We present a robust alternative to principal component analysis (PCA) --- called elliptical component analysis (ECA) --- for analyzing high dimensional, elliptically distributed data. ECA estimates the eigenspace of the covariance matrix of the elliptical data. To cope with heavy-tailed elliptical distributions, a mult…
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48 results for “sparse set”
Sparse-RS framework efficiently attacks models with sparse perturbations.
problem Efficiently attacking models with sparse perturbations in the black-box setting.
method Random search-based Sparse-RS framework for score-based attacks.
result Sparse-RS achieves state-of-the-art success rate and query efficiency.
Picasso is a new library for sparse learning problems in R and Python.
problem Sparse learning problems in high-dimensional data analysis.
method Unified framework of pathwise coordinate optimization with efficient active set selection strategies.
result picasso can efficiently handle large-scale problems.
Study identifies methods for handling sparse data in web settings with contextual bandits.
problem Handling sparse data in web settings with contextual bandits.
method Identified and categorized methods for addressing sparse data issues.
result Updated understanding of sparse data problems using contextual bandits in web settings.
Sparse coding approximates the data sample as a sparse linear combination of some basic codewords and uses the sparse codes as new presentations. In this paper, we investigate learning discriminative sparse codes by sparse coding in a semi-supervised manner, where only a few training samples are labeled. By using the m…
Collaborative Regressionq-bio.QM
We consider the scenario where one observes an outcome variable and sets of features from multiple assays, all measured on the same set of samples. One approach that has been proposed for dealing with this type of data is ``sparse multiple canonical correlation analysis'' (sparse mCCA). All of the current sparse mCCA t…
New algorithms learn sparse set functions in non-orthogonal Fourier bases.
problem Learning sparse set functions in non-orthogonal Fourier bases.
method Novel algorithms using non-orthogonal Fourier transforms.
result At most queries for non-zero Fourier coefficients.
Study confirms sparse coding in whole brain using MRI data.
problem Sparse coding in the whole brain's neural activities.
method Applied various matrix factorization methods to fMRI data.
result Sparse coding hypothesis in information representation in the whole human brain is confirmed.
Many conventional statistical procedures are extremely sensitive to seemingly minor deviations from modeling assumptions. This problem is exacerbated in modern high-dimensional settings, where the problem dimension can grow with and possibly exceed the sample size. We consider the problem of robust estimation of sparse…
The goal of predictive sparse coding is to learn a representation of examples as sparse linear combinations of elements from a dictionary, such that a learned hypothesis linear in the new representation performs well on a predictive task. Predictive sparse coding algorithms recently have demonstrated impressive perform…
Oracle inequality for sparse neural nets adapts to unknown structure.
problem Sparse deep neural nets in nonparametric regression.
method Gibbs posterior distribution with Metropolis-adjusted Langevin algorithms and mixture of uniform priors.
result Oracle inequality showing adaptation to unknown regularity and structure, achieving minimax-optimal rate of convergence.
New methods show sparse portfolios offer no advantage over mean-variance in diversification.
problem Investment diversification and risk management with sparse portfolios.
method Developed and implemented a new estimation procedure for sparse second-order stochastic spanning using a greedy algorithm and Linear Programming.
result No benefit from expanding a sparse opportunity set beyond 45 assets; optimal sparse portfolio reduces tail risk.
Taxicab correspondence analysis visualizes sparse text data sets.
problem Visualization of extremely sparse contingency tables.
method Robust variant of correspondence analysis for sparse data.
result Visualized an 8265-dimensional textual data set.
This paper establishes conditions for sparse signal recovery with sparse measurements.
problem Recovering the support of a sparse signal using noisy projections with sparse measurement matrices.
method Establishes sufficient conditions for successful sparse recovery using sparse measurement matrices.
result A phase transition threshold for sparse recovery in the sparse setting is discovered, revealing a trade-off between sampling complexity and measurement sparsity.
Continuous-time mirror descent solves sparse phase retrieval efficiently.
problem Recovering sparse signals from magnitude-only measurements.
method Continuous-time mirror descent applied to unconstrained empirical risk minimization problem.
result Mirror descent recovers -sparse vectors with minimum non-zero entry order of from Gaussian measurements.
In this thesis we discuss machine learning methods performing automated variable selection for learning sparse predictive models. There are multiple reasons for promoting sparsity in the predictive models. By relying on a limited set of input variables the models naturally counteract the overfitting problem ubiquitous …
Solving Statistical Mechanics on Sparse Graphs with Feedback Set Variational Autoregressive Networkscond-mat.stat-mech
We propose a method for solving statistical mechanics problems defined on sparse graphs. It extracts a small Feedback Vertex Set (FVS) from the sparse graph, converting the sparse system to a much smaller system with many-body and dense interactions with an effective energy on every configuration of the FVS, then learn…
We propose and analyze a novel framework for learning sparse representations, based on two statistical techniques: kernel smoothing and marginal regression. The proposed approach provides a flexible framework for incorporating feature similarity or temporal information present in data sets, via non-parametric kernel sm…
Paper proposes a working set algorithm for non-convex sparse regression with provable convergence.
problem Estimating sparse linear models from high-dimensional data using non-convex regularizers.
method FireWorks algorithm based on non-convex reformulation and leveraging residual geometry.
result Convergence to a stationary point of the full problem with provable guarantees.
In this paper we formally analyse the use of sparse filtering algorithms to perform covariate shift adaptation. We provide a theoretical analysis of sparse filtering by evaluating the conditions required to perform covariate shift adaptation. We prove that sparse filtering can perform adaptation only if the conditional…
The paper analyzes uncertainty quantification in sparse Gaussian process regression with a Brownian motion prior.
problem Analyzing uncertainty in sparse Gaussian process regression with a Brownian motion prior.
method Theoretical guarantees and limitations for pointwise credible sets are derived for a rescaled Brownian motion prior with a sparse variational Gaussian process method.
result Theoretical characterization of asymptotic frequentist coverage for credible sets, distinguishing conservative and overconfident cases.
Sparse coding has been popularly used as an effective data representation method in various applications, such as computer vision, medical imaging and bioinformatics, etc. However, the conventional sparse coding algorithms and its manifold regularized variants (graph sparse coding and Laplacian sparse coding), learn th…
New algorithms approximate Rashomon set for sparse models, aiding expert interaction.
problem Lack of interaction between models and domain experts in classical machine learning.
method Approximate Rashomon set of sparse, generalized additive models using ellipsoids.
result Efficiently approximated Rashomon set facilitates model selection and exploration.
New method for community detection in sparse directed SBMs with exact recovery guarantees.
problem Exact recovery in sparse directed SBMs, especially with growing communities.
method Two-stage procedure: neighborhood-smoothing followed by -means clustering.
result Exact recovery of all community labels with probability tending to one under mild sparsity and separation conditions.
The paper tackles reward-relevance in offline RL with sparse decision dynamics.
problem Offline reinforcement learning with sparse decision dynamics and estimation sparsity.
method Reward-filtered least-squares policy evaluation using thresholded lasso.
result The method provides theoretical guarantees with sample complexity dependent on sparse component size.
Paper develops IFTRR to solve sparse generalized eigenvalue problems efficiently.
problem Finding the leading eigenvector with at most k nonzero entries in sparse generalized eigenvalue problems.
method Inverse-free truncated Rayleigh-Ritz method (IFTRR) with a new truncation strategy.
result IFTRR efficiently finds the support set of the leading eigenvector for large scale problems.
Given two sets of variables, derived from a common set of samples, sparse Canonical Correlation Analysis (CCA) seeks linear combinations of a small number of variables in each set, such that the induced canonical variables are maximally correlated. Sparse CCA is NP-hard. We propose a novel combinatorial algorithm for s…
Transformers excel at sparse token selection, surpassing FCNs in both worst and average cases.
problem Sparse token selection task
method One-layer transformer trained with gradient descent
result Transformers learn sparse token selection and exhibit strong out-of-distribution length generalization
Improved online Lasso reduces regret in sparse linear contextual bandits.
problem Sparse linear contextual bandit problem with inefficient sampling.
method Perturbed adversary approach to alleviate sampling inefficiency.
result Online Lasso achieves regret bound.
msPCA solves sparse PCA for multiple components efficiently.
problem Sparse principal component analysis with multiple components.
method Alternating maximization algorithm for sparse loading vectors, with orthogonality or zero correlation constraints.
result Achieves high variance explained with sparse components and controlled feasibility violations.
A new NMF variant tackles underdetermined problems with sparse and separable assumptions.
problem Underdetermined blind source separation, especially multispectral image unmixing.
method Sparse Separable Nonnegative Matrix Factorization (SSNMF) combining separability and sparsity assumptions. Algorithm based on SNPA and sparse nonnegative least squares.
result In noiseless settings, the algorithm recovers true underlying sources.
We present a supervised-learning algorithm from graph data (a set of graphs) for arbitrary twice-differentiable loss functions and sparse linear models over all possible subgraph features. To date, it has been shown that under all possible subgraph features, several types of sparse learning, such as Adaboost, LPBoost, …
We compute an approximate Fréchet mean for sets of sparse graphs.
problem Characterizing the location of a set of graphs in a metric space.
method We use the pseudometric defined by the ℓ₂ norm of eigenvalues of adjacency matrices.
result We describe an algorithm to approximate the Fréchet mean of a set of graphs.
New method improves robust sparse association estimation.
problem Outliers in high-dimensional data.
method Splitting robust estimation into optimization phases, using augmented Lagrangian and adaptive gradient descent.
result Improved precision over existing methods.
Improves content allocation in educational platforms with sparse data.
problem Imbalanced content allocation and delayed convergence in adaptive strategies.
method Introduces WAPTS, an algorithm that refines Thompson Sampling for data-sparse environments.
result Demonstrates earlier and more reliable identification of promising treatments.
Paper develops an efficient method for conformal prediction in sparse linear models.
problem Computing conformal prediction sets for sparse linear models is computationally infeasible.
method Numerical continuation techniques to approximate the solution path efficiently.
result The method accurately approximates conformal prediction sets for sparse linear models.
Proposes PSCCA for estimating correlations and canonical correlations in sparse count data.
problem Estimating correlations and canonical correlations in sparse count data from next-generation sequencing.
method Probabilistic approach for sparse count data sets (PSCCA).
result PSCCA outperforms other methods in estimating true correlations and canonical correlations at the natural parameter level.
Sparse support vector machine (SVM) is a popular classification technique that can simultaneously learn a small set of the most interpretable features and identify the support vectors. It has achieved great successes in many real-world applications. However, for large-scale problems involving a huge number of samples a…
New methods tackle robust reinforcement learning in sparse, corrupted data.
problem Tackles robust reinforcement learning in sparse, corrupted data.
method Proposes actor-critic methods with sparse robust estimator oracles.
result First non-vacuous guarantees in high-dimensional sparse MDPs with single-policy concentrability coverage.
Efficient sparse attention reduces self-attention complexity and improves model performance.
problem Quadratic compute and memory requirements of self-attention for long sequences.
method Content-based sparse attention with dynamic routing module.
result Routing Transformer achieves state-of-the-art performance on various benchmarks.
Paper proposes ASCCA for sparse CCA with trace Lasso regularization.
problem Sparse CCA in high-dimensional settings with correlated variables.
method Trace Lasso regularization, reformulated to Riemannian manifolds, inexact augmented Lagrangian method.
result Improved stability and interpretation of sparse CCA.
We propose a nonparametric method for detecting nonlinear causal relationship within a set of multidimensional discrete time series, by using sparse additive models (SpAMs). We show that, when the input to the SpAM is a -mixing time series, the model can be fitted by first approximating each unknown function with a …
Paper tackles NAS problem by modeling it as a sparse supernet.
problem Neural Architecture Search (NAS) problem, particularly Mixed-Path Search.
method Model NAS as a sparse supernet with sparsity constraints. Use hierarchical accelerated proximal gradient algorithm for optimization.
result Proposed method finds compact, general, and powerful neural architectures.
New algorithms find half-optimal independent sets in sparse graphs.
problem Finding large independent sets in sparse random graphs.
method Low-degree polynomial algorithms.
result Low-degree polynomial algorithms can find independent sets of half-optimal size.
The paper analyzes methods for sparse Bayesian regression in nonlinear system identification.
problem Learning sparse models in Bayesian regression with nonlinear applications.
method Two classes of methods: regularization and thresholding based, built on automatic relevance determination (ARD).
result Analytical demonstration of favorable performance with sparse solutions in linear problems.
New method for linear bandits with unknown sparsity, improving sparse regret bounds.
problem Sparse regret bounds for unknown sparsity and adversarial action sets.
method Combines online to confidence set conversions with randomized model selection over nested confidence sets.
result First sparse regret bounds for unknown sparsity and adversarial action sets.
Improved Sparse Polyak for high-dimensional M-estimation with sparser solutions.
problem High-dimensional M-estimation problems with potential loss of sparsity and accuracy.
method Variant of Sparse Polyak with optimal thresholding operators.
result Retains desirable scaling properties while achieving sparser and more accurate solutions.
Proposes efficient Bayesian logistic regression for large sparse datasets.
problem Infeasibility of theoretical Bayesian methods for large sparse feature sets.
method Low complexity analytical approximations for sparse online logistic and probit regressions.
result Empirical results show superior performance compared to more complex methods.