LASE improves local network structure visualization by targeting locally low-dimensional regions.
problem Global spectral embedding fails to capture local geometric features in sparse, transitive networks.
method Local Adjacency Spectral Embedding (LASE) using weighted spectral decomposition.
result LASE reveals locally low-dimensional structure, improving local reconstruction and visualization.
Method identifies key features for clustering in high-dimensional data.
problem Understanding hidden patterns in high-dimensional data.
method Unsupervised feature selection based on discriminative power.
result 27 key transcription factors identified, 18 known to define cell states.
Improved RL value function approximation using graph-based feature learning.
problem Accurate value function approximation in high-dimensional state or action spaces.
method Representation policy iteration (RPI) with graph-based feature learning algorithms.
result Node2vec and Variational Graph Auto-Encoder outperform PVFs in low-dimensional feature space.
New model for high rank matrix completion with online and batch methods.
problem Matrix completion for high rank matrices with latent structure.
method Kernel trick to map data into a high dimensional feature space, explicit parametrization of low dimensional subspace, online fitting procedure.
result Online method can handle streaming data and adapt to non-stationary latent structure.
LIT-LVM improves linear predictors by estimating interaction terms with latent vectors.
problem Accurately estimating coefficients for interaction terms in linear predictors.
method Structured regularization using latent vectors to represent features.
result LIT-LVM achieves superior prediction accuracy compared to other methods.
Wasserstein Autoencoders improve model efficiency and interpretability for low-dimensional data.
problem Limited statistical guarantees for WAEs in low-dimensional data.
method Proper network architecture selection and analysis of expected excess risk convergence rates.
result WAEs can learn data distributions efficiently when intrinsic dimension is considered.
CM algorithm improves MMI classifications for unseen instances.
problem Improving classification accuracy for unseen instances using MMI criterion.
method Introduces CM algorithm for MMI classifications, combining semantic and Shannon channels for matching.
result Achieves high mutual information (99%) with minimal iterations in low-dimensional feature spaces.
In a regression setting we propose algorithms that reduce the dimensionality of the features while simultaneously maximizing a statistical measure of dependence known as distance correlation between the low-dimensional features and a response variable. This helps in solving the prediction problem with a low-dimensional…
Develops interpretable low-dimensional kernels with conic discriminant functions.
problem Improving interpretability in kernel-based classification models.
method Gradually constructs simple feature maps leading to interpretable low-dimensional kernels.
result Obtains high accuracy results without extensive hyperparameter tuning.
Method determines latent dimensionality in international trade flows.
problem Finding meaningful low-dimensional latent features in high-dimensional international trade data.
method Proposes a latent dimension determination method based on clustering of nonnegative RESCAL decompositions.
result Validates the latent features against empirical economic facts.
The high-dimensional data setting, in which p >> n, is a challenging statistical paradigm that appears in many real-world problems. In this setting, learning a compact, low-dimensional representation of the data can substantially help distinguish signal from noise. One way to achieve this goal is to perform subspace le…
Feature selection is a dimensionality reduction technique that selects a subset of representative features from high dimensional data by eliminating irrelevant and redundant features. Recently, feature selection combined with sparse learning has attracted significant attention due to its outstanding performance compare…
BO optimized for high dimensions using feature space learning.
problem Scalability of BO to high-dimensional problems.
method Joint learning of low-dimensional feature space and reconstruction mapping.
result Optimization in lower-dimensional subspace simplifies BO problem.
Study on feature learning in Leaky ResNets, explaining bottleneck structure.
problem Understanding feature learning in deep neural networks.
method Lagrangian and Hamiltonian reformulation of representation geodesics.
result Emergence of a bottleneck structure in large effective depth networks.
Kernel models learn low-dimensional predictive subspaces from input data.
problem Learning effective feature transformations in kernel models.
method Study of a compositional kernel ridge regression model.
result Global minimizers of the objective function identify the subspace with high probability.
A new method embeds labels and group information for efficient multi-label classification.
problem Efficient multi-label classification with label sparsity and group structure.
method Identifies label groups, embeds labels and features in a low-dimensional space preserving sparsity and group structure.
result Our method outperforms state-of-the-art algorithms on benchmark datasets.
Visual observations of dynamic phenomena, such as human actions, are often represented as sequences of smoothly-varying features . In cases where the feature spaces can be structured as Riemannian manifolds, the corresponding representations become trajectories on manifolds. Analysis of these trajectories is challengin…
New method scales features for better clustering.
problem Irregular features disrupt classification.
method Spectral clustering with modified feature scales.
result Outperforms existing methods in experiments.
This paper improves conditional multidimensional scaling for incomplete data.
problem Handling missing data in known features for multidimensional scaling.
method Proposes a method to learn low-dimensional configurations with missing known feature values.
result Can learn low-dimensional configurations and impute missing values.
Pruning of redundant or irrelevant instances of data is a key to every successful solution for pattern recognition. In this paper, we present a novel ranking-selection framework for low-length but highly correlated instances. Instead of working in the low-dimensional instance space, we learn a supervised projection to …
Study shows how diffusion models learn on low-dimensional manifolds.
problem Learning efficiency of diffusion models on manifolds.
method Analyzes denoising score matching with random feature neural networks.
result Sample complexity scales linearly with intrinsic dimension, not ambient dimension.
Approximating non-linear kernels using feature maps has gained a lot of interest in recent years due to applications in reducing training and testing times of SVM classifiers and other kernel based learning algorithms. We extend this line of work and present low distortion embeddings for dot product kernels into linear…
New algorithm estimates intrinsic dimension of discrete datasets.
problem Inaccuracies in using continuous methods for discrete datasets.
method Introduced an algorithm to infer intrinsic dimension of discrete spaces.
result Demonstrated accuracy on benchmark datasets and found a small intrinsic dimension in a metagenomic dataset.
We present a method for finding high density, low-dimensional structures in noisy point clouds. These structures are sets with zero Lebesgue measure with respect to the D-dimensional ambient space and belong to a d<D dimensional space. We call them "singular features." Hunting for singular features corresponds to f…
This paper describes a method for learning low-dimensional approximations of nonlinear dynamical systems, based on neural-network approximations of the underlying Koopman operator. Extended Dynamic Mode Decomposition (EDMD) provides a useful data-driven approximation of the Koopman operator for analyzing dynamical syst…
We consider dynamic pricing with many products under an evolving but low-dimensional demand model. Assuming the temporal variation in cross-elasticities exhibits low-rank structure based on fixed (latent) features of the products, we show that the revenue maximization problem reduces to an online bandit convex optimiza…
Word embedding maps words into a low-dimensional continuous embedding space by exploiting the local word collocation patterns in a small context window. On the other hand, topic modeling maps documents onto a low-dimensional topic space, by utilizing the global word collocation patterns in the same document. These two …
We propose Power Slow Feature Analysis, a gradient-based method to extract temporally slow features from a high-dimensional input stream that varies on a faster time-scale, as a variant of Slow Feature Analysis (SFA) that allows end-to-end training of arbitrary differentiable architectures and thereby significantly ext…
Robust method learns nonlinear structures robustly to noise.
problem Learning nonlinear structures in noisy data.
method Robust Non-Linear Matrix Factorization (RNLMF).
result RNLMF achieves noticeable improvements in denoising and clustering.
Data-efficient reinforcement learning (RL) in continuous state-action spaces using very high-dimensional observations remains a key challenge in developing fully autonomous systems. We consider a particularly important instance of this challenge, the pixels-to-torques problem, where an RL agent learns a closed-loop con…
We study the approximate nearest neighbour method for cost-sensitive classification on low-dimensional manifolds embedded within a high-dimensional feature space. We determine the minimax learning rates for distributions on a smooth manifold, in a cost-sensitive setting. This generalises a classic result of Audibert an…
In this paper, we propose the distributed tree kernels (DTK) as a novel method to reduce time and space complexity of tree kernels. Using a linear complexity algorithm to compute vectors for trees, we embed feature spaces of tree fragments in low-dimensional spaces where the kernel computation is directly done with dot…
We consider the binary classification problem when data are large and subject to unknown but bounded uncertainties. We address the problem by formulating the nonlinear support vector machine training problem with robust optimization. To do so, we analyze and propose two bounding schemes for uncertainties associated to …
We investigate the effect of the dimensionality of the representations learned in Deep Neural Networks (DNNs) on their robustness to input perturbations, both adversarial and random. To achieve low dimensionality of learned representations, we propose an easy-to-use, end-to-end trainable, low-rank regularizer (LR) that…
The approximation of nonlinear kernels via linear feature maps has recently gained interest due to their applications in reducing the training and testing time of kernel-based learning algorithms. Current random projection methods avoid the curse of dimensionality by embedding the nonlinear feature space into a low dim…
Deep neural networks have been demonstrated to be vulnerable to adversarial attacks, where small perturbations intentionally added to the original inputs can fool the classifier. In this paper, we propose a defense method, Featurized Bidirectional Generative Adversarial Networks (FBGAN), to extract the semantic feature…
The interpretation of complex high-dimensional data typically requires the use of dimensionality reduction techniques to extract explanatory low-dimensional representations. However, in many real-world problems these representations may not be sufficient to aid interpretation on their own, and it would be desirable to …
Unsupervised method selects genes for tumor subtype discovery.
problem High-dimensional tumor gene expression data with noisy variables and heterogeneity.
method Autoencoders for latent space learning, Multiple Kernel Learning for feature selection, clustering.
result Lower redundancy and better clustering performance compared to benchmarks.
Mamba efficiently learns low-dimensional targets in-context via feature extraction.
problem Learning low-dimensional targets in context for computational efficiency.
method Test-time feature learning of a single-index model using Mamba's pretrained linear-time sequence model.
result Mamba achieves efficient in-context learning of low-dimensional targets via feature extraction.
Proposes a method to learn from multiple views with low-rank embeddings.
problem Learning from multiple views with varying correlations is challenging.
method Multi-view Locality Low-rank Embedding (MvL2E) method that uses low-rank representations and centroid-based scheme.
result MvL2E achieves comparable performance with previous methods on benchmark datasets.
This paper investigates the theoretical foundations of metric learning, focused on three key questions that are not fully addressed in prior work: 1) we consider learning general low-dimensional (low-rank) metrics as well as sparse metrics; 2) we develop upper and lower (minimax)bounds on the generalization error; 3) w…
A new framework CL embeds features and labels for multi-label classification.
problem Exponential growth of output space in multi-label classification.
method Compact Learning (CL) framework that embeds features and labels simultaneously.
result CMLL maximizes label-feature dependency and minimizes label space loss.
Although the recent progress in the deep neural network has led to the development of learnable local feature descriptors, there is no explicit answer for estimation of the necessary size of a neural network. Specifically, the local feature is represented in a low dimensional space, so the neural network should have mo…
Study on low-dimensional adversarial perturbations in classification models.
problem Understanding and quantifying the effectiveness of low-dimensional adversarial perturbations.
method Analytical lower-bounds for fooling rate, considering binary classifiers under generic regularity conditions.
result Rigorous explanation for the success of heuristic methods in generating low-dimensional adversarial perturbations.
CADGMM detects anomalies by capturing complex correlations in data.
problem Detecting anomalies in complex, unstructured data.
method CADGMM uses a graph structure to encode correlations, then a dual-encoder to learn low-dimensional latent space, followed by a Gaussian Mixture Model for anomaly detection.
result CADGMM effectively detects anomalies in real-world datasets.
This paper tackles high-dimensional Bayesian optimization by projecting a manifold into a lower space.
problem High-dimensional optimization of expensive functions with limited labeled data.
method Random linear projection of a manifold embedded in high-dimensional space, combined with semi-supervised learning of the manifold's geometry.
result Our approach outperforms existing high-dimensional BO methods in various synthetic and real-world applications.
Solves kernel dimension reduction while making features interpretable.
problem Making kernel dimension reduction methods interpretable.
method Projects onto a subspace before kernel feature mapping, using ISM for optimization.
result Extends ISM's theoretical guarantees to a family of kernels, enabling broader applicability.
Adversarial robustness in multi-index models is as easy as standard learning.
problem Adversarial robustness in high-dimensional multi-index models.
method Proves that hidden directions of multi-index models offer a Bayes optimal low-dimensional projection for robustness against ℓ2-bounded adversarial perturbations. result Adversarially robust learning is as easy as standard learning, requiring no additional samples.