arXiv research

Bayesian methods reduce variance in subspace identification for small data sets.

Paper unifies subspace identification and DMD for dynamical systems.

SIG model identifies invariant variables for MSDA with fewer domain constraints.

Paper introduces Prob-SSI for robust OMA in noisy data.

We propose a conjugate gradient type optimization technique for the computation of the Karcher mean on the set of complex linear subspaces of fixed dimension, modeled by the so-called Grassmannian. The identification of the Grassmannian with Hermitian projection matrices allows an accessible introduction of the geometr…

Projective DP-SGD reduces privacy error by identifying low-dimensional gradient subspaces.

It is often the case that, within an online recommender system, multiple users share a common account. Can such shared accounts be identified solely on the basis of the userprovided ratings? Once a shared account is identified, can the different users sharing it be identified as well? Whenever such user identification …

Subspace identification is a classical and very well studied problem in system identification. The problem was recently posed as a convex optimization problem via the nuclear norm relaxation. Inspired by robust PCA, we extend this framework to handle outliers. The proposed framework takes the form of a convex optimizat…

This work presents GROUSE (Grassmanian Rank-One Update Subspace Estimation), an efficient online algorithm for tracking subspaces from highly incomplete observations. GROUSE requires only basic linear algebraic manipulations at each iteration, and each subspace update can be performed in linear time in the dimension of…

Paper analyzes and improves GPSP algorithm for block sparse signal recovery.

Robust PCA, the problem of PCA in the presence of outliers has been extensively investigated in the last few years. Here we focus on Robust PCA in the column sparse outlier model. The existing methods for column sparse outlier model assumes either the knowledge of the dimension of the lower dimensional subspace or the …

Optimizes parameters in high-dimensional spaces for practical applications.

Kernel models learn low-dimensional predictive subspaces from input data.

In this paper we consider the problem of group invariant subspace clustering where the data is assumed to come from a union of group-invariant subspaces of a vector space, i.e. subspaces which are invariant with respect to action of a given group. Algebraically, such group-invariant subspaces are also referred to as su…

Active sampling selects few points for accurate model reduction of high-fidelity systems.

This paper solves matrix blind joint block diagonalization with noise.

Paper recovers multi-subspace matrices from permuted data.

New algorithm identifies outliers in PCA without needing parameters.

New algorithm catches moving subspaces in bandit problems.

Efficient algorithms for low-rank bandits using subspace recovery.

In this paper we present deterministic conditions for success of sparse subspace clustering (SSC) under missing data, when data is assumed to come from a Union of Subspaces (UoS) model. We consider two algorithms, which are variants of SSC with entry-wise zero-filling that differ in terms of the optimization problems u…

This paper considers the problem of completing a matrix with many missing entries under the assumption that the columns of the matrix belong to a union of multiple low-rank subspaces. This generalizes the standard low-rank matrix completion problem to situations in which the matrix rank can be quite high or even full r…

In this paper we present deterministic analysis of sufficient conditions for sparse subspace clustering under missing data, when data is assumed to come from a Union of Subspaces (UoS) model. In this context we consider two cases, namely Case I when all the points are sampled at the same co-ordinates, and Case II when …

The paper analyzes system identification with finite data.

New method identifies latent components in PNL mixtures without strong assumptions.

EOMR improves regression accuracy in chaotic systems by identifying relevant feature subsets and subspaces.

Paper proves noise-tolerant SSC using greedy methods under coherence conditions.

Sparse Bayesian learning algorithm for estimating interaction kernels in Motsch-Tadmor model.

ISOKANN learns collective variables and effective dynamics for metastable transitions.

New algorithm updates eigenvectors of evolving graphs efficiently.

Paper models Alzheimer's disease using genotypic, phenotypic, and cognitive data.

We address the structure identification and the uniform approximation of sums of ridge functions $f(x)=\sum_{i=1}^m g_i(a_i\cdot x)$ on ${\mathbb R}^d$, representing a general form of a shallow feed-forward neural network, from a small number of query samples. Higher order differentiation, as used in our constructive a…

Unified framework for disentangled representations using mechanistic independence.

Hidden Markov models have successfully been applied as models of discrete time series in many fields. Often, when applied in practice, the parameters of these models have to be estimated. The currently predominating identification methods, such as maximum-likelihood estimation and especially expectation-maximization, a…

The paper develops Kalman filters for unknown systems with sample complexity bounds.

Over the past years Robust PCA has been established as a standard tool for reliable low-rank approximation of matrices in the presence of outliers. Recently, the Robust PCA approach via nuclear norm minimization has been extended to matrices with linear structures which appear in applications such as system identificat…

We identify and approximate weights of two-layer neural networks from few samples.

Constructs equivariant embeddings of Hermitian symmetric spaces into tangent spaces.

Proposes methods to identify and estimate counterfactual distributions with confounding.

This paper addresses network anomography, that is, the problem of inferring network-level anomalies from indirect link measurements. This problem is cast as a low-rank subspace tracking problem for normal flows under incomplete observations, and an outlier detection problem for abnormal flows. Since traffic data is lar…

Using the L^2 norm of the Higgs field as a Morse function, we study the moduli spaces of U(p,q)-Higgs bundles over a Riemann surface. We require that the genus of the surface be at least two, but place no constraints on (p,q). A key step is the identification of the function's local minima as moduli spaces of holomorph…

New spectral methods improve matrix estimation in RL with low-rank structure.

Proposes a spectral method for jointly smooth functions on multiple manifolds.

Paper uses random projection to preserve subspace structure for efficient data analysis.

Detects missing tensor signals in a KS subspace with high probability.

Paper bounds subspace estimator error from noisy projections.

PCA is one of the most widely used dimension reduction techniques. A related easier problem is "subspace learning" or "subspace estimation". Given relatively clean data, both are easily solved via singular value decomposition (SVD). The problem of subspace learning or PCA in the presence of outliers is called robust su…

Study on vector fields on Lie groups reveals surprising algebraic coincidences.