Study examines how measurement errors impact clustering algorithms.
problem Impact of measurement errors on clustering algorithms.
method Monte Carlo study of two clustering algorithms: GMM with merging and DBSCAN.
result Systematic measurement errors are more problematic for clustering than random errors.
Causal discovery algorithms infer causal relations from data based on several assumptions, including notably the absence of measurement error. However, this assumption is most likely violated in practical applications, which may result in erroneous, irreproducible results. In this work we show how to obtain an upper bo…
Sources of variability in experimentally derived data include measurement error in addition to the physical phenomena of interest. This measurement error is a combination of systematic components, originating from the measuring instrument, and random measurement errors. Several novel biological technologies, such as ma…
New complexity measures explain overparameterized models' surprising performance.
problem Understanding why overparameterized models generalize well despite fitting training data.
method Reinterpreting classical degrees of freedom in a random-X setting.
result Random-X prediction error better explains generalization in complex models.
In this paper I present an extended implementation of the Random ferns algorithm contained in the R package rFerns. It differs from the original by the ability of consuming categorical and numerical attributes instead of only binary ones. Also, instead of using simple attribute subspace ensemble it employs bagging and …
Random Fourier features model reconstructs wind fields from sparse measurements.
problem Reconstructing wind fields from limited data.
method Random Fourier features approximating velocity field with adaptive sampling.
result Random Fourier features model outperforms benchmarks.
New method uses Coulomb gases for Monte Carlo integration with reduced errors.
problem Reducing integration errors in numerical algorithms.
method Using Gibbs measures with a large deviations approach.
result Preserves large deviation principle for improved integration.
Independent component analysis (ICA) is a method for recovering statistically independent signals from observations of unknown linear combinations of the sources. Some of the most accurate ICA decomposition methods require searching for the inverse transformation which minimizes different approximations of the Mutual I…
The paper analyzes sparse high-dimensional linear regression with random design and unknown error variance, providing adaptiveness and concentration rates.
problem Sparse high-dimensional linear regression with random design and unknown error variance.
method Analysis of posterior concentration rates, employing techniques to address model misspecification.
result Adaptiveness and concentration rates of the posterior for sparse high-dimensional linear regression.
Paper proves a Central Limit Theorem for Random Forest Permutation Importance Measure.
problem Lack of theoretical analysis of Random Forest Permutation Importance Measure (RFPIM).
method Formal proof using U-Statistics theory, deviating from conventional Random Forest model.
result Established a Central Limit Theorem for RFPIM.
New method detects causal relationships from noisy measurements.
problem Discover causal relationships from noisy, imperfect measurements.
method Transformed Independent Noise (TIN) condition and ordered group decomposition.
result Identifies causal graph structure without over-complete ICA.
A new clustering algorithm for functional data using binary trees.
problem Clustering multivariate functional data with measurement errors.
method Recursive binary tree splitting for data clustering.
result Good performance in various complex settings, including vehicle trajectories.
Machine learning models estimate nutrient concentrations from water quality surrogates.
problem Estimating high frequency nutrient concentrations from limited in-situ measurements.
method Used machine learning (Random Forests) to estimate nutrient concentrations using surrogate measures.
result Reduced RMSE by up to 60.1% compared to linear models, with additional sensors not providing significant benefits.
Study improves accuracy of risk measures using advanced algorithms.
problem Computing accurate risk measures for financial losses.
method Nested stochastic approximation and multilevel acceleration.
result Established central limit theorems for estimation errors.
Study improves prediction accuracy and uncertainty for mobile sensor data using randomized neural networks.
problem Improving prediction accuracy and uncertainty for mobile sensor data.
method Cross-validation and uncertainty determination for randomized neural networks.
result Improved out-of-sample performance and confidence intervals for prediction error.
New algorithm improves regression error bounds and accelerates performance for low noise.
problem Nonparametric least square regression in RKHS with optimal error bounds.
method Kernel Truncated Randomized Ridge Regression (KTRRR) with optimal generalization error bounds.
result Faster finite-time and asymptotic rates on low noise problems.
This work tightens generalization error bounds using Wasserstein distance.
problem Improving expected generalization error bounds in machine learning.
method Introduces bounds based on Wasserstein distance for various settings.
result New, tighter bounds based on relative entropy and other information measures.
Optimizes embedding accuracy for data variance and error.
problem Efficiently embedding data while minimizing distortion.
method Uses Johnson-Lindenstrauss embeddings with orthogonal matrices and singular-value latent variables.
result Achieves best accuracy in variance, mean-squared error, and length distortion.
The conformalClassification package implements Transductive Conformal Prediction (TCP) and Inductive Conformal Prediction (ICP) for classification problems. Conformal Prediction (CP) is a framework that complements the predictions of machine learning algorithms with reliable measures of confidence. TCP gives results wi…
New method tackles tensor regression with robust Kaczmarz approach.
problem Reconstructing tensor signals from corrupted measurements.
method Quantile-based randomized Kaczmarz method for tensor linear systems.
result Improved convergence and robustness to adversarial corruptions.
A new perfectly truthful calibration measure improves prediction reliability.
problem Improving the reliability of predictions by ensuring they are conditionally unbiased.
method Designing a simple, perfectly truthful calibration measure called ATB.
result ATB is the first perfectly truthful calibration measure in the batch setting.
Proposes a new method for localized uncertainty quantification in random forests using proximity measures.
problem Localized uncertainty quantification in random forests for improved reliability of predictions.
method Forming localized distributions of Out-Of-Bag (OOB) errors around nearby points defined by similarity measures (proximities) to create prediction intervals for regression and trust scores for classification.
result Localized prediction intervals and trust scores enhance model accuracy and provide higher accuracy-rejection AUC scores than competing methods.
Randomly chosen support makes sparse linear regression easy.
problem Sparse linear regression with random support.
method Random support selection for efficient prediction.
result Prediction error ε with N=extpoly(k,logd,1/ε) samples and extpoly(d,N) run-time. This paper connects RND, deep ensembles, and Bayesian inference, providing a unified theoretical perspective.
problem Uncertainty quantification in deep learning models.
method Analysis of Random Network Distillation (RND) within the neural tangent kernel framework.
result The uncertainty signal from RND is equivalent to the predictive variance of a deep ensemble and can be made to mirror the centered posterior predictive distribution of Bayesian inference.
Paper uses Random Matrix Theory for optimal training-testing data split.
problem Finding ideal training-testing data split for linear regression.
method Random Matrix Theory applied to Gaussian multivariate data.
result Ideal training and test sizes derived for any model.
Quantum machine learning tackles large datasets with randomized measurements.
problem Efficiently process large, high-dimensional datasets on quantum computers.
method Randomized measurements to scale linearly with dataset size and quadratic for post-processing.
result Substantial speed-up for noisy quantum computers, enabling image classification.
Suppose that we observe y∈Rn and X∈Rn×m in the following errors-in-variables model: \begin{eqnarray*} y & = & X_0 β^* +ε\\ X & = & X_0 + W, \end{eqnarray*} where X0 is an n×m design matrix with independent subgaussian row vectors, ε∈Rn is a noise vecto…
Study on adversarial robustness in neural networks across initialization and training phases.
problem Understanding adversarial robustness in neural networks during different learning stages.
method Analyzes adversarial robustness in various scenarios of over-parameterized networks with quadratic targets and infinite samples.
result Robustness can worsen when test error improves, and vice versa, revealing new tradeoffs.
The contour maps of the error of historical resp. parametric estimates for large random portfolios optimized under the risk measure Expected Shortfall (ES) are constructed. Similar maps for the sensitivity of the portfolio weights to small changes in the returns as well as the VaR of the ES-optimized portfolio are also…
Paper assesses error estimates of Random Forests classification.
problem Quantitative assessment of Random Forests error estimates.
method Theoretical and empirical investigation of various error estimation methods.
result Random Forests' error estimates are closer to true error rate than average prediction error.
Randomness is crucial for stability in learning and statistics, especially for differential privacy.
problem Quantifying the amount of randomness needed for algorithmic stability.
method Weak-to-strong boosting theorem for stability, characterizing randomness complexity of PAC Learning.
result Randomness complexity is tightly controlled by the best replication probability of any deterministic algorithm solving the task.
The number of trees T in the random forest (RF) algorithm for supervised learning has to be set by the user. It is controversial whether T should simply be set to the largest computationally manageable value or whether a smaller T may in some cases be better. While the principle underlying bagging is that "more trees a…
Modeling functional data, this study uncovers the size-and-shape of functions under noisy observations.
problem Uncertainty in recovering a fixed effect function from noisy observations.
method Bayesian functional mixed model with priors on unitary transformations.
result It is possible to recover the size-and-shape of a square-integrable function μ. We study high-dimensional asymptotic performance limits of binary supervised classification problems where the class conditional densities are Gaussian with unknown means and covariances and the number of signal dimensions scales faster than the number of labeled training samples. We show that the Bayes error, namely t…
A new method approximates the Sliced-Wasserstein distance without random projections.
problem Efficiently approximating the Sliced-Wasserstein distance for machine learning applications.
method Utilizing the concentration of measure phenomenon to develop a deterministic approximation.
result The approximation error goes to zero as the dimension increases, under a weak dependence condition.
New framework improves worst-case generalization bounds for stochastic optimization.
problem Challenges in providing generalization guarantees for stochastic optimization algorithms.
method Introduces random set stability and empirically relevant complexity measures to avoid intractable mutual information terms.
result Bounded worst-case generalization error in terms of random set stability and empirically relevant complexity measures.
Double descent in condition number shows peak at equal dimensions.
problem Estimating function from random measurements.
method Analyzing the condition number of random matrices.
result Condition number is highest when d=n. In this paper we measured the stability of stochastic gradient method (SGM) for learning an approximated Fourier primal support vector machine. The stability of an algorithm is considered by measuring the generalization error in terms of the absolute difference between the test and the training error. Our problem is to…
Study loop corrections in random feature models affecting training and test errors.
problem Analyzing loop corrections in random feature models to understand training and test errors.
method Statistical physics and effective field theory approach to study loop corrections.
result Derived loop corrections to training error, test error, and generalization gap.
This work analyzes discrete diffusion models using stochastic integrals, providing error bounds and insights.
problem Error analysis for discrete diffusion models remains less understood.
method Proposes a comprehensive framework based on Lévy-type stochastic integrals.
result Obtains the first error bound for the τ-leaping scheme in KL divergence. Paper proposes diagnostics for error and variance estimation in randomized matrix computations.
problem Safe use of randomized matrix algorithms in applications.
method Leave-one-out error estimator and jackknife resampling method.
result Provides rapid diagnostics to assess quality of randomized matrix computations.
A fast bootstrap method estimates cross-validation standard error.
problem Uncertainty quantification in cross-validation estimates.
method Random-effects model to estimate variance component.
result Valid confidence intervals for model performance.
DIET tests conditional independence using marginal dependence measures of residual information.
problem Computational intractability of conditional randomization tests (CRTs).
method DIET avoids fitting large models by leveraging marginal independence statistics of information residuals.
result DIET achieves higher power than other tractable CRTs on synthetic and real benchmarks.
Eigenvalues of random hyperbolic surface covers converge to hyperbolic plane's.
problem Eigenvalue rigidity of random hyperbolic surface covers.
method Selberg trace formula and polynomial method.
result Distribution of eigenvalues converges to hyperbolic plane's spectral measure.
Algorithm recovers factors of rank-1 matrices from noisy measurements.
problem Estimating factors of a rank-1 matrix from nonlinearly transformed and noisy measurements.
method Alternating minimization with random initialization and analysis of empirical error recursion.
result Algorithm converges geometrically fast from random initialization, with sharp guarantees.
PEC improves class-incremental learning by measuring prediction error.
problem Challenges in class-incremental learning, particularly forgetting and class imbalance.
method Prediction Error-based Classification (PEC) measures prediction error of a model trained on data from a class.
result PEC outperforms other methods in class-incremental learning across multiple benchmarks.
Unified framework for estimating random forest prediction errors.
problem Estimating prediction errors for random forests.
method Novel estimator of conditional prediction error distribution function.
result Proposed estimators enable competitive prediction intervals.
Completely random measures (CRM) represent the key building block of a wide variety of popular stochastic models and play a pivotal role in modern Bayesian Nonparametrics. A popular representation of CRMs as a random series with decreasing jumps is due to Ferguson and Klass (1972). This can immediately be turned into a…