This article is devoted to the problem of predicting the value taken by a random permutation , describing the preferences of an individual over a set of numbered items say, based on the observation of an input/explanatory r.v. e.g. characteristics of the individual), when error is measured…
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48 results for “ranking median regression”
Convex cores found for group actions on median spaces.
problem Understanding group actions on median spaces without metric or topology.
method Introduced convex cores for actions on finite-rank median algebras.
result Actions on median spaces have nonempty convex cores.
We construct compactifications for median spaces with compact intervals, generalising Roller boundaries of cube complexes. Examples of median spaces with compact intervals include all finite rank median spaces and all proper median spaces of infinite rank. Our methods also work for general median algebra…
New concept of coarse medians for higher rank symmetric spaces.
problem Understanding medians in higher rank symmetric spaces.
method Introducing coarse -median spaces and proving their existence.
result Existence of coarse higher medians on divisible and quasi-homogeneous convex domains.
We prove a version of the Tits alternative for groups acting on complete, finite rank median spaces. This shows that group actions on finite rank median spaces are much more restricted than actions on general median spaces. Along the way, we extend to median spaces the Caprace-Sageev machinery and part of Hagen's theor…
Study shows how certain spaces can be mapped to R^n with specific properties.
problem Characterizing and mapping locally compact median spaces of finite rank.
method Analyzing the combinatorics of halfspaces and properties of isometric actions.
result Spaces with certain actions are isometric to R^n, and orbits are discrete.
This research tackles multiclass classification by introducing a method for label ranking.
problem The challenge is to predict a sorted list of labels based on input features.
method Inspired by ranking median regression, the One-Versus-One (OVO) approach is used to achieve optimal ranking.
result The OVO approach yields an optimal ranking of labels with overwhelming probability under noise conditions.
New method for summarizing ranking distributions using consensus ranking distributions.
problem Summarizing ranking distributions efficiently and accurately.
method Introducing consensus ranking distributions and a top-down tree-structured statistical algorithm.
result Optimal distortion can be expressed as a function of pairwise probabilities, enabling efficient learning methods.
Finite rank median spaces are a simultaneous generalisation of finite dimensional cube complexes and real trees. If is an irreducible lattice in a product of rank one simple Lie groups, we show that every action of on a complete, finite rank median space has a global fixed point. This is in sharp…
Three privacy-preserving methods for median regression are proposed.
problem Protecting individual privacy in median regression analysis.
method Three privacy-preserving methods: finite smoothing, iterative, and greedy coordinate descent.
result Numerical results show varying performance across different sample sizes.
We consider the non-parametric regression problem under Huber's -contamination model, in which an fraction of observations are subject to arbitrary adversarial noise. We first show that a simple local binning median step can effectively remove the adversary noise and this median estimator is minimax optimal up t…
This paper extends Median-of-Means to new learning problems involving pairwise comparisons.
problem Learning from pairwise comparisons in machine learning.
method Segmenting data into blocks, comparing pairs of decision rules, and declaring the winner based on majority performance.
result The Median-of-Means approach maintains robustness and performance under various sampling schemes.
A new method for fast and robust sparsity learning over networks.
problem Efficiently learning sparse models in decentralized networks.
method Decentralized surrogate median regression (deSMR) method.
result Linear convergence rate with a simple implementation.
Coarse cubical rigiditymath.GR
Groups with specific properties have similar cubulations and coarse median structures.
problem Understanding the structure of certain groups through cubical coarsening.
method Analyzing right-angled Artin and Coxeter groups, focusing on automorphisms and cubulations.
result Automorphisms of specific groups preserve coarse median structures and have nice fixed subgroups.
This work studies applications and generalizations of a simple estimation technique that provides exponential concentration under heavy-tailed distributions, assuming only bounded low-order moments. We show that the technique can be used for approximate minimization of smooth and strongly convex losses, and specificall…
Paper develops a new algorithm for sparse signal recovery.
problem Sparse signal recovery from noisy observations.
method Iterative Stochastic Optimization using Stochastic Mirror Descent.
result Linear convergence during preliminary phase of the routine.
DiPriMe forests use private medians to create balanced tree splits for privacy-protected data.
problem Privacy concerns in training random forests due to multiple data queries.
method Proposes DiPriMe forests, which use a private median to generate balanced splits, ensuring differential privacy.
result DiPriMe forests achieve high utility while maintaining differential privacy, as shown both theoretically and empirically.
A regularized risk minimization procedure for regression function estimation is introduced that achieves near optimal accuracy and confidence under general conditions, including heavy-tailed predictor and response variables. The procedure is based on median-of-means tournaments, introduced by the authors in [8]. It is …
This paper introduces depth functions for ranking data, improving statistical summaries.
problem Lack of comprehensive statistical summaries for ranking data.
method Metric-based depth functions on symmetric group to define rankings, depths, and procedures.
result Novel depth functions provide a more informative summary of ranking data.
Novel algorithm resists Byzantine attacks in federated learning for PCA and LRCS.
problem Byzantine attacks in federated learning for PCA and LRCS.
method Subspace-Median algorithm for federated PCA, altGDmin for LRCS.
result Provably Byzantine-resilient communication-efficient and sample-efficient algorithms.
LLM forecasting benchmarks suffer from information leakage, which confounds model performance.
problem LLM forecasting benchmarks suffer from information leakage.
method A retrieval-augmented LLM forecaster observes only decision-time information.
result The full pipeline obtains a median monthly Spearman rank IC of +0.154.
A main goal of regression is to derive statistical conclusions on the conditional distribution of the output variable Y given the input values x. Two of the most important characteristics of a single distribution are location and scale. Support vector machines (SVMs) are well established to estimate location functions …
The paper studies automorphisms of RAAGs and RACGs, proving properties of their fixed subgroups.
problem Fixed subgroups of automorphisms of RAAGs and RACGs.
method Introducing coarse-median preserving automorphisms and proving properties of fixed subgroups.
result Fixed subgroups of RAAGs and RACGs are finitely generated, undistorted, and quasi-convex.
New method improves mean estimation for heavy-tailed data.
problem Estimating mean of heavy-tailed distributions.
method Median-of-Means (MoM) with symmetrization technique.
result Improved sample complexity bound for mean estimation.
Study robust linear regression without distributional assumptions for heavy-tailed responses.
problem Linear regression with heavy-tailed responses and no distributional assumptions.
method Combining truncated least squares, median-of-means, and aggregation theory to construct a non-linear estimator.
result Achieves excess risk of order with optimal sub-exponential tail.
Optimal multitask learning method for sparse heterogeneous datasets.
problem Efficiently learning from multiple related datasets with sparse task-specific differences.
method MOLAR estimator, combining weighted median and shrinkage.
result Improves estimation error dependence on data dimension compared to task-wise least squares.
New method certifies regression robustness without data distribution assumptions.
problem Certifying robustness of regression models against poisoning attacks.
method Reduces certified regression to certified classification using median decision function.
result Proposes six new provably-robust regression models.
Quantile regression improves urban water demand forecasting.
problem Improving probabilistic urban water demand forecasting.
method Comparing five quantile regression algorithms and their combinations for one-day ahead forecasting.
result Linear boosting algorithm performs best for probabilistic urban water demand forecasting.
The main goal of this paper is a detailed study of asymptotic cones of the mapping class groups. In particular, we prove that every asymptotic cone of a mapping class group has a bi-Lipschitz equivariant embedding into a product of real trees, sending limits of hierarchy paths onto geodesics, and with image a median su…
We show how to reduce the process of predicting general order statistics (and the median in particular) to solving classification. The accompanying theoretical statement shows that the regret of the classifier bounds the regret of the quantile regression under a quantile loss. We also test this reduction empirically ag…
We survey some of the recent advances in mean estimation and regression function estimation. In particular, we describe sub-Gaussian mean estimators for possibly heavy-tailed data both in the univariate and multivariate settings. We focus on estimators based on median-of-means techniques but other methods such as the t…
We develop a unified approach for classification and regression support vector machines for data subject to right censoring. We provide finite sample bounds on the generalization error of the algorithm, prove risk consistency for a wide class of probability measures, and study the associated learning rates. We apply th…
For massive data sets, efficient computation commonly relies on distributed algorithms that store and process subsets of the data on different machines, minimizing communication costs. Our focus is on regression and classification problems involving many features. A variety of distributed algorithms have been proposed …
Nonconvex Low-Rank Matrix Recovery with Arbitrary Outliers via Median-Truncated Gradient Descentcs.IT
Recent work has demonstrated the effectiveness of gradient descent for directly recovering the factors of low-rank matrices from random linear measurements in a globally convergent manner when initialized properly. However, the performance of existing algorithms is highly sensitive in the presence of outliers that may …
New method speeds up NIR spectroscopy calibration by 400x.
problem Efficient preprocessing selection in NIR spectroscopy.
method Operator-adaptive PLS and Ridge regression.
result Significant reduction in fitting time with comparable prediction quality.
New method for neural networks to predict histogram data.
problem Lack of principled approach for histogram regression.
method Pinball loss applied to cumulative histogram.
result Accuracy similar to EMD with less computational cost.
Unique median structures found in hyperbolic spaces.
problem Uniqueness of median structures in hyperbolic spaces.
method Analyzing product of hyperbolic spaces and properties of relative hyperbolicity.
result Non-hyperbolic pants graphs can have unique median structures.
Study on median algebra structures on Euclidean spaces and manifolds with local CAT(0) cubulation.
problem Understanding median algebra structures on Euclidean spaces and manifolds.
method Showed local CAT(0) cubulation for median structures on ER homology manifolds.
result Median structures on ER homology manifolds have a local CAT(0) cubulation structure.
We show that uniform lattices of isometries of products of real hyperbolic spaces act properly discontinuously and cocompactly on a median space. For lattices in products of at least two factors, this is the strongest degree of compatibility possible with the median geometry. Our theorem is also relevant for potential …
R2T hybrid model improves robust regression for asymmetric noise.
problem Least-squares regression fails with asymmetric structured noise.
method Transformer encoder, compression NN, fixed symbolic equation.
result Median regression MSE of 6e-6 to 3.5e-5 on synthetic data.
Median Shapesmath.DG
We introduce and begin to explore the mean and median of finite sets of shapes represented as integral currents. The median can be computed efficiently in practice, and we focus most of our theoretical and computational attention on medians. We consider questions on the existence and regularity of medians. While the me…
Paper finds a lower bound for estimating low-rank matrices in logistic regression.
problem Estimating low-rank coefficient matrices in logistic regression.
method Derives a minimax lower bound on the risk.
result The bound depends on matrix dimensions, rank, and sample size.
Rank regression from pairwise comparisons requires many comparisons to accurately learn model parameters.
problem Learning model parameters for rank regression from noisy pairwise comparisons.
method Uniform random pairwise comparisons to estimate model parameters with a given accuracy.
result Learning model parameters requires a number of comparisons proportional to .
ACFS optimizes spectral risk under decision-dependent uncertainty using adaptive forest sampling.
problem Minimizing spectral risk with decision-dependent uncertainty.
method ACFS integrates Generalised Random Forests, CEM-guided exploration, rank-weighted augmentation, and multi-start refinement.
result ACFS achieves lowest median oracle spectral risk on both benchmarks.
This paper is a short summary of our recent work on the medians and means of probability measures in Riemannian manifolds. Firstly, the existence and uniqueness results of local medians are given. In order to compute medians in practical cases, we propose a subgradient algorithm and prove its convergence. After that, F…
Reduced-rank method improves least-squares regression under output regularity.
problem Least-squares regression with infinite dimensional outputs.
method Reduced-rank method for solving least-squares problems with output regularity assumptions.
result Learning bounds and improved statistical performance compared to full-rank method.
Private statistical inference methods improve confidence interval lengths.
problem Constructing private confidence intervals with differential privacy.
method Proposed two private variants of non-parametric bootstrap.
result Achieve similar coverage accuracy to non-private methods with shorter intervals.
A method for estimating the median of gradients in stochastic optimization.
problem Robust gradient estimation in stochastic optimization for various applications.
method Stochastic Proximal Point Method for median gradient estimation.
result The proposed method can converge even under heavy-tailed, state-dependent noise.