The paper is devoted to generalization of well-known Michael's Selection theorem on the case of extension dimension.
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48 results for “dimension selection”
Variable selection and dimension reduction are two commonly adopted approaches for high-dimensional data analysis, but have traditionally been treated separately. Here we propose an integrated approach, called sparse gradient learning (SGL), for variable selection and dimension reduction via learning the gradients of t…
An efficient algorithm selects the correct number of latent dimensions in multidimensional probit models.
problem Determining the correct number of latent dimensions in multidimensional probit graded response models.
method Adaptive Bayesian dimension selection framework using cumulative ordered spike-and-slab (COSS) prior and Albert--Chib latent response augmentation.
result The proposed method accurately recovers latent structures and avoids repeated model fitting.
Study provides bounds for estimating intrinsic dimension using Gaussian kernels.
problem Estimating intrinsic dimension from data.
method Finite-sample concentration and anti-concentration bounds for Gaussian kernel sums.
result Explicit dependence on sample size, bandwidth, and geometric parameters.
Introduces greedy feature selection for classifier-dependent feature ranking.
problem Feature selection for classification tasks.
method Greedy feature selection, identifying the most important feature at each step based on the selected classifier.
result Theoretical and numerical benefits of greedy feature selection.
Efficient and Robust Bayesian Selection of Hyperparameters in Dimension Reduction for Visualizationstat.ML
Efficient auto-tuning for DR hyperparameters with BO.
problem Hyperparameter selection in DR for large-scale datasets.
method Bayesian optimization with surrogate model, normalization, subsampling.
result Robust and efficient hyperparameter selection for DR algorithms.
Paper proposes adaptive parameter selection for KGD algorithms.
problem Improving parameter selection for kernel-based gradient descent.
method Integrates bias-variance analysis with splitting method, introduces empirical effective dimension.
result Adaptive parameter selection strategy achieves optimal generalization error bound.
Paper proposes an unsupervised feature selection algorithm with stability guarantees.
problem Feature selection for dimension reduction and interpretability.
method Proposes a novel unsupervised feature selection algorithm with stability guarantees.
result The algorithm has superior generalization performance and stable selected features.
FedSel uses local differential privacy to protect data privacy in federated SGD.
problem Privacy leakage from gradients in federated SGD.
method Two-stage framework with top-k dimension selection and gradient accumulation.
result FedSel reduces privacy leakage by privately selecting important dimensions.
SkMM selects data for finetuning by balancing bias and variance.
problem Balancing bias and variance in high-dimensional finetuning.
method Gradient sketching for bias reduction and moment matching for variance reduction.
result Gradient sketching selects samples efficiently and accurately.
Paper improves Lasso for S&P500 index tracking with post-selection inference.
problem Index tracking for S&P500 with many applications.
method Used Lasso for dimension reduction and post-selection inference.
result Lasso method for S&P500 index tracking shows high performance.
We study the problem of detecting change points (CPs) that are characterized by a subset of dimensions in a multi-dimensional sequence. A method for detecting those CPs can be formulated as a two-stage method: one for selecting relevant dimensions, and another for selecting CPs. It has been difficult to properly contro…
Study reduces dimensions for -means clustering for better accuracy.
problem Improving accuracy of -means clustering with high-dimensional data.
method Four randomized algorithms: two feature selection and two feature extraction.
result Provably accurate approximations of -means clustering are obtained.
Unsupervised dimension selection is an important problem that seeks to reduce dimensionality of data, while preserving the most useful characteristics. While dimensionality reduction is commonly utilized to construct low-dimensional embeddings, they produce feature spaces that are hard to interpret. Further, in applica…
Scalable feature selection improves GBDT model training speed.
problem Efficiently selecting features for GBDT models in high-dimensional settings.
method Developed a scalable forward feature selection method using group testing.
result Significant speedups in training time with competitive model performance.
Bayesian non-parametric model selects latent dimensions automatically.
problem Non-linear, sparse latent variable selection.
method Indian buffet process prior, random Fourier approximation, MCMC sampling.
result Superior performance on synthetic, biological, and text datasets.
New method selects relevant dimensions for better prediction in mixtures.
problem Learning mixtures with limited components for prediction tasks.
method Prediction-focused modeling for mixtures.
result Improves prediction performance compared to non-focused models.
Semi-supervised learning improves classification in high dimensions.
problem Combining labeled and unlabeled data for high-dimensional classification.
method Information theoretic and computational lower bounds analysis for feature selection.
result Semi-supervised learning is advantageous for classification in high dimensions.
High-dimensional data in many machine learning applications leads to computational and analytical complexities. Feature selection provides an effective way for solving these problems by removing irrelevant and redundant features, thus reducing model complexity and improving accuracy and generalization capability of the…
Sparse PCA selects variables with FDR control for improved performance.
problem Sparse PCA selects irrelevant variables when maximizing explained variance.
method Proposes FDR-controlled selection using T-Rex selector.
result Significant performance improvement over traditional sparse PCA.
Dimensionality reduction (DR) on the manifold includes effective methods which project the data from an implicit relational space onto a vectorial space. Regardless of the achievements in this area, these algorithms suffer from the lack of interpretation of the projection dimensions. Therefore, it is often difficult to…
This paper deals with a new filter algorithm for selecting the smallest subset of features carrying all the information content of a data set (i.e. for removing redundant features). It is an advanced version of the fractal dimension reduction technique, and it relies on the recently introduced Morisita estimator of Int…
We extend the Bayesian Information Criterion (BIC), an asymptotic approximation for the marginal likelihood, to Bayesian networks with hidden variables. This approximation can be used to select models given large samples of data. The standard BIC as well as our extension punishes the complexity of a model according to …
AgFlow: Fast Model Selection of Penalized PCA via Implicit Regularization Effects of Gradient Flowcs.LG
AgFlow speeds up model selection in penalized PCA.
problem Efficient model selection in penalized PCA for HDLSS settings.
method Implicit regularization effect of gradient flow to reduce computation complexity.
result AgFlow achieves the complete solution path of L2-penalized PCA.
Feature selection is an important challenge in machine learning. It plays a crucial role in the explainability of machine-driven decisions that are rapidly permeating throughout modern society. Unfortunately, the explosion in the size and dimensionality of real-world datasets poses a severe challenge to standard featur…
A new algorithm reduces regret in high-dimensional online learning problems.
problem High-dimensional covariates with unknown reward function.
method BV-LASSO algorithm incorporating binning and voting for nonparametric variable selection.
result Achieves optimal regret .
In this paper, we propose a test, called Flagged-1-Bit (F1B) test, to study the intrinsic capability of recurrent neural networks in sequence learning. Four different recurrent network models are studied both analytically and experimentally using this test. Our results suggest that in general there exists a conflict be…
New algorithms for clustering and dimension reduction using relative von Neumann entropy.
problem Clustering and dimension reduction for complex data sets.
method Construct graphs from data points, select graph maximizing relative von Neumann entropy, use eigenvectors for dimension reduction.
result Outperforms existing methods on non-trivial data sets.
New algorithms improve model selection in linear bandits with optimal regret.
problem Adapting to unknown model dimension in linear bandits.
method Proposes Pareto optimal algorithms that match a new lower bound.
result No algorithm can achieve regret for all .
Algorithm learns from both labeled and arbitrary test examples, giving guarantees for bounded VC dimension classes.
problem Learning from arbitrary test examples, not just perturbations.
method Selective transductive learning algorithm that outputs abstaining predictions.
result Nontrivial guarantees for bounded VC dimension classes with arbitrary train and test distributions.
New BO method efficiently optimizes high-dimensional functions by automatically selecting variables.
problem Efficiently optimizing functions with high-dimensional domains.
method Exploits variable selection to automatically learn sub-spaces without pre-specified dimensions.
result Empirically validated on synthetic and real problems, demonstrating efficiency.
This work develops rigorous theoretical basis for the fact that deep Bayesian neural network (BNN) is an effective tool for high-dimensional variable selection with rigorous uncertainty quantification. We develop new Bayesian non-parametric theorems to show that a properly configured deep BNN (1) learns the variable im…
Predictive Correlation Screening: Application to Two-stage Predictor Design in High Dimensionstat.ML
We introduce a new approach to variable selection, called Predictive Correlation Screening, for predictor design. Predictive Correlation Screening (PCS) implements false positive control on the selected variables, is well suited to small sample sizes, and is scalable to high dimensions. We establish asymptotic bounds f…
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…
Model selection is indispensable to high-dimensional sparse modeling in selecting the best set of covariates among a sequence of candidate models. Most existing work assumes implicitly that the model is correctly specified or of fixed dimensions. Yet model misspecification and high dimensionality are common in real app…
This paper improves model selection with cross-validation using domain knowledge.
problem Improving model selection with cross-validation risk estimation.
method Establishes distribution-free deviation bounds using VC dimension, formalizes Learning Spaces based on domain knowledge.
result Enhanced generalization through selection of candidate models based on domain knowledge.
As an emerging research direction, online streaming feature selection deals with sequentially added dimensions in a feature space while the number of data instances is fixed. Online streaming feature selection provides a new, complementary algorithmic methodology to enrich online feature selection, especially targets t…
Efficient knockoffs for large-scale feature selection.
problem Large-scale feature selection problems.
method Gaussian model-X knockoffs with efficient methods for solving semidefinite programs.
result Efficient knockoffs can be generated with linear complexity in the dimension.
New method selects better graphs for GGM inference in small sample sizes.
problem Inference of conditional correlations in high-dimensional data with limited samples.
method Composite procedure combining nodewise edge selection and penalised likelihood maximisation.
result Our method produces graphs closer to the true distribution with better KL divergence.
Variable screening is a fast dimension reduction technique for assisting high dimensional feature selection. As a preselection method, it selects a moderate size subset of candidate variables for further refining via feature selection to produce the final model. The performance of variable screening depends on both com…
In this study, we propose an automatic learning method for variables selection based on Lasso in epidemiology context. One of the aim of this approach is to overcome the pretreatment of experts in medicine and epidemiology on collected data. These pretreatment consist in recoding some variables and to choose some inter…
Novel privatization framework for high-dimensional variable selection with differential privacy.
problem High-dimensional controlled variable selection with rigorous FDR control under differential privacy constraints.
method Gaussian Johnson-Lindenstrauss Transformation for privatizing the knockoff matrix.
result The proposed private variable selection procedure maintains statistical power even under strict privacy budgets.
Dimension reduction and variable selection are performed routinely in case-control studies, but the literature on the theoretical aspects of the resulting estimates is scarce. We bring our contribution to this literature by studying estimators obtained via L1 penalized likelihood optimization. We show that the optimize…
The current study proposes a dimension reduction method, stepwise support vector machine (SVM), to reduce the dimensions of large p small n datasets. The proposed method is compared with other dimension reduction methods, namely, the Pearson product difference correlation coefficient (PCCs), recursive feature eliminati…
Variationality of conformal geodesics fails in higher dimensions.
problem The variationality of conformal geodesics in higher dimensions.
method Analysis of conformal geodesics in three and higher dimensions.
result Variationality fails in both parametrized and un-parametrized conformal geodesics in higher dimensions.
New method corrects Laplace/BIC errors in singular models, revealing effective dimension.
problem Laplace/BIC errors in singular models due to incorrect effective dimension assumption.
method RLCT (real log canonical threshold) to correct effective dimension in linear models.
result Correct evidence slope and effective dimension estimation in linear settings.
Scale-adaptive and robust intrinsic dimension estimation via optimal neighbourhood identificationstat.ML
This work introduces a protocol to automatically select the correct range of scales for meaningful Intrinsic Dimension estimation.
problem The Intrinsic Dimension (ID) varies with scale in real-world datasets, leading to erroneous results.
method The protocol selects the correct range of scales by ensuring constant density of data points.
result The method provides a robust and scale-adaptive approach to estimating meaningful Intrinsic Dimension.
Novel unsupervised feature selection method using multi-step Markov transition probability.
problem Neglected relationships between non-adjacent data points in feature selection.
method MMFS (Multi-step Markov transition probability for Feature Selection) approach, employing positive and negative viewpoints.
result MMFS effectively maintains data structure in unsupervised feature selection.