Related papers: Learning overcomplete, low coherence dictionaries …
We investigate the impact of high-order moments on the learning dynamics of an online Independent Component Analysis (ICA) algorithm under a high-dimensional data model composed of a weighted sum of two non-Gaussian random variables. This…
Sparse Principal Component Analysis (PCA) methods are efficient tools to reduce the dimension (or the number of variables) of complex data. Sparse principal components (PCs) are easier to interpret than conventional PCs, because most…
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…
Independent Component Analysis (ICA) is intended to recover the mutually independent sources from their linear mixtures, and F astICA is one of the most successful ICA algorithms. Although it seems reasonable to improve the performance of F…
Multiview analysis aims at extracting shared latent components from data samples that are acquired in different domains, e.g., image, text, and audio. Classic multiview analysis, e.g., canonical correlation analysis (CCA), tackles this…
We propose a new high dimensional semiparametric principal component analysis (PCA) method, named Copula Component Analysis (COCA). The semiparametric model assumes that, after unspecified marginally monotone transformations, the…
Previous analytical studies of on-line Independent Component Analysis (ICA) learning rules have focussed on asymptotic stability and efficiency. In practice the transient stages of learning will often be more significant in determining the…
Principal Component Analysis (PCA) is a widely utilized technique for dimensionality reduction; however, its inherent lack of interpretability-stemming from dense linear combinations of all feature-limits its applicability in many domains.…
The framework of variational autoencoders allows us to efficiently learn deep latent-variable models, such that the model's marginal distribution over observed variables fits the data. Often, we're interested in going a step further, and…
Spatial Independent Component Analysis (ICA) decomposes the time by space functional MRI (fMRI) matrix into a set of 1-D basis time courses and their associated 3-D spatial maps that are optimized for mutual independence. When applied to…
We propose a new method to detect deepfake images using the cue of the source feature inconsistency within the forged images. It is based on the hypothesis that images' distinct source features can be preserved and extracted after going…
Unsupervised representation learning seeks to recover latent generative factors, yet standard methods relying on statistical independence often fail to capture causal dependencies. A central challenge is identifiability: as established in…
Machine learning models are prone to capturing the spurious correlations between non-causal attributes and classes, with counterfactual data augmentation being a promising direction for breaking these spurious associations. However,…
We study computational-statistical gaps for improper learning in sparse linear regression. More specifically, given $n$ samples from a $k$-sparse linear model in dimension $d$, we ask what is the minimum sample complexity to efficiently (in…
Linear principal component analysis (PCA) can be extended to a nonlinear PCA by using artificial neural networks. But the benefit of curved components requires a careful control of the model complexity. Moreover, standard techniques for…
Modern vision pipelines increasingly rely on pretrained image encoders whose representations are reused across tasks and models, yet these representations are often overcomplete and model-specific. We propose a simple, training-free method…
Canonical correlation analysis (CCA) describes the associations between two sets of variables by maximizing the correlation between linear combinations of the variables in each data set. However, in high-dimensional settings where the…
As a seminal tool in self-supervised representation learning, contrastive learning has gained unprecedented attention in recent years. In essence, contrastive learning aims to leverage pairs of positive and negative samples for…
Principal Component Analysis (PCA) is a method for estimating a subspace given noisy samples. It is useful in a variety of problems ranging from dimensionality reduction to anomaly detection and the visualization of high dimensional data.…
Principal component analysis (PCA) is a widely used technique for data analysis and dimension reduction with numerous applications in science and engineering. However, the standard PCA suffers from the fact that the principal components…