A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Online detection of abrupt changes in high-dimensional data streams.
problem Detecting abrupt changes in high-dimensional, streaming data with multiple subspaces.
method Dynamic sparse subspace learning approach with multiple structural change-point model, Bayesian information criterion for penalty coefficients selection, and Pruned Exact Linear Time algorithm.
result Effectiveness demonstrated through simulation and real gesture data studies.
Robust PCA methods are typically batch algorithms which requires loading all observations into memory before processing. This makes them inefficient to process big data. In this paper, we develop an efficient online robust principal component methods, namely online moving window robust principal component analysis (OMW…
Dynamic robust PCA refers to the dynamic (time-varying) extension of robust PCA (RPCA). It assumes that the true (uncorrupted) data lies in a low-dimensional subspace that can change with time, albeit slowly. The goal is to track this changing subspace over time in the presence of sparse outliers. We develop and study …
Subspace clustering refers to the problem of clustering unlabeled high-dimensional data points into a union of low-dimensional linear subspaces, assumed unknown. In practice one may have access to dimensionality-reduced observations of the data only, resulting, e.g., from "undersampling" due to complexity and speed con…
Neural recordings are nonstationary time series, i.e. their properties typically change over time. Identifying specific changes, e.g. those induced by a learning task, can shed light on the underlying neural processes. However, such changes of interest are often masked by strong unrelated changes, which can be of physi…
This work studies two interrelated problems - online robust PCA (RPCA) and online low-rank matrix completion (MC). In recent work by Candès et al., RPCA has been defined as a problem of separating a low-rank matrix (true data), L:=[ℓ1,ℓ2,…ℓt,…,ℓtmax] and a sparse matrix (outliers…
To each ribbon graph we assign a so-called L-space, which is a Lagrangian subspace in an even-dimensional vector space with the standard symplectic form. This invariant generalizes the notion of the intersection matrix of a chord diagram. Moreover, the actions of Morse perestroikas (or taking a partial dual) and Vassil…
Unified framework for disentangled representations using mechanistic independence.
problem Identifiability of disentangled latent factors under statistical dependencies.
method Introduces mechanistic independence to characterize latent factors by their actions on observed variables, proposing various independence criteria.
result Establishes conditions for identifiability of latent subspaces without statistical assumptions.
We present SEBOOST, a technique for boosting the performance of existing stochastic optimization methods. SEBOOST applies a secondary optimization process in the subspace spanned by the last steps and descent directions. The method was inspired by the SESOP optimization method for large-scale problems, and has been ada…
EigenGAN discovers interpretable dimensions in GAN layers for semantic control.
problem Lack of explicit dimensions to control semantic attributes in GAN layers.
method EigenGAN embeds linear subspaces with orthogonal bases into each generator layer, learning eigen-dimensions corresponding to semantic attributes via adversarial training.
result EigenGAN can produce samples with continuous changes corresponding to specific semantic attributes.
Recent work in distance metric learning has focused on learning transformations of data that best align with provided sets of pairwise similarity and dissimilarity constraints. The learned transformations lead to improved retrieval, classification, and clustering algorithms due to the better adapted distance or similar…
In this paper, we analyze the geometric structure of an Euclidean submanifold whose osculating spaces form a nonconstant family of proper subspaces of the same dimension. We prove that if the rate of change of the osculating spaces is small, then the submanifold must be a (submanifold of a) ruled submanifold of a very …
We consider the problem of efficient randomized dimensionality reduction with norm-preservation guarantees. Specifically we prove data-dependent Johnson-Lindenstrauss-type geometry preservation guarantees for Ho's random subspace method: When data satisfy a mild regularity condition -- the extent of which can be estima…
A geometric string solution has background fields in overlapping coordinate patches related by diffeomorphisms and gauge transformations, while for a non-geometric background this is generalised to allow transition functions involving duality transformations. Non-geometric string backgrounds arise from T-duals and mirr…
This paper describes a novel approach to change-point detection when the observed high-dimensional data may have missing elements. The performance of classical methods for change-point detection typically scales poorly with the dimensionality of the data, so that a large number of observations are collected after the t…
Detecting emergence of a low-rank signal from high-dimensional data is an important problem arising from many applications such as camera surveillance and swarm monitoring using sensors. We consider a procedure based on the largest eigenvalue of the sample covariance matrix over a sliding window to detect the change. T…
This work examines how adversarial vulnerability changes with the dimensionality of the subspace of perturbations.
problem Understanding adversarial vulnerability in constrained input spaces.
method Investigates adversarial vulnerability in subspace V of the input space X with varying dimensions, using PGD attacks and analyzing the dependence on ε and dim(V)/dim(X).
result Adversarial success of PGD attacks is a monotonically increasing function of $ε( rac{dim(V)}{dim(X)})^{ rac{1}{q}}$.