in tissues and organs. As a consequence, the…
Motivated by cutting-edge applications like cryo-electron microscopy (cryo-EM), the Multi-Reference Alignment (MRA) model entails the learning of an unknown signal from repeated measurements of its images under the latent action of a group…
Sparse coding refers to the pursuit of the sparsest representation of a signal in a typically overcomplete dictionary. From a Bayesian perspective, sparse coding provides a Maximum a Posteriori (MAP) estimate of the unknown vector under a…
In this paper, we introduce a general extension of linear sparse component analysis (SCA) approaches to postnonlinear (PNL) mixtures. In particular, and contrary to the state-of-art methods, our approaches use a weak sparsity source…
Identifying co-varying causal elements in very high dimensional feature space with internal structures, e.g., a space with as many as millions of linearly ordered features, as one typically encounters in problems such as whole genome…
Factor analysis is a statistical technique that explains correlations among observed random variables with the help of a smaller number of unobserved factors. In traditional full factor analysis, each observed variable is influenced by…
We present a novel Bayesian approach for high-dimensional grouped regression under sparsity. We leverage a sparse projection method that uses a sparsity-inducing map to derive an induced posterior on a lower-dimensional parameter space. Our…