In this paper, we proved the mass angular momentum inequality\cite{D1}\cite{ChrusLiWe}\cite{SZ} for axisymmetric, asymptotically flat, vacuum constraint data sets with small trace. Given an initial data set with small trace, we construct a boost evolution spacetime of the Einstein vacuum equations as \cite{ChOM}. Then …
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48 results for “small data sets”
Novel approach for SEM in small samples with .
problem Small sample size and issues in factor-based SEM.
method Reformulates covariance structure into self-covariance and cross-covariance, defines a feasible set with relative error constraint.
result Improved stability and directional information in small-sample settings.
Bayesian methods reduce variance in subspace identification for small data sets.
problem High variance in traditional subspace identification methods for large models or small sample sizes.
method Investigation of Bayesian estimation solutions (regularized and shrinkage estimators) for subspace identification.
result Bayesian estimators reduce estimation risk by up to 40% compared to traditional methods.
In this paper, we confront the problem of deep learning's big labeled data requirements, offer a rule based strategy for extreme augmentation of small data sets and apply that strategy with the image to image translation model by Isola et al. (2016) to automate cel style cartoon coloring with very limited training data…
Many classification applications require accurate probability estimates in addition to good class separation but often classifiers are designed focusing only on the latter. Calibration is the process of improving probability estimates by post-processing but commonly used calibration algorithms work poorly on small data…
Generative Latent Implicit Conditional Optimization (GLICO) learns from small samples.
problem Learning from small labeled datasets.
method Generative Latent Implicit Conditional Optimization (GLICO) learns a latent space and generator from small labeled data.
result GLICO synthesizes new samples for every class using as few as 10 examples per class.
We propose a novel method to train deep convolutional neural networks which learn from multiple data sets of varying input sizes through weight sharing. This is an advantage in chemometrics where individual measurements represent exact chemical compounds and thus signals cannot be translated or resized without disturbi…
Estimates policy performance in small-data settings without sacrificing data.
problem Poor performance of cross-validation in small-data optimization.
method Uses sensitivity analysis to estimate gradient of optimal objective value.
result Explicit high-probability bounds on error of estimator for small-data, large-scale problems.
Investigates tight PAC-Bayes bounds for small datasets.
problem Tightening PAC-Bayes bounds for small data.
method Generic PAC-Bayes theorem, meta-learning, synthetic tasks.
result PAC-Bayes bounds are competitive with Chernoff bounds but not as tight.
A form of generalisation error known as Off Training Set (OTS) error was recently introduced in [Wolpert, 1996b], along with a theorem showing that small training set error does not guarantee small OTS error, unless assumptions are made about the target function. Here it is shown that the applicability of this theorem …
One significant challenge to scaling entity resolution algorithms to massive datasets is understanding how performance changes after moving beyond the realm of small, manually labeled reference datasets. Unlike traditional machine learning tasks, when an entity resolution algorithm performs well on small hold-out datas…
Unified Bayesian model for multi-modal, small sample size biomedical data classification.
problem Classifying high-dimensional, multi-modal biomedical data with small sample sizes.
method Combines multi-modal data views into a latent space, prunes irrelevant features, and uses dual kernels for small sample size scenarios.
result Outperforms state-of-the-art models and identifies features aligned with existing markers.
Augment small datasets with synthetic backgrounds to train lightweight CNNs for human pose estimation.
problem Training CNNs from limited real-world data for human pose estimation.
method Synthetic background substitution for data augmentation.
result Improves generalization to unseen environments.
The study tackles forgery in machine unlearning, showing that forging is limited and can be detected.
problem Adversarial crafting of data to mimic model behavior without removing information.
method Developed a framework to analyze -forging sets and proved their measure decay.
result The forging set measure decays as , providing evidence against false unlearning claims.
Binary classification improves with a small fraction of corrupted labels.
problem Binary classification with corrupted labels.
method Established corruption as a form of regularization and computed upper bounds on estimation error.
result Corruption is beneficial only up to a small fraction of the total sample, scaling with the square root of the sample size.
Gaussian Processes (GPs) are known to provide accurate predictions and uncertainty estimates even with small amounts of labeled data by capturing similarity between data points through their kernel function. However traditional GP kernels are not very effective at capturing similarity between high dimensional data poin…
Develops a framework to test excessive influence of small data subsets.
problem Identifying when small data subsets significantly impact model conclusions.
method Formalizes the concept of most influential sets, deriving influence formulas and extreme value distributions.
result Allows rigorous hypothesis testing for excessive influence, resolving contested findings.
The two-sample hypothesis testing problem is studied for the challenging scenario of high dimensional data sets with small sample sizes. We show that the two-sample hypothesis testing problem can be posed as a one-class set classification problem. In the set classification problem the goal is to classify a set of data …
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%).
The paper explores how smaller data sets can lead to better model selection decisions.
problem Model selection in small data regimes.
method Empirical study of generalization performance with varying training set sizes.
result Training on smaller subsets of data can lead to more reliable model selection decisions.
PPI++ uses machine learning predictions to improve inference from small datasets.
problem Efficient inference from small labeled datasets with high-quality predictions.
method Adapts prediction-powered inference (PPI) to compute confidence sets for any parameter dimensionality.
result Improves classical intervals using only labeled data, always yielding better results.
Dirichlet process mixture (DPM) models tend to produce many small clusters regardless of whether they are needed to accurately characterize the data - this is particularly true for large data sets. However, interpretability, parsimony, data storage and communication costs all are hampered by having overly many clusters…
Deep networks and forests perform differently with small samples.
problem Comparing deep networks and decision forests for small sample sizes.
method Unified view of both methods as partition and vote schemes, empirical comparison on various datasets.
result Forests excel with small tabular and structured data, deep nets better with larger samples.
We present an efficient coreset construction algorithm for large-scale Support Vector Machine (SVM) training in Big Data and streaming applications. A coreset is a small, representative subset of the original data points such that a models trained on the coreset are provably competitive with those trained on the origin…
Biological networks are a very convenient modelling and visualisation tool to discover knowledge from modern high-throughput genomics and postgenomics data sets. Indeed, biological entities are not isolated, but are components of complex multi-level systems. We go one step further and advocate for the consideration of …
ALBU improves LDA performance on small datasets.
problem Limited data impairs variational Bayes in LDA.
method Approximate Loopy Belief message passing algorithm.
result ALBU learns latent distributions more accurately than VB, especially for smaller data sets.
FedFaiREE addresses fairness in decentralized learning with small samples.
problem Ensuring fairness in decentralized federated learning with limited data.
method FedFaiREE is a post-processing algorithm for distribution-free fair learning in decentralized settings with small samples.
result FedFaiREE provides theoretical guarantees for both fairness and accuracy in decentralized environments.
Differential privacy for simple linear regression protects small datasets from individual data leaks.
problem Protecting sensitive personal information in small datasets from individual data leaks.
method Differential privacy algorithms for simple linear regression tailored for small datasets (tens to hundreds of datapoints).
result Robust estimators like Theil-Sen perform well on small datasets, but standard algorithms improve as dataset size increases.
The Willmore Flow of Graphs with Boundary Data: Low-Regularity Initial Data and Global Convergencemath.AP
Analyzes Willmore flow for graphs with boundary data, proving existence and convergence.
problem Willmore flow of graphs with boundary conditions over bounded domains.
method Developed low-regularity theory, reformulated graphical equation, used time-weighted parabolic Hölder spaces.
result Proved short-time and global existence for initial data in and Lipschitz, with exponential convergence.
In this paper, we propose a method for training neural networks when we have a large set of data with weak labels and a small amount of data with true labels. In our proposed model, we train two neural networks: a target network, the learner and a confidence network, the meta-learner. The target network is optimized to…
Scaling clustering algorithms to massive data sets is a challenging task. Recently, several successful approaches based on data summarization methods, such as coresets and sketches, were proposed. While these techniques provide provably good and small summaries, they are inherently problem dependent - the practitioner …
Kernel methods offer the flexibility to learn complex relationships in modern, large data sets while enjoying strong theoretical guarantees on quality. Unfortunately, these methods typically require cubic running time in the data set size, a prohibitive cost in the large-data setting. Random feature maps (RFMs) and the…
SmallML predicts customer churn for SMEs with small data, improving accuracy by 24.2 points.
problem AI exclusion of SMEs due to data scale mismatch.
method Bayesian transfer learning with hierarchical pooling and conformal prediction.
result 96.7% AUC on 100 obs SMEs, 24.2 point improvement over logistic regression.
New methods detect objects in industrial settings with little training data.
problem Lack of training data limits object detection in industrial settings.
method Adapted Faster R-CNN and Scaled Yolov4-p5 architectures for small training data.
result Both models can distinguish unknown objects from homogeneous backgrounds.
A new algorithm for robust causal discovery in small sample sizes.
problem Limited data leads to weak conditional independence tests in causal discovery.
method Proposes a -PC algorithm that bounds conditioning set size for robust causal discovery.
result The -PC algorithm enables more robust causal discovery in small sample sizes.
New algorithms adapt to friendly environments in online learning.
problem Oracle-efficient algorithms struggle with friendly environments.
method Follow-the-perturbed-leader algorithms with approximability condition.
result Best-of-both-worlds bound in oracle-efficient setting.
Bayesian Federated Inference improves statistical model estimation from multicenter data.
problem Combining data from different medical centers is challenging due to regulatory and logistic issues.
method Bayesian Federated Inference (BFI) framework for multicenter data.
result BFI framework infers additional features of the posterior parameter distribution, capturing more information than Federated Learning.
Robust Importance Sampling for Error Estimation in the Context of Optimal Bayesian Transfer Learningstat.ML
Paper introduces a new method for error estimation in classification tasks with limited data.
problem Challenges in designing accurate classifiers and evaluating their performance with limited training data.
method Introduces a novel Bayesian MMSE estimator for optimal Bayesian transfer learning (OBTL) using Monte Carlo importance sampling.
result Proposed OBTL error estimation scheme outperforms standard methods, especially in small-sample settings.
Paper introduces a method to infer causal direction from limited data.
problem Inference of causal direction from limited observational data.
method Meta learning combined with causal inference to create a generative model.
result The method accurately infers causal direction across various dataset sizes.
Differentially Private Linear Regression and Synthetic Data Generation with Statistical Guaranteescs.LG
Proposes a method for differentially private linear regression and synthetic data generation.
problem Lack of valid inference and synthetic data generation methods for small-scale datasets in privacy-aware settings.
method Gaussian differentially private linear regression with bias-corrected estimator and SDG procedure.
result Improves accuracy and provides valid confidence intervals for downstream tasks.
We focus on developing a novel scalable graph-based semi-supervised learning (SSL) method for a small number of labeled data and a large amount of unlabeled data. Due to the lack of labeled data and the availability of large-scale unlabeled data, existing SSL methods usually encounter either suboptimal performance beca…
Out-of-Distribution Detection from Small Training Sets using Bayesian Neural Network Classifierscs.LG
Bayesian Neural Networks improve OOD detection with limited data.
problem Limited training data hinders reliable OOD detection.
method Bayesian Neural Networks with expected logit vectors.
result Bayesian methods outperform deterministic methods in small data settings.
Study examines mean estimation in high dimensions with small data.
problem Efficiently estimating mean in high-dimensional data with limited data size.
method Extensive experimentation of various mean estimation techniques.
result Developed robust methods for mean estimation with low data size.
Human labeling of data can be very time-consuming and expensive, yet, in many cases it is critical for the success of the learning process. In order to minimize human labeling efforts, we propose a novel active learning solution that does not rely on existing sources of unlabeled data. It uses a small amount of labeled…
Method generates prototypes from small datasets for efficient learning.
problem Efficiently learning from small datasets with soft labels.
method Modular method for generating soft-label prototypical lines and Hierarchical Soft-Label Prototype k-Nearest Neighbor algorithm.
result High classification accuracy with significantly fewer prototypes than classes.
The CLT fails for LLM evaluations with small data, leading to underestimation of uncertainty.
problem Inaccurate uncertainty estimates in LLM evaluations with small datasets.
method Alternative frequentist and Bayesian methods for uncertainty quantification.
result CLT-based methods underestimate uncertainty in small data settings.
Selective removal of data subsets can efficiently unlearn unwanted distributions.
problem Efficiently removing unwanted data subsets without losing important information.
method Formalized as distributional unlearning, using Kullback-Leibler divergence constraints to select a small subset of data.
result Proposed method achieves corresponding log-loss bounds and is quadratically more sample-efficient than random removal.
Robustly estimates mean with quantized data and corruption.
problem Mean estimation under quantization and adversarial corruption.
method Constructs multivariate robust estimators in two settings.
result Optimal estimators up to logarithmic factors.