Support vector regression (SVR) has been widely used to reduce the high computational cost of computer simulation. SVR assumes the input parameters have equal sample sizes, but unequal sample sizes are often encountered in engineering practices. To solve this issue, a new prediction approach based on SVR, namely as hig…
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48 results for “low sample size”
We introduce and develop a novel approach to outlier detection based on adaptation of random subspace learning. Our proposed method handles both high-dimension low-sample size and traditional low-dimensional high-sample size datasets. Essentially, we avoid the computational bottleneck of techniques like minimum covaria…
In statistical connectomics, the quantitative study of brain networks, estimating the mean of a population of graphs based on a sample is a core problem. Often, this problem is especially difficult because the sample or cohort size is relatively small, sometimes even a single subject. While using the element-wise sampl…
We consider the problem of providing nonparametric confidence guarantees for undirected graphs under weak assumptions. In particular, we do not assume sparsity, incoherence or Normality. We allow the dimension to increase with the sample size . First, we prove lower bounds that show that if we want accurate infe…
SPreVcs.GR
SPREV simplifies visualization of complex labeled datasets.
problem Challenges of reducing dimensions and visualizing labeled datasets with small class size, high dimensionality, and low sample size.
method SPREV uses a novel dimensionality reduction technique integrating geometric principles.
result SPREV effectively visualizes hidden patterns in complex labeled datasets.
LoCoV reduces portfolio optimization errors from sample covariance matrices.
problem Large errors in sample covariance matrix for optimal portfolio weights.
method LoCoV (low dimension covariance voting) algorithm to reduce these errors.
result LoCoV outperforms classical methods in portfolio optimization experiments.
In high-dimension, low-sample size (HDLSS) data, it is not always true that closeness of two objects reflects a hidden cluster structure. We point out the important fact that it is not the closeness, but the "values" of distance that contain information of the cluster structure in high-dimensional space. Based on this …
We consider the problem of exact recovery of any matrix of rank from a small number of observed entries via the standard nuclear norm minimization framework. Such low-rank matrices have degrees of freedom . We show that any arbitrary low-rank matrices can be recovered exa…
High-dimensional data models, often with low sample size, abound in many interdisciplinary studies, genomics and large biological systems being most noteworthy. The conventional assumption of multinormality or linearity of regression may not be plausible for such models which are likely to be statistically complex due …
Proposes a novel classification criterion for high-dimensional data with few samples.
problem Challenges in classifying high-dimensional data with limited samples.
method Tolerance similarity criterion and No-separated Data Maximum Dispersion classifier (NPDMD).
result NPDMD outperforms state-of-the-art methods in various real-world applications.
Proposes a VAE for HDLSS data augmentation.
problem Data augmentation in HDLSS settings with small sample sizes.
method Geometry-based variational autoencoder with latent space modeling.
result Significant improvement in classification metrics (e.g., balanced accuracy from 66.3% to 74.3%).
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.
Classification and clustering are both important topics in statistical learning. A natural question herein is whether predefined classes are really different from one another, or whether clusters are really there. Specifically, we may be interested in knowing whether the two classes defined by some class labels (when t…
Unified framework for statistical inference of low-rank tensors.
problem Statistical inference for tensors in high-dimensional data.
method Unified framework using debiasing and tangent space projection.
result Achieves asymptotic normality and minimax-optimal confidence intervals.
Enhances classification accuracy on low data sets using synthetic data.
problem Low sample size in data augmentation.
method Variational Autoencoder and manifold sampling.
result Significant improvement in classification accuracy (e.g., 88.6% vs 80.7%).
NPMD uses CNNs to optimize policies on low-dimensional manifolds, reducing sample complexity.
problem Explaining the effectiveness of deep policy gradient methods in high-dimensional RL.
method Neural policy mirror descent (NPMD) with CNNs, considering state spaces as low-dimensional manifolds.
result NPMD finds ε-optimal policies with O(ε^(-d/α-2)) samples, leveraging low-dimensional structure.
In this paper, we consider asymptotic properties of the support vector machine (SVM) in high-dimension, low-sample-size (HDLSS) settings. We show that the hard-margin linear SVM holds a consistency property in which misclassification rates tend to zero as the dimension goes to infinity under certain severe conditions. …
Feature selection from wide datasets leads to misleading results.
problem Feature selection in wide datasets with few samples can lead to misleading results.
method Derived sample size requirement for declaring features different, used real datasets to illustrate issues.
result Feature selection from very wide datasets may lead to misleading results.
Time series forecasting is one of the most active research topics. Machine learning methods have been increasingly adopted to solve these predictive tasks. However, in a recent work, these were shown to systematically present a lower predictive performance relative to simple statistical methods. In this work, we counte…
pmsims R package uses Gaussian process for flexible sample size estimation in clinical models.
problem Determining adequate sample size for clinical prediction models.
method Simulation-based Gaussian process search for flexible sample size estimation.
result Gaussian process-based method produces more stable sample size estimates, especially in challenging settings.
CoreFlow models matrix-valued distributions efficiently, preserving shared low-rank structure.
problem Learning matrix-valued distributions from high-dimensional and incomplete data.
method Low-rank flow model that learns shared row/column subspaces and trains a normalizing flow on the core.
result CoreFlow improves generation quality in few-sample regimes and remains competitive in data-rich settings.
BDC compresses both sample size and dimensionality of large datasets.
problem Large datasets in both sample size and dimensionality.
method Two-stage framework using Decoded MMD, Reconstruction MMD, and Encoded MMD.
result BDC achieves comparable or superior performance with lower cost and higher compression rates.
Study generalizes matrix completion with side info in low noise settings.
problem Matrix completion with side information in low noise conditions.
method Inductive matrix completion with i.i.d. subgaussian noise, uniform sampling, and side information.
result Generalization bounds with noise scaling, convergence to zero, and logarithmic dependence on matrix size.
New BE dimension measure reveals rich RL problems with sample-efficient algorithms.
problem Finding sample-efficient algorithms for complex RL problems.
method Introducing Bellman Eluder (BE) dimension and designing GOLF and OLIVE algorithms.
result GOLF and OLIVE algorithms learn near-optimal policies for low BE dimension problems with polynomial samples.
RFSVM uses learned RF similarity for HDLSS classification.
problem High dimension, low sample size classification problems.
method Transposes RFD approach to HDLSS classification using RF similarity as SVM kernel.
result RFSVM outperforms existing methods for HDLSS problems.
This paper improves sample efficiency in noisy inductive matrix completion with side-information.
problem Improving sample efficiency in noisy inductive matrix completion with side-information.
method Nonconvex projected gradient descent algorithm with spectral initialization.
result Achieves linear convergence and stable recovery at a sample complexity governed by the effective side-information dimension.
Paper introduces VDE, a variance-reduced determinant estimator.
problem Estimating determinants with low variance and efficiency.
method Combines variational inference and spherical normalizing flows.
result VDE achieves zero variance in ideal cases, requiring only one sample.
Unrolled neural networks emerged recently as an effective model for learning inverse maps appearing in image restoration tasks. However, their generalization risk (i.e., test mean-squared-error) and its link to network design and train sample size remains mysterious. Leveraging the Stein's Unbiased Risk Estimator (SURE…
Quasi-orthonormal encoding reduces high dimensionality for categorical data.
problem High dimensionality and low sample size issues in categorical data encoding.
method Quasi-orthonormal encoding (QOE) for categorical data.
result QOE reduces dimensionality and improves machine learning performance.
Study shows more data improves model explanations, aiding reliable knowledge extraction.
problem Challenges in deriving reliable knowledge from machine learning models due to the Rashōmon effect.
method Examined the influence of sample size on explanations from models in a Rashōmon set using SHAP.
result Explanations from <128 samples are highly variable, but agreement improves with more data.
We investigate the sample size requirement for exact recovery of a high order tensor of low rank from a subset of its entries. In the Tucker decomposition framework, we show that the Riemannian optimization algorithm with initial value obtained from a spectral method can reconstruct a tensor of size $n\times n \times\c…
Sample measures of top centile contributions to the total (concentration) are downward biased, unstable estimators, extremely sensitive to sample size and concave in accounting for large deviations. It makes them particularly unfit in domains with power law tails, especially for low values of the exponent. These estima…
Deep Kronecker Networkstat.ML
DKN adapts to medical imaging data with limited samples and interpretable models.
problem Medical imaging data's unique nature makes general methods like CNN unsuitable.
method DKN uses a Kronecker product structure to adapt to low sample size and provide interpretable models.
result DKN achieves prediction power comparable to CNN and provides model interpretability.
New classifiers for HDLSS data classify without tuning, robustly.
problem Classification of high-dimensional data with small samples.
method Data-adaptive energy distance classifiers, free of tuning parameters.
result Perfect classification in HDLSS asymptotic regime under general conditions.
Deep Feature Screening: Feature Selection for Ultra High-Dimensional Data via Deep Neural Networksstat.ML
DeepFS uses deep neural networks to select significant features in ultra high-dimensional data.
problem Challenges in traditional feature selection methods for high-dimensional, low-sample-size data.
method Two-step nonparametric approach combining deep neural networks and feature screening.
result DeepFS effectively identifies significant features with high precision for ultra high-dimensional data.
In this paper, we investigate the sample size requirement for exact recovery of a high order tensor of low rank from a subset of its entries. We show that a gradient descent algorithm with initial value obtained from a spectral method can, in particular, reconstruct a tensor of multilinear ranks $…
The paper presents new metrics to quantify and test for (i) the equality of distributions and (ii) the independence between two high-dimensional random vectors. We show that the energy distance based on the usual Euclidean distance cannot completely characterize the homogeneity of two high-dimensional distributions in …
Bipartite ranking is an important supervised learning problem; however, unlike regression or classification, it has a quadratic dependence on the number of samples. To circumvent the prohibitive sample cost, many recent work focus on stochastic gradient-based methods. In this paper we consider an alternative approach, …
Locally sparse neural networks improve interpretability for biomedical tabular data.
problem Overfitting and lack of interpretability in neural networks for tabular biomedical data.
method Locally sparse neural network with a gating network to select relevant features.
result The method outperforms state-of-the-art models in synthetic and real-world biomedical datasets.
Particle Markov chain Monte Carlo techniques rank among current state-of-the-art methods for probabilistic program inference. A drawback of these techniques is that they rely on importance resampling, which results in degenerate particle trajectories and a low effective sample size for variables sampled early in a prog…
New scalable MCMC sampling for nonsymmetric DPPs speeds up computations.
problem Efficient sampling for nonsymmetric DPPs with low-rank kernels.
method Enhanced rejection sampling with efficient proposal distribution construction.
result Sublinear runtime for scalable MCMC sampling of -NDPPs.
Approximating mutual information of high-dimensional variables using learned representationsq-bio.QM
LMI approximates mutual information in high dimensions using learned low-dimensional representations.
problem Estimating mutual information between high-dimensional variables is challenging due to sample size limitations.
method Developed a method called latent MI (LMI) approximation that applies a nonparametric MI estimator to low-dimensional representations learned by a simple model architecture.
result LMI can approximate MI well for variables with >10^3 dimensions if their dependence structure has low intrinsic dimensionality.
Study spectral estimators for multi-index models to recover low-dimensional signal subspaces.
problem Recovering low-dimensional signal subspaces in multi-index models.
method Spectral estimators for multi-index models.
result Precise asymptotic characterization of spectral methods' performance, revealing a phase transition for weak recovery.
New algorithm achieves optimal clustering for sparse centers with high dimensions.
problem Statistical and computational limits of clustering sparse centers with high dimensions.
method Sparse clustering algorithm based on sparse PCA.
result Achieves minimax optimal misclustering rate under certain conditions.
dtSNE preserves local densities in low-dimensional embeddings.
problem Local density differences are not accurately preserved in tSNE and UMAP.
method dtSNE, which approximately conserves local densities.
result dtSNE provides more accurate local density depictions.
This work establishes always-valid risk bounds for online matrix completion.
problem Challenges in establishing always-valid concentration inequalities for online matrix completion.
method Combines non-asymptotic martingale concentration and regularized low-rank matrix regression.
result Establishes always-valid risk bound process for online matrix completion.
Density-Softmax improves uncertainty estimation and robustness without sampling, reducing model size and latency.
problem Sampling-based uncertainty estimation methods suffer from large model size and high latency.
method Combines a Lipschitz-constrained feature extractor with the softmax layer to create a sampling-free deterministic framework.
result Density-Softmax reduces over-confidence under distribution shifts and achieves competitive results in uncertainty and robustness.
Improved predictive posterior density estimation through optimized importance sampling.
problem Low signal-to-noise ratio in posterior predictive densities.
method Optimized importance sampling using a test-time variational proxy.
result Significantly improved estimates of predictive posterior densities.