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Wavelet Transforms are a widely used technique for decomposing a signal into coefficient vectors that correspond to distinct frequency/scale bands while retaining time localization. This property enables an adaptive analysis of signals at…
The concept of quantum correlation matrix for observables leads to the application of the PCA (Principal Component Analysis) also for quantum system in Hilbert space. It is shown that, in the case of a 2x2 spin system where the observables…
Deep latent-variable models learn representations of high-dimensional data in an unsupervised manner. A number of recent efforts have focused on learning representations that disentangle statistically independent axes of variation by…
With automated measurements, large data sets can be assembled with relative ease. Often these data sets have a large degree of variance. Nonetheless, we hope to find groups within the data set with shared distinguishing characteristics.…
In representation learning and non-linear dimension reduction, there is a huge interest to learn the 'disentangled' latent variables, where each sub-coordinate almost uniquely controls a facet of the observed data. While many regularization…
Solving structured systems of linear equations in a non-centralized fashion is an important step in many distributed optimization and control algorithms. Fast convergence is required in manifold applications. Known decentralized algorithms,…
The existing experimental evidence on the vector and axial-vector coupling constants, $G_V$ and $G_A$, for neutron $\beta$-decay exhibits two prominent problems: (i) the unitarity for the first row of the CKM matrix seems violated; (ii) one…
Reciprocal transformations mix the role of the dependent and independent variables to achieve simpler versions or even linearized versions of nonlinear PDEs. These transformations help in the identification of a plethora of PDEs available…
We consider the problem of decomposing a large covariance matrix into the sum of a low-rank matrix and a diagonally dominant matrix, and we call this problem the "Diagonally-Dominant Principal Component Analysis (DD-PCA)". DD-PCA is an…
Singular value decomposition (SVD) based principal component analysis (PCA) breaks down in the high-dimensional and limited sample size regime below a certain critical eigen-SNR that depends on the dimensionality of the system and the…
Principal component analysis (PCA) is a widely employed statistical tool used primarily for dimensionality reduction. However, it is known to be adversely affected by the presence of outlying observations in the sample, which is quite…
We study distributed principal component analysis (PCA) in high-dimensional settings under the spiked model. In such regimes, sample eigenvectors can deviate significantly from population ones, introducing a persistent bias. Existing…
We study a distributed estimation problem in which two remotely located parties, Alice and Bob, observe an unlimited number of i.i.d. samples corresponding to two different parts of a random vector. Alice can send $k$ bits on average to…
Decoupling inequalities disentangle complex dependence structures of random objects so that they can be analyzed by means of standard tools from the theory of independent random variables. We study decoupling inequalities for vector-valued…
Recognizing elementary underlying concepts from observations (disentanglement) and generating novel combinations of these concepts (compositional generalization) are fundamental abilities for humans to support rapid knowledge learning and…
We consider large random matrices with a general slowly decaying correlation among its entries. We prove universality of the local eigenvalue statistics and optimal local laws for the resolvent away from the spectral edges, generalizing the…
We analyze the Accelerated Noisy Power Method, an algorithm for Principal Component Analysis in the setting where only inexact matrix-vector products are available, which can arise for instance in decentralized PCA. While previous works…
Modeling variability in tensor decomposition methods is one of the challenges of source separation. One possible solution to account for variations from one data set to another, jointly analysed, is to resort to the PARAFAC2 model. However,…
An algorithm is described for the construction of actions for scalar, spinor, and vector gauge fields that remains well-defined when the metric is degenerate and that involve no contravariant tensor fields. These actions produce the…
We propose three measures of mutual dependence between multiple random vectors. All the measures are zero if and only if the random vectors are mutually independent. The first measure generalizes distance covariance from pairwise dependence…