arXiv research

Study explores GAN dynamics for high-dimensional subspace learning.

Research explores flat subspaces in complex projective manifolds using Okounkov bodies.

Geometric framework for SPD matrices preserving subspace structures.

Investigates projections onto explicit subspaces and their variance effects.

New algorithm tackles bilinear bandit problem with low-rank structure.

MISC finds multiple independent clusterings in different subspaces.

WPCA improves subspace recovery robustness to outliers.

Deep ensembles improve model accuracy and robustness, but their theoretical underpinnings are not fully understood.

Study shows how varying levels of supervision and orthonormality constraints affect generalization errors in subspace fitting.

We investigate a Gaussian mixture model (GMM) with component means constrained in a pre-selected subspace. Applications to classification and clustering are explored. An EM-type estimation algorithm is derived. We prove that the subspace containing the component means of a GMM with a common covariance matrix also conta…

Study analyzes perturbations in singular subspaces under random noise.

A method to visualize multidimensional local subspaces using implicit differentiation.

SGD updates align with a low-rank subspace but do not lead to further loss reduction.

This work improves sample efficiency in meta-learning for nonlinear tasks.

A geometric analysis of the time series of returns has been performed in the past and it implied that the most of the systematic information of the market is contained in a space of small dimension. Here we have explored subspaces of this space to find out the relative performance of portfolios formed from the companie…

Study on using random subspaces for ERM with various loss functions.

FCMSC combines multi-view data through feature concatenation for improved clustering.

The paper explores subspaces in hyperbolic lattices and their arithmetic properties.

LDAdam optimizes large models with low memory by adapting to lower-dimensional subspaces.

Researchers use active subspaces to quantify uncertainty in deep generative models for molecular design.

Weakly-supervised RL identifies meaningful tasks, improving performance in complex environments.

Subspace models play an important role in a wide range of signal processing tasks, and this paper explores how the pairwise geometry of subspaces influences the probability of misclassification. When the mismatch between the signal and the model is vanishingly small, the probability of misclassification is determined b…

This paper explores and analyzes two randomized designs for robust Principal Component Analysis (PCA) employing low-dimensional data sketching. In one design, a data sketch is constructed using random column sampling followed by low dimensional embedding, while in the other, sketching is based on random column and row …

We introduce the blind subspace deconvolution (BSSD) problem, which is the extension of both the blind source deconvolution (BSD) and the independent subspace analysis (ISA) tasks. We examine the case of the undercomplete BSSD (uBSSD). Applying temporal concatenation we reduce this problem to ISA. The associated `high …

A new geometry-preserving method for interpreting compositional data.

A new method clusters multi-view data by sharing a common trace-norm of coefficient matrices.

New algorithms optimize matrix manifolds, converging faster than existing methods.

Paper introduces G-LowTESTR for efficient tensor bandits.

A new method for SVGD reduces variance in high dimensions.

Novel approach embeds loss tunnels in neural networks, revealing insights into their structure.

Scalable NAS by factorizing operators into subspaces.

In a recent paper Baker and Bowler introduced matroids over hyperfields, offering a common generalization of matroids, oriented matroids, and linear subspaces of based vector spaces. This paper introduces the notion of a topological hyperfield and explores the generalization of Grassmannians and realization spaces to t…

A method for high-dimensional Bayesian optimization reduces dimensionality using EDR and Gaussian process.

The Nyström method improves learning efficiency for convex losses.

In multi-label learning, each sample is associated with several labels. Existing works indicate that exploring correlations between labels improve the prediction performance. However, embedding the label correlations into the training process significantly increases the problem size. Moreover, the mapping of the label …

Canonical correlation analysis (CCA) is a fundamental statistical tool for exploring the correlation structure between two sets of random variables. In this paper, motivated by recent success of applying CCA to learn low dimensional representations of high dimensional objects, we propose to quantify the estimation loss…

A new method reduces high-dimensional parameter spaces for faster numerical tasks.

It is now known that an extended Gaussian process model equipped with rescaling can adapt to different smoothness levels of a function valued parameter in many nonparametric Bayesian analyses, offering a posterior convergence rate that is optimal (up to logarithmic factors) for the smoothness class the true function be…

Improved Bandit PCA with optimal regret bound.

Optimizes parameters in high-dimensional spaces for practical applications.

We explore the potential of a popular distributional semantics vector space model, word2vec, for capturing meaningful relationships in ecological (complex polyphonic) music. More precisely, the skip-gram version of word2vec is used to model slices of music from a large corpus spanning eight musical genres. In this newl…

Paper detects adversarial attacks in sound classification models.

This paper extends neural collapse to regression problems, revealing key features and structures.

ASEBO optimizes complex functions by learning optimal sensing directions.

A new adaptive kNN classifier outperforms Random Forests.

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…

We will develop simple relations between the arc-lengths of a pair of geodesics that share common end-points. The two geodesics differ only by the requirement that one is constrained to lie in a subspace of the parent manifold. We will present two applications of our results. In the first example we explore the converg…

Proposes a method for multi-view clustering that integrates consistent and complementary graph regularizers.