We assess cluster stability by trimming extreme points and tracking data range reduction.
problem Assessing stability of one-dimensional clusters.
method Probabilistic method using diameter-shrinkage ratio to track data range reduction.
result Our method achieves higher accuracy than classical tests in small or noisy samples.
Improved Frank-Wolfe algorithm for constrained convex optimization with nearest extreme point oracle.
problem Constrained smooth convex minimization with limited linear optimization oracle access.
method Frank-Wolfe algorithm with nearest extreme point oracle.
result Improved complexity bounds for specific feasible sets, including linear convergence for 0ext−−1 polytopes. We show that any n-dimensional nonnegatively curved Alexandrov space with the maximal possible number of extremal points is isometric to a quotient space of Euclidean n -space by an action of a crystallographic group. We describe all such actions.
Trimming helps in conformal prediction when it separates anomaly scores.
problem Effectiveness of trimming in conformal prediction under contamination.
method Analyse fixed-threshold trimming as a replacement of the contaminated calibration law with a retained law.
result Trimming helps when it separates anomaly scores, reducing clean-target coverage to a one-dimensional score-CDF transfer problem.
We consider the problem of robustifying high-dimensional structured estimation. Robust techniques are key in real-world applications which often involve outliers and data corruption. We focus on trimmed versions of structurally regularized M-estimators in the high-dimensional setting, including the popular Least Trimme…
New method trims network data to resist adversarial contamination.
problem Adversarial contamination in network data affects statistical and algorithmic performance.
method Proposes a new trimming method operating in model space to address both block and white noise contamination.
result Demonstrates superior performance in simulations compared to direct trimming.
Nonconvex penalty methods for sparse modeling in linear regression have been a topic of fervent interest in recent years. Herein, we study a family of nonconvex penalty functions that we call the trimmed Lasso and that offers exact control over the desired level of sparsity of estimators. We analyze its structural prop…
We describe a general framework for measuring risks, where the risk measure takes values in an abstract cone. It is shown that this approach naturally includes the classical risk measures and set-valued risk measures and yields a natural definition of vector-valued risk measures. Several main constructions of risk meas…
We relate trimmed sums of twists in cylinders along a typical Teichmuller geodesic to the area Siegel-Veech constant.
New method solves sparse approximation problem using trimmed lasso and generalized soft-min penalties.
problem Sparse approximation or best subset selection problem.
method Regularized approach with trimmed lasso and generalized soft-min penalties.
result The trimmed lasso provides sparse recovery guarantees and a practical optimization algorithm.
New core inflation measure predicts future headline inflation.
problem Creating a better measure of core inflation for timely policy decisions.
method Assemblage Regression, a nonnegative ridge regression that optimizes subcomponent weights.
result Significant improvements in forecasting medium-term inflation developments.
Gaussian Graphical Models (GGMs) are popular tools for studying network structures. However, many modern applications such as gene network discovery and social interactions analysis often involve high-dimensional noisy data with outliers or heavier tails than the Gaussian distribution. In this paper, we propose the Tri…
A method for estimating parameters from entangled single-sample distributions, robust to high-noise data.
problem Estimating common parameters from entangled single-sample distributions.
method Iterative trimming of samples to estimate the parameter.
result The method can tolerate a constant fraction of high-noise data points.
New conditions ensure Dantzig-Wolfe relaxation matches rank-constrained optimization problems.
problem Rank-constrained optimization problems with linear matrix inequalities.
method Investigates Dantzig-Wolfe relaxation and develops conditions for exactness.
result Conditions for extreme point, convex hull, and objective exactness.
Alpha-trimming prunes trees in random forests to improve predictive performance.
problem Improving predictive performance of random forests by locally adaptive tree pruning.
method Alpha-trimming is a fast pruning algorithm that prunes trees in a random forest based on signal-to-noise ratio, controlled by a tuning parameter.
result Alpha-trimming often lowers mean squared prediction error compared to fully grown random forests.
New method prevents neural network breakdown by combining trimmed loss and variation regularization.
problem Outlier contamination in neural network training.
method Integrates transformed trimmed loss and higher-order variation regularization.
result Ensures robustness to outlier contamination with a high functional breakdown point.
Paper proposes robust gossip algorithms for mean and trimmed mean estimation.
problem Vulnerability of mean-based gossip algorithms to malicious nodes.
method Developed extsc{GoRank} for rank estimation and extsc{GoTrim} for trimmed mean estimation.
result Established convergence rates for rank and trimmed mean estimation.
We consider the signed density of the extremal points of (two-dimensional) scalar fields with a Gaussian distribution. We assign a positive unit charge to the maxima and minima of the function and a negative one to its saddles. At first, we compute the average density for a field in half-space with Dirichlet boundary c…
TrIM improves gradient-based dimension reduction and regression.
problem Efficiently identifying relevant feature subspace for high-dimensional regression.
method Introduced TrIM forest, an iterative approach using Mondrian forest and EGOP estimate.
result Consistency guarantees and convergence rates for EGOP matrix and random forest estimator.
New algorithm robustly estimates sparse models in high dimensions with corrupted data.
problem Estimating latent variable models with arbitrarily corrupted samples in high dimensional space.
method Trimmed (Gradient) Expectation Maximization with trimming gradients and hard thresholding steps.
result The algorithm converges to near optimal statistical rate geometrically under certain conditions.
Estimates GLMs robustly against label corruptions.
problem Learning GLMs under adversarial label corruptions.
method Iterative trimmed maximum likelihood estimator.
result Achieves minimax near-optimal risk.
We propose a robust elastic net (REN) model for high-dimensional sparse regression and give its performance guarantees (both the statistical error bound and the optimization bound). A simple idea of trimming the inner product is applied to the elastic net model. Specifically, we robustify the covariance matrix by trimm…
This paper considers the problem of removing costly features from a Bayesian network classifier. We want the classifier to be robust to these changes, and maintain its classification behavior. To this end, we propose a closeness metric between Bayesian classifiers, called the expected classification agreement (ECA). Ou…
A new robust GP regression algorithm that trims outliers improves model accuracy.
problem Severe bias in GP regression due to data contamination by outliers.
method Iterative trimming of extreme data points.
result Significantly outperforms standard and robust GP variants in most test cases.
Given an iterated function system of affine dilations with fixed points the vertices of a regular polygon, we characterize which points in the limit set lie on the boundary of its convex hull.
TRIM improves interpretability of deep neural networks in cosmology.
problem Understanding which features a deep neural network uses in a transformed space.
method TRIM (Transformation IMportance) attributes importances to features in a transformed space.
result Combining TRIM with contextual decomposition helps identify physical features learned by DNNs.
Analyzes convex structures in Teichmüller space unit tangent spheres.
problem Characterize faces and extreme points of unit tangent spheres in Teichmüller space.
method Analyzes Finsler infinitesimal balls of Thurston metric, characterizes faces, exposed faces, and extreme points.
result Characterizes faces and extreme points of unit tangent spheres in Teichmüller space.
Let Wn be the class of C∞ complete simply connected n−dimensional manifolds without conjugate points. The hyperbolic space as well as Euclidean space are good examples of such manifolds. Let and let A be a subset of W. This article aims at characterization and bu…
We develop a fast, tractable technique called Net-Trim for simplifying a trained neural network. The method is a convex post-processing module, which prunes (sparsifies) a trained network layer by layer, while preserving the internal responses. We present a comprehensive analysis of Net-Trim from both the algorithmic a…
New method measures model variability from stochastic optimization.
problem Measuring model quality obscured by stochastic optimization.
method Robust hypothesis testing and novel summary statistic.
result Shows α-trimming level is more expressive than performance metrics. Paper proposes a framework to identify and obfuscate sensitive features via information density estimation.
problem Identifying and protecting sensitive attributes from leakage in obfuscation mechanisms.
method Information density estimation to identify leaking features, followed by a targeted obfuscation mechanism.
result Proven leakage guarantee in terms of Eγ-divergence for the obfuscation mechanism. Density ratio estimation is a vital tool in both machine learning and statistical community. However, due to the unbounded nature of density ratio, the estimation procedure can be vulnerable to corrupted data points, which often pushes the estimated ratio toward infinity. In this paper, we present a robust estimator wh…
New algorithm reduces ERM problem size while maintaining accuracy.
problem Empirical risk minimization problem size reduction.
method Adaptive Deterministic Uniform-Weight Trimming (ADUWT) algorithm.
result Uniform (1±ε) relative-error approximation for ERM objective. Improved robust regression for heavy-tailed and contaminated data.
problem Linear regression with heavy-tailed and adversarially contaminated covariates and responses.
method Applying a filtering algorithm to covariates and then using Huber regression, least trimmed squares, or least absolute deviation estimators on the remaining data.
result Near-optimal error rates achieved for the Huber regression estimator.
Combines VaR and ES forecasts from a large pool of methods.
problem Combining forecasts from a large pool of VaR and ES methods.
method Adapted interval forecast combination methods, including trimmed means and mixtures approach.
result Trimmed mean combinations, mixtures method, and performance-based weighting delivered strong results.
Robust Trimmed k-means improves clustering with outliers and mixed data.
problem Real-world data often contains outliers and mixed membership clusters, complicating traditional clustering methods.
method Proposes Robust Trimmed k-means (RTKM) that robustifies k-means for both single- and multi-membership data.
result RTKM outperforms other methods on multi-membership data with outliers and single membership data with outliers.
Paper develops robust OPF method using contextual information.
problem Optimal Power Flow problem under incomplete uncertainty knowledge.
method Distributionally robust chance-constrained formulation with probability trimmings and optimal transport.
result Distributional robustness improves expected cost and system reliability.
Using a trimming approach, we investigate a k-means type method based on Bregman divergences for clustering data possibly corrupted with clutter noise. The main interest of Bregman divergences is that the standard Lloyd algorithm adapts to these distortion measures, and they are well-suited for clustering data sampled …
Efficiently estimates mixed effects models with nonlinear components and constraints.
problem Estimating mixed effects models with nonlinear components and constraints.
method Developed an efficient approach for mixed effects models with trimming in the marginal likelihood.
result More accurate and computationally efficient estimates in the presence of outliers.
Clustering, or unsupervised classification, is a task often plagued by outliers. Yet there is a paucity of work on handling outliers in clustering. Outlier identification algorithms tend to fall into three broad categories: outlier inclusion, outlier trimming, and post hoc outlier identification methods, with the forme…
A new robust regression method handles outliers in high-dimensional data.
problem Outliers in high-dimensional data make conventional regression methods ineffective.
method Robust penalized least squares of depth trimmed residuals regression.
result The new method outperforms existing methods in estimation and prediction accuracy.
Proposes a sensitivity framework to handle limited overlap in causal inference.
problem Limited overlap between treated and control groups in observational studies.
method Sensitivity framework based on worst-case confidence bounds on bias introduced by trimming.
result Protects against spurious findings by quantifying uncertainty in regions with limited overlap.
Efficiently clusters data with weak assumptions, robust to contamination.
problem General-shaped clustering under weak parametric assumptions with data contamination.
method Two-step hybrid robust clustering algorithm combining trimmed k-means and hierarchical agglomeration.
result Outperforms state-of-the-art methods in various applications.
We introduce and analyze a new technique for model reduction for deep neural networks. While large networks are theoretically capable of learning arbitrarily complex models, overfitting and model redundancy negatively affects the prediction accuracy and model variance. Our Net-Trim algorithm prunes (sparsifies) a train…
Convex geometry explains optimal neural network parameters.
problem Understanding optimal parameters in over-parameterized neural networks.
method Convex geometry, extreme points, linear spline interpolation, kernel matrix, cutting-plane algorithm.
result Optimal network parameters can be characterized as interpretable closed-form formulas.
We study polar orbitopes, i.e. convex hulls of orbits of a polar representation of a compact Lie group. The face structure is studied by means of the gradient momentum map and it is shown that every face is exposed and is again a polar orbitope. Up to conjugation the faces are completely determined by the momentum poly…
Recent studies on automatic neural architectures search have demonstrated significant performance, competitive to or even better than hand-crafted neural architectures. However, most of the existing network architecture tend to use residual, parallel structures and concatenation block between shallow and deep features …
Robust CG methods avoid data corruption and solve structured statistical estimation problems.
problem Data corruption and heavy-tailed data in structured statistical estimation.
method Robustification of Conditional Gradient (CG) type methods using Huber's corruption model and robust mean gradient estimation.
result Robust CG methods converge linearly with correct sample complexity, even for high-dimensional problems.