Study ridge ensembles in proportional feature-to-sample size regime, proving risk equivalence and GCV consistency.
problem Characterizing and optimizing ridge ensembles in proportional feature-to-sample size regimes.
method Proportional asymptotics analysis, GCV for tuning, proving risk equivalence.
result Risk of optimal full ridgeless ensemble matches optimal ridge predictor's risk.
The paper analyzes the risk of bagging regularized M-estimators under proportional asymptotics.
problem Characterizing the risk of ensemble estimators trained with subsamples and regularizers.
method Developed a consistent estimator for the risk of ensemble estimators under proportional asymptotics.
result Optimal subsample size k⋆ tends to be in the overparameterized regime for the full-ensemble estimator. Theory and method for reducing prediction variance in noisy feature-subsampled ridge ensembles.
problem Reduction of prediction variance in noisy data with feature bagging.
method Developed analytical learning curves for noisy ridge ensembles, introduced heterogeneous feature ensembling.
result Subsampling shifts the double-descent peak, leading to improved performance over a single linear predictor.
Proposes a new method for nonlinear Bayesian updates using ensemble kernel regression.
problem Nonlinear and non-Gaussian Bayesian updates for complex systems.
method Combines Kalman filtering for observed components and kernel density estimation for unobserved components, with subsampling and clustering.
result Reduces estimation errors in highly nonlinear scenarios compared to standard linear updates.
New ensemble method improves model stability exponentially.
problem Improving model stability for discontinuous base learners.
method Selecting the most frequently generated model from subsamples.
result Exponentially decaying tails for excess risk.
A deep learning subsampling technique improves modulation classification accuracy.
problem Improving modulation classification accuracy in wireless communication systems.
method Proposes a data-driven subsampling strategy using deep neural networks to simulate signal removal.
result Improves classification accuracy to higher levels than traditional methods.
Ensemble methods that average over a collection of independent predictors that are each limited to a subsampling of both the examples and features of the training data command a significant presence in machine learning, such as the ever-popular random forest, yet the nature of the subsampling effect, particularly of th…
Develops an empirical likelihood framework for random forests and ensembles.
problem Quantifying the statistical uncertainty of random forests and ensembles.
method Empirical likelihood framework exploiting the incomplete U-statistic structure of ensemble predictions. result Modified empirical likelihood statistic achieves accurate coverage and practical reliability.
A new method detects outliers using ensembles of Dirichlet process mixtures.
problem Challenges in unsupervised outlier detection using Dirichlet process mixtures.
method Ensembles of Dirichlet process Gaussian mixtures with random subspace and subsampling.
result Empirically outperforms existing approaches in unsupervised outlier detection.
New insights into how randomization affects greedy model selection.
problem Understanding the impact of feature subsampling on greedy model selection.
method Investigated greedy forward selection with feature subsampling, proving effects on bias and variance.
result Ensembling with feature subsampling reduces both bias and variance, unlike convex base learners.
ECV method optimizes ensemble parameters for randomized ensembles.
problem Efficient tuning of ensemble parameters in randomized ensembles.
method ECV (Extrapolated Cross-Validation) method for tuning ensemble and subsample sizes.
result ECV yields δ-optimal ensembles for squared prediction risk.
New equivalences found between subsampling and ridge regularization methods.
problem Establishing precise structural and risk equivalences between subsampling and ridge regularization.
method Proved structural and risk equivalences between subsample ridge estimators and different ridge regularization levels and subsample aspect ratios.
result Optimally tuned ridge regression exhibits a monotonic prediction risk in the data aspect ratio.
Study detects P-type bifurcations in single system realizations using unreliable kernel density estimates.
problem Detecting P-type bifurcations in signals with unreliable kernel density estimates.
method Create persistence diagrams from single system realization, statistically analyze resulting set, compare point process modeling methods.
result Subsampling outperforms other point process modeling methods in predicting P-type bifurcations.
This research improves model interpretability and uncertainty estimation for deep learning models on non-iid data.
problem Improving interpretability and uncertainty estimation for deep learning models on non-iid data.
method 4 UQ approaches (BNN, SWAG, MC dropout, ensemble) applied to ARMED MEDL models.
result Ensemble approaches, especially with 90% subsampling, provide best performance in prediction and uncertainty estimation.
Develops asymptotic theory for deep Cox models to enable valid inference.
problem Theoretical gaps in deep neural network estimators for Cox models.
method Asymptotic distribution theory linking in-sample optimization error to population risk.
result Pointwise and multivariate asymptotic normality for subsampled ensemble estimators.
Novel U-learning method for predicting continuous outcomes from high-dimensional data.
problem Challenges in making valid inferences on predictions from high-dimensional inputs.
method U-learning via combinatory multi-subsampling for ensemble predictions and confidence intervals.
result Valid inferences on predictions from Lasso and neural networks.
COMET is a single-pass MapReduce algorithm for learning on large-scale data. It builds multiple random forest ensembles on distributed blocks of data and merges them into a mega-ensemble. This approach is appropriate when learning from massive-scale data that is too large to fit on a single machine. To get the best acc…
MFRDE uses medians of forest estimators to robustly estimate densities in noisy data.
problem Robust density estimation in the presence of outliers.
method MFRDE uses pointwise median operation on forest density estimators fitted on subsampled datasets.
result MFRDE achieves robustness against all outliers while maintaining accuracy for density estimation.
This work develops formal statistical inference procedures for machine learning ensemble methods. Ensemble methods based on bootstrapping, such as bagging and random forests, have improved the predictive accuracy of individual trees, but fail to provide a framework in which distributional results can be easily determin…
The paper analyzes bagging in overparameterized learning, deriving risk properties and optimal subsample sizes.
problem Characterizing the risk of bagged predictors in overparameterized settings.
method General strategy using classical results on simple random sampling, specialized for ridge and ridgeless predictors.
result Derives exact asymptotic risk of bagged ridge and ridgeless predictors under various conditions.
Random forests remain among the most popular off-the-shelf supervised learning algorithms. Despite their well-documented empirical success, however, until recently, few theoretical results were available to describe their performance and behavior. In this work we push beyond recent work on consistency and asymptotic no…
Study shows how feature weighting affects neural network regularization.
problem Understanding how feature weighting influences neural network regularization.
method Derived equivalence paths connecting different weighting matrices and ridge regularization levels.
result Ridge estimators trained on weighted features are asymptotically equivalent when evaluated against test vectors.
We improve prediction risk estimation for large datasets using sketching and ridge regression.
problem Estimating prediction risks for large datasets efficiently and accurately.
method Random matrix theory, generalized cross validation, sketched ridge regression ensembles, and ensemble trick.
result Consistent risk estimation and prediction intervals for large-scale datasets.
Classification outperforms regression in portfolio construction, yielding higher Sharpe ratios.
problem Determining which machine learning approach (classification vs. regression) is more effective for portfolio construction.
method Used stacking ensemble of gradient boosted tree, random forest, and neural network models.
result Classification yields higher Sharpe ratios and economically significant alphas compared to regression.
This study shows how social insects and machine learning methods share a common mathematical framework.
problem Understanding how decentralized systems achieve optimal decision-making.
method Developed a rigorous mathematical framework to show isomorphism between ant colonies and ensemble machine learning.
result Demonstrated that ant colony decision-making and random forest learning implement identical variance reduction strategies through decorrelation of identical units.
Random forests have proven to be reliable predictive algorithms in many application areas. Not much is known, however, about the statistical properties of random forests. Several authors have established conditions under which their predictions are consistent, but these results do not provide practical estimates of ran…
FastForest boosts Random Forest speed by 24%.
problem Efficiency in processing speed for Random Forest.
method Subsample Aggregating, Logarithmic Split-Point Sampling, Dynamic Restricted Subspacing.
result Average 24% increase in processing speed with accuracy maintained.
Causal discovery can be a powerful tool for investigating causality when a system can be observed but is inaccessible to experiments in practice. Despite this, it is rarely used in any scientific or medical fields. One of the major hurdles preventing the field of causal discovery from having a larger impact is that it …
A new method selects a representative subsample for efficient kernel density estimation.
problem Selecting a representative subsample without model assumptions.
method Optimal transport techniques for model-free subsampling with an efficient algorithm.
result The selected subsample can be used for efficient density estimation with derived convergence rates and optimal bandwidth.
In this paper we demonstrate that tempering Markov chain Monte Carlo samplers for Bayesian models by recursively subsampling observations without replacement can improve the performance of baseline samplers in terms of effective sample size per computation. We present two tempering by subsampling algorithms, subsampled…
This paper optimizes subsampling for large datasets using Poisson distribution.
problem Efficiently subsample large datasets for quasi-likelihood estimation.
method Derives optimal Poisson subsampling probabilities and develops a distributed subsampling framework.
result Consistent and asymptotically normal estimators are obtained.
The paper learns compact implicit surface maps from streaming data using an ensemble of sparse Gaussian processes.
problem Creating compact and accurate implicit surface maps from streaming range data.
method An ensemble of sparse Gaussian process experts, incrementally adjusted, trades-off between model complexity and prediction error.
result The approach learns compact and accurate implicit surface models comparable to or better than exact GP regression with subsampled data.
Large sample size brings the computation bottleneck for modern data analysis. Subsampling is one of efficient strategies to handle this problem. In previous studies, researchers make more fo- cus on subsampling with replacement (SSR) than on subsampling without replacement (SSWR). In this paper we investigate a kind of…
A new method for feature importance inference without data splitting.
problem Feature importance inference for machine learning models.
method Minipatch ensembles for model-agnostic, distribution-free inference.
result Asymptotic validity of confidence intervals without data splitting.
This paper explains CART random forests using stochastic control theory.
problem Understanding the inner workings of CART random forests.
method Developed a stochastic-control perspective on CART random forests, interpreting feature subsampling as a random feasible action set and the split rule as a policy.
result Established that the CART policy is locally stabilizing but globally suboptimal for the forest objective.
A significant hurdle for analyzing large sample data is the lack of effective statistical computing and inference methods. An emerging powerful approach for analyzing large sample data is subsampling, by which one takes a random subsample from the original full sample and uses it as a surrogate for subsequent computati…
We study the problem of subsampling in differential privacy (DP), a question that is the centerpiece behind many successful differentially private machine learning algorithms. Specifically, we provide a tight upper bound on the Rényi Differential Privacy (RDP) (Mironov, 2017) parameters for algorithms that: (1) subsamp…
A new model-free subsampling method using uniform designs is proposed.
problem Model-based subsampling methods are often dependent on model assumptions.
method Developed a criterion (GEFD) and a model-free subsampling method based on uniform designs.
result The proposed method outperforms random sampling and is robust under diverse model specifications.
A new method reduces variance in SGMCMC by preferentially subsampling data.
problem High variance in stochastic gradient estimates impacts sampler performance.
method Use a non-uniform probability distribution to preferentially subsample data points and adaptively adjust subsample size.
result Maintains accuracy while substantially reducing average subsample size.
For massive data, the family of subsampling algorithms is popular to downsize the data volume and reduce computational burden. Existing studies focus on approximating the ordinary least squares estimate in linear regression, where statistical leverage scores are often used to define subsampling probabilities. In this p…
Unified framework for subsampling mechanisms with tighter privacy guarantees.
problem Improving privacy in machine learning models through subsampling.
method Conditional optimal transport for deriving mechanism-specific subsampling guarantees.
result Tighter privacy bounds for subsampled mechanisms compared to traditional methods.
RAMPART ranks top-k features more accurately than existing methods.
problem Accurate ranking of important features in machine learning.
method Adaptive sequential halving strategy combined with ensembling techniques.
result RAMPART achieves the correct top-k ranking with high probability.
The Sampled Gaussian Mechanism's noise level decreases with larger subsampling rates, improving privacy-utility trade-offs.
problem Improving privacy-utility trade-offs in differentially private stochastic optimization.
method Proof of a conjecture about the Sampled Gaussian Mechanism's noise level and subsampling rate relationship.
result A rigorous proof of the conjecture, completing the proof of Theorem 6.2 in the original paper.
Group-equivariant subsampling layers improve CNNs' equivariance.
problem Non-translation equivariance in subsampling operations.
method Translation and group-equivariant subsampling/upsampling layers.
result Group-equivariant autoencoders learn equivariant representations.
Develops a method to optimize hyperparameters for subsampling methods.
problem Optimizing hyperparameters for subsampling methods to improve estimator efficiency.
method Careful theoretical analysis leading to an optimal choice of hyperparameters.
result Improves the statistical efficiency of subsampling estimators without extra CPU time.
New insights into privacy guarantees for subsampled mechanisms under composition.
problem Tight privacy guarantees for the composition of subsampled differentially private mechanisms.
method Addressed confusion points in privacy accounting for subsampled mechanisms, providing examples and counterexamples.
result Privacy guarantees for subsampled mechanisms differ significantly between Poisson subsampling and sampling without replacement.
We describe an adaptation of the simulated annealing algorithm to nonparametric clustering and related probabilistic models. This new algorithm learns nonparametric latent structure over a growing and constantly churning subsample of training data, where the portion of data subsampled can be interpreted as the inverse …
Hamiltonian Monte Carlo (HMC) samples efficiently from high-dimensional posterior distributions with proposed parameter draws obtained by iterating on a discretized version of the Hamiltonian dynamics. The iterations make HMC computationally costly, especially in problems with large datasets, since it is necessary to c…