# Variance

Source: [Variance](<https://www.sota2.com/research/dataset/variance>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

## Benchmarks

Page 1 of 2. This is an index page, not the full collection.

- [Next index page](<https://www.sota2.com/research/dataset/variance.md?page=2>): Follow this link to discover more pages.

- [Out-of-sample random-X Regression on Spiked Covariance Model (d/N=0.9, noise=1)](<https://www.sota2.com/research/sota/out-of-sample-random-x-regression-on-spiked-covariance-model-d-n-0-9-noise-1.md>): Out-of-sample random-X regression; Spiked covariance model d/N = 0.9, noise = 1 synthetic (out-of-sample).

- [Covariance matrix estimation on Block covariance structure](<https://www.sota2.com/research/sota/covariance-matrix-estimation-on-block-covariance-structure.md>): Covariance matrix estimation; Block covariance structure.

- [Covariance Estimation on Factor covariance structure synthetic](<https://www.sota2.com/research/sota/covariance-estimation-on-factor-covariance-structure-synthetic.md>): Covariance Estimation; Factor covariance structure synthetic.

- [Principal Component Estimation on Gaussian setting with mean-shift and covariance-shift contamination synthetic (test)](<https://www.sota2.com/research/sota/principal-component-estimation-on-gaussian-setting-with-mean-shift-and-covariance-shift-contamination-synthetic-test.md>): Principal Component Estimation; Gaussian setting with mean-shift and covariance-shift contamination synthetic (test).

- [Regression on Synthetic Spiked Covariance d/N = 0.9 (out-of-sample)](<https://www.sota2.com/research/sota/regression-on-synthetic-spiked-covariance-d-n-0-9-out-of-sample.md>): Regression; Synthetic Spiked Covariance d/N = 0.9 (out-of-sample).

- [Sparse Covariance Matrix Estimation on Sparse Covariance Structure](<https://www.sota2.com/research/sota/sparse-covariance-matrix-estimation-on-sparse-covariance-structure.md>): Sparse Covariance Matrix Estimation; Sparse Covariance Structure.

- [Linear Regression on Linear Regression Equi-correlation Covariance (r=0.2)](<https://www.sota2.com/research/sota/linear-regression-on-linear-regression-equi-correlation-covariance-r-0-2.md>): Linear Regression; Linear Regression Equi-correlation Covariance, r=0.2.

- [Change Point Detection on Variance change synthetic data](<https://www.sota2.com/research/sota/change-point-detection-on-variance-change-synthetic-data.md>): Change Point Detection; Variance change synthetic data.

- [Change-point detection on Synthetic high-dimensional data (variance change Σ = 2Id)](<https://www.sota2.com/research/sota/change-point-detection-on-synthetic-high-dimensional-data-variance-change-2id.md>): Change-point detection; Synthetic high-dimensional data (variance change Σ = 2Id).

- [Out-of-sample Mean Squared Error Estimation on Spiked covariance model N = 200](<https://www.sota2.com/research/sota/out-of-sample-mean-squared-error-estimation-on-spiked-covariance-model-n-200.md>): Out-of-sample Mean Squared Error Estimation; Spiked covariance model N = 200.

- [Optimization Convergence on Synthetic covariance matrices n=10, E14 setup (test)](<https://www.sota2.com/research/sota/optimization-convergence-on-synthetic-covariance-matrices-n-10-e14-setup-test.md>): Optimization Convergence; Synthetic covariance matrices n=10, E14 setup (test).

- [Instruction following on AlpacaEval High-Variance (Top 20%) 2.0](<https://www.sota2.com/research/sota/instruction-following-on-alpacaeval-high-variance-top-20-percent-2-0.md>): Instruction following; AlpacaEval High-Variance (Top 20%) 2.0.

- [Multi-turn Instruction Following on MT-Bench High-Variance (Top 20%)](<https://www.sota2.com/research/sota/multi-turn-instruction-following-on-mt-bench-high-variance-top-20-percent.md>): Multi-turn instruction following; MT-Bench High-Variance (Top 20%).

- [Online Conformal Prediction on Variance Changepoint](<https://www.sota2.com/research/sota/online-conformal-prediction-on-variance-changepoint.md>): Online Conformal Prediction; Variance Changepoint.

- [Ranking and Selection on Gaussian instances unknown variance](<https://www.sota2.com/research/sota/ranking-and-selection-on-gaussian-instances-unknown-variance.md>): Selection of a good alternative (Ranking and Selection); Gaussian instances unknown variance.

- [Recovery performance on state-dependent variance dynamics (simulation)](<https://www.sota2.com/research/sota/recovery-performance-on-state-dependent-variance-dynamics-simulation.md>): Recovery performance; state-dependent variance dynamics (simulation).

- [Linear Regression on Linear Regression Identity Covariance](<https://www.sota2.com/research/sota/linear-regression-on-linear-regression-identity-covariance.md>): Linear Regression; Linear Regression Identity Covariance.

- [Graph Estimation on Synthetic Graphs Variance Shifting GBF](<https://www.sota2.com/research/sota/graph-estimation-on-synthetic-graphs-variance-shifting-gbf.md>): Graph Estimation; Synthetic Graphs Variance Shifting GBF.

- [Portfolio Optimization on S&P 500 Minimum Variance Portfolios](<https://www.sota2.com/research/sota/portfolio-optimization-on-s-and-p-500-minimum-variance-portfolios.md>): Portfolio Optimization; S&P 500 stocks Minimum Variance Portfolios.

- [Variance Recovery on Variance Collapse diagnostic d=200 synthetic (test)](<https://www.sota2.com/research/sota/variance-recovery-on-variance-collapse-diagnostic-d-200-synthetic-test.md>): Variance Recovery; Variance Collapse diagnostic d=200 synthetic (test).

- [Variance Recovery on Variance Collapse diagnostic d=100 synthetic (test)](<https://www.sota2.com/research/sota/variance-recovery-on-variance-collapse-diagnostic-d-100-synthetic-test.md>): Variance Recovery; Variance Collapse diagnostic d=100 synthetic (test).

- [Variance Recovery on Variance Collapse diagnostic d=50 synthetic (test)](<https://www.sota2.com/research/sota/variance-recovery-on-variance-collapse-diagnostic-d-50-synthetic-test.md>): Variance Recovery; Variance Collapse diagnostic d=50 synthetic (test).

- [Variance Recovery on Variance Collapse diagnostic (d=20) synthetic (test)](<https://www.sota2.com/research/sota/variance-recovery-on-variance-collapse-diagnostic-d-20-synthetic-test.md>): Variance Recovery; Variance Collapse diagnostic (d=20) synthetic (test).

- [Variance Recovery on Variance Collapse diagnostic (d=10) synthetic (test)](<https://www.sota2.com/research/sota/variance-recovery-on-variance-collapse-diagnostic-d-10-synthetic-test.md>): Variance Recovery; Variance Collapse diagnostic (d=10) synthetic (test).

- [Correlation Matrix Segmentation on Synthetic noise variance 0.2](<https://www.sota2.com/research/sota/correlation-matrix-segmentation-on-synthetic-noise-variance-0-2.md>): Correlation Matrix Segmentation; Synthetic noise variance 0.2.

- [Approximate Bayesian Inference on Inverse-gamma prior and normal-variance likelihood Wide Meta-prior](<https://www.sota2.com/research/sota/approximate-bayesian-inference-on-inverse-gamma-prior-and-normal-variance-likelihood-wide-meta-prior.md>): Approximate Bayesian Inference; Inverse-gamma prior and normal-variance likelihood Wide Meta-prior.

- [Approximate Bayesian Inference on Inverse-gamma prior and normal-variance likelihood Narrow Meta-prior](<https://www.sota2.com/research/sota/approximate-bayesian-inference-on-inverse-gamma-prior-and-normal-variance-likelihood-narrow-meta-prior.md>): Approximate Bayesian Inference; Inverse-gamma prior and normal-variance likelihood Narrow Meta-prior.

- [Anomaly Detection on Anomaly-IntraVariance (Group 1)](<https://www.sota2.com/research/sota/anomaly-detection-on-anomaly-intravariance-group-1.md>): Anomaly Detection; Anomaly-IntraVariance (Group 1).

- [Anomaly Detection on Anomaly-IntraVariance Group 1 (test)](<https://www.sota2.com/research/sota/anomaly-detection-on-anomaly-intravariance-group-1-test.md>): Anomaly Detection; Anomaly-IntraVariance Group 1 (test).

- [Anomaly Localization on Anomaly-IntraVariance 1.0 (Group 2)](<https://www.sota2.com/research/sota/anomaly-localization-on-anomaly-intravariance-1-0-group-2.md>): Anomaly Localization; Anomaly-IntraVariance 1.0 (Group 2).

- [Anomaly Detection on Anomaly-IntraVariance 1.0 (Group 2)](<https://www.sota2.com/research/sota/anomaly-detection-on-anomaly-intravariance-1-0-group-2.md>): Anomaly Detection; Anomaly-IntraVariance 1.0 (Group 2).

- [ATE Estimation on Environment family variance ratios up to ~100x (held-out)](<https://www.sota2.com/research/sota/ate-estimation-on-environment-family-variance-ratios-up-to-100x-held-out.md>): ATE Estimation; Environment family variance ratios up to ~100x (held-out).

- [Causal Discovery on unit-variance-noise (100 datasets)](<https://www.sota2.com/research/sota/causal-discovery-on-unit-variance-noise-100-datasets.md>): Causal Discovery; unit-variance-noise (100 datasets).

- [Probabilistic Time Series Forecasting on Synthetic Quadratic Variance (test)](<https://www.sota2.com/research/sota/probabilistic-time-series-forecasting-on-synthetic-quadratic-variance-test.md>): Probabilistic Time Series Forecasting; Synthetic Quadratic Variance (test).

- [Probabilistic Time Series Forecasting on Synthetic Linear Variance (test)](<https://www.sota2.com/research/sota/probabilistic-time-series-forecasting-on-synthetic-linear-variance-test.md>): Probabilistic Time Series Forecasting; Synthetic Linear Variance (test).

- [Time Series Forecasting on Synthetic Quadratic variance](<https://www.sota2.com/research/sota/time-series-forecasting-on-synthetic-quadratic-variance.md>): Time Series Forecasting; Synthetic Quadratic variance.

- [Time Series Forecasting on Synthetic Linear variance](<https://www.sota2.com/research/sota/time-series-forecasting-on-synthetic-linear-variance.md>): Time Series Forecasting; Synthetic Linear variance.

- [Covariance matrix estimation on Toeplitz covariance structure ϱ = 0.9, p = 4000](<https://www.sota2.com/research/sota/covariance-matrix-estimation-on-toeplitz-covariance-structure-0-9-p-4000.md>): Covariance matrix estimation; Toeplitz covariance structure ϱ = 0.9, p = 4000.

- [Covariance matrix estimation on Toeplitz covariance structure ϱ = 0.7, p = 3000](<https://www.sota2.com/research/sota/covariance-matrix-estimation-on-toeplitz-covariance-structure-0-7-p-3000.md>): Covariance matrix estimation; Toeplitz covariance structure ϱ = 0.7, p = 3000.

- [Covariance matrix estimation on Toeplitz covariance structure ϱ = 0.5, p = 2000](<https://www.sota2.com/research/sota/covariance-matrix-estimation-on-toeplitz-covariance-structure-0-5-p-2000.md>): Covariance matrix estimation; Toeplitz covariance structure ϱ = 0.5, p = 2000.

- [Covariance matrix estimation on Toeplitz covariance structure ϱ = 0.3, p = 4000](<https://www.sota2.com/research/sota/covariance-matrix-estimation-on-toeplitz-covariance-structure-0-3-p-4000.md>): Covariance matrix estimation; Toeplitz covariance structure ϱ = 0.3, p = 4000.

- [Covariance matrix estimation on Toeplitz covariance structure (ρ = 0.1, p = 2000)](<https://www.sota2.com/research/sota/covariance-matrix-estimation-on-toeplitz-covariance-structure-0-1-p-2000.md>): Covariance matrix estimation; Toeplitz covariance structure (ϱ = 0.1, p = 2000).

- [Covariance matrix estimation on Toeplitz covariance structure ℘ = 0.1, p = 1000](<https://www.sota2.com/research/sota/covariance-matrix-estimation-on-toeplitz-covariance-structure-0-1-p-1000.md>): Covariance matrix estimation; Toeplitz covariance structure ϱ = 0.1, p = 1000.

- [LLM Alignment Evaluation on Qwen2.5-14B-Instruct High-Variance (Top 20%)](<https://www.sota2.com/research/sota/llm-alignment-evaluation-on-qwen2-5-14b-instruct-high-variance-top-20-percent.md>): LLM Alignment Evaluation; Qwen2.5-14B-Instruct High-Variance (Top 20%).

- [Change-point detection on Variance jumps (RI)](<https://www.sota2.com/research/sota/change-point-detection-on-variance-jumps-ri.md>): Change-point detection; Variance jumps.

- [Change-point detection on Variance jumps](<https://www.sota2.com/research/sota/change-point-detection-on-variance-jumps.md>): Change-point detection; Variance jumps.

- [EEG Classification on Real EEG covariance SPD(22) (27 subject split pairs)](<https://www.sota2.com/research/sota/eeg-classification-on-real-eeg-covariance-spd-22-27-subject-split-pairs.md>): EEG Classification; Real EEG covariance SPD(22) (27 subject split pairs).

- [Geometric Alignment on Real EEG covariance SPD(22) (27 subject/split pairs)](<https://www.sota2.com/research/sota/geometric-alignment-on-real-eeg-covariance-spd-22-27-subject-split-pairs.md>): Geometric Alignment; Real EEG covariance SPD(22) (27 subject/split pairs).

- [Ridge Regression on Spiked covariance model N=500 synthetic](<https://www.sota2.com/research/sota/ridge-regression-on-spiked-covariance-model-n-500-synthetic.md>): Ridge Regression; Spiked covariance model N=500 synthetic.

- [Ridge Regression on Spiked covariance model synthetic (N=100)](<https://www.sota2.com/research/sota/ridge-regression-on-spiked-covariance-model-synthetic-n-100.md>): Ridge Regression; Spiked covariance model synthetic (N=100).

- [Ridge Regression on Spiked covariance model N=20 synthetic](<https://www.sota2.com/research/sota/ridge-regression-on-spiked-covariance-model-n-20-synthetic.md>): Ridge Regression; Spiked covariance model N=20 synthetic.

- [Causal Discovery on Mixed Physics 100:0 variance:mean ratio](<https://www.sota2.com/research/sota/causal-discovery-on-mixed-physics-100-0-variance-mean-ratio.md>): Causal Discovery; Mixed Physics 100:0 variance:mean ratio.

- [Causal Discovery on Mixed Physics 75:25 variance:mean ratio](<https://www.sota2.com/research/sota/causal-discovery-on-mixed-physics-75-25-variance-mean-ratio.md>): Causal Discovery; Mixed Physics 75:25 variance:mean ratio.

- [Causal Discovery on Mixed Physics 50:50 variance:mean ratio](<https://www.sota2.com/research/sota/causal-discovery-on-mixed-physics-50-50-variance-mean-ratio.md>): Causal Discovery; Mixed Physics 50:50 variance:mean ratio.

- [Spiked Covariance Estimation on Elliptical Student-t (df=4.5, ε=0.1 Huber)](<https://www.sota2.com/research/sota/spiked-covariance-estimation-on-elliptical-student-t-df-4-5-0-1-huber.md>): Spiked Covariance Estimation; Spiked covariance benchmark under elliptical Student-t (df=4.5) with ε = 0.1 Huber contamination.

- [Variational Inference on Variance Collapse d=200](<https://www.sota2.com/research/sota/variational-inference-on-variance-collapse-d-200.md>): Variational Inference; Variance Collapse d=200.

- [Variational Inference on Variance Collapse (d=50)](<https://www.sota2.com/research/sota/variational-inference-on-variance-collapse-d-50.md>): Variational Inference; Variance Collapse (d=50).

- [DAG Recovery on 200-node ER4 Graphs (Gaussian Noise, Variance=5.0)](<https://www.sota2.com/research/sota/dag-recovery-on-200-node-er4-graphs-gaussian-noise-variance-5-0.md>): Directed Acyclic Graph (DAG) recovery; 200-node ER4 graphs homoscedastic Gaussian noise, variance = 5.0.

- [DAG Recovery on 200-node ER4 graphs homoscedastic Gaussian noise, variance = 1.0](<https://www.sota2.com/research/sota/dag-recovery-on-200-node-er4-graphs-homoscedastic-gaussian-noise-variance-1-0.md>): Directed Acyclic Graph (DAG) recovery; 200-node ER4 graphs homoscedastic Gaussian noise, variance = 1.0.

- [Independence testing on Variance distribution (test)](<https://www.sota2.com/research/sota/independence-testing-on-variance-distribution-test.md>): Independence testing; Variance distribution (test).

- [Circle Packing on World12D large variance](<https://www.sota2.com/research/sota/circle-packing-on-world12d-large-variance.md>): Circle Packing; World12D large variance.

- [Circle Packing on Weather large variance](<https://www.sota2.com/research/sota/circle-packing-on-weather-large-variance.md>): Circle Packing; Weather large variance.

- [Circle Packing on Olive large variance](<https://www.sota2.com/research/sota/circle-packing-on-olive-large-variance.md>): Circle Packing; Olive large variance.

- [Circle Packing on MNIST64 large variance](<https://www.sota2.com/research/sota/circle-packing-on-mnist64-large-variance.md>): Circle Packing; MNIST64 large variance.

- [Circle Packing on ExtYaleB large variance](<https://www.sota2.com/research/sota/circle-packing-on-extyaleb-large-variance.md>): Circle Packing; ExtYaleB large variance.

- [Circle Packing on Ecoli large variance](<https://www.sota2.com/research/sota/circle-packing-on-ecoli-large-variance.md>): Circle Packing; Ecoli large variance.

- [Circle Packing on Dermatology large variance](<https://www.sota2.com/research/sota/circle-packing-on-dermatology-large-variance.md>): Circle Packing; Dermatology large variance.

- [Circle Packing on Boston large variance](<https://www.sota2.com/research/sota/circle-packing-on-boston-large-variance.md>): Circle Packing; Boston large variance.

- [Circle Packing on World12D small circle radii variance](<https://www.sota2.com/research/sota/circle-packing-on-world12d-small-circle-radii-variance.md>): Circle Packing; World12D small circle radii variance.

- [Circle Packing on Weather small circle radii variance](<https://www.sota2.com/research/sota/circle-packing-on-weather-small-circle-radii-variance.md>): Circle Packing; Weather small circle radii variance.

- [Circle Packing on Olive small circle radii variance](<https://www.sota2.com/research/sota/circle-packing-on-olive-small-circle-radii-variance.md>): Circle Packing; Olive small circle radii variance.

- [Circle Packing on MNIST64 small circle radii variance](<https://www.sota2.com/research/sota/circle-packing-on-mnist64-small-circle-radii-variance.md>): Circle Packing; MNIST64 small circle radii variance.

- [Circle Packing on ExtYaleB small circle radii variance](<https://www.sota2.com/research/sota/circle-packing-on-extyaleb-small-circle-radii-variance.md>): Circle Packing; ExtYaleB small circle radii variance.

- [Circle Packing on Ecoli small circle radii variance](<https://www.sota2.com/research/sota/circle-packing-on-ecoli-small-circle-radii-variance.md>): Circle Packing; Ecoli small circle radii variance.

- [Circle Packing on Dermatology small circle radii variance](<https://www.sota2.com/research/sota/circle-packing-on-dermatology-small-circle-radii-variance.md>): Circle Packing; Dermatology small circle radii variance.

- [Circle Packing on Boston small circle radii variance](<https://www.sota2.com/research/sota/circle-packing-on-boston-small-circle-radii-variance.md>): Circle Packing; Boston small circle radii variance.

- [Sparse covariance estimation (Upper Bound) on k-sparse covariance model Problem 1](<https://www.sota2.com/research/sota/sparse-covariance-estimation-upper-bound-on-k-sparse-covariance-model-problem-1.md>): Sparse covariance estimation (Upper Bound); k-sparse covariance model Problem 1.

- [Log-density Estimation on 2-component diagonal-covariance GMMs d=100, n=2048 context (test)](<https://www.sota2.com/research/sota/log-density-estimation-on-2-component-diagonal-covariance-gmms-d-100-n-2048-context-test.md>): Log-density Estimation; 2-component diagonal-covariance GMMs d=100, n=2048 context (test).

- [Score Estimation on 2-component diagonal-covariance GMMs d=100, n=2048 context (test)](<https://www.sota2.com/research/sota/score-estimation-on-2-component-diagonal-covariance-gmms-d-100-n-2048-context-test.md>): Score Estimation; 2-component diagonal-covariance GMMs d=100, n=2048 context (test).

- [Anomaly Detection on Anomaly-IntraVariance 1.0 (test)](<https://www.sota2.com/research/sota/anomaly-detection-on-anomaly-intravariance-1-0-test.md>): Anomaly Detection; Anomaly-IntraVariance 1.0 (test).