Graph neural networks (GNNs) have been shown to replicate convolutional neural networks' (CNNs) superior performance in many problems involving graphs. By replacing regular convolutions with linear shift-invariant graph filters (LSI-GFs), GNNs take into account the (irregular) structure of the graph and provide meaning…
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A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
168,738 papers · 148 categories
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48 results for “generalized median filtering”
M2M tackles zero-shot structured noise suppression in images.
problem Structured noise with strong anisotropic correlations in real-world images.
method M2M introduces a novel sampling strategy that generates pseudo-independent sub-image pairs from a single noisy input, using directional interpolation and generalized median filtering.
result M2M consistently outperforms state-of-the-art zero-shot methods under correlated noise.
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…
Paper addresses fault-tolerance in distributed machine learning with stochastic gradient descent.
problem Fault-tolerance in distributed stochastic gradient descent (D-SGD) for machine learning.
method Proposes norm-based comparative gradient elimination (CGE) to robustify D-SGD against Byzantine faulty agents.
result CGE guarantees fault-tolerance against a bounded fraction of Byzantine agents under standard stochastic assumptions.
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 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.
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.
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…
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…
The consistency of Fréchet medians is proved for probability measures in proper metric spaces. In the context of Riemannian manifolds, assuming that the probability measure has more than a half mass lying in a convex ball and verifies some concentration conditions, the positions of its Fréchet medians are estimated. It…
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.
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.
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.
tl;dr: no, it cannot, at least not on average on the standard archive problems. We assess whether using six smoothing algorithms (moving average, exponential smoothing, Gaussian filter, Savitzky-Golay filter, Fourier approximation and a recursive median sieve) could be automatically applied to time series classificatio…
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 …
New method for estimating median and mean with high probability privacy.
problem Estimating median and mean with differential privacy.
method Propose, Test, Release (PTR) mechanism with concentration inequalities.
result First sub-Gaussian high probability bounds for differentially private median and mean estimation.
New method explains survival analysis models using median-SHAP.
problem Need for explainable AI in medical applications, especially for survival analysis.
method Introduces median-SHAP for explaining survival analysis models.
result Conventionally used mean anchor point can lead to misleading interpretations; median-SHAP provides a better approach.
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.
This paper introduces online algorithms to estimate robust geometric median in large data streams.
problem Detecting outliers in large data sets using robust statistical measures.
method Online stochastic Newton methods for estimating the geometric median.
result Rates of convergence for online estimation of the geometric median.
The study finds that maximizing median returns is the only viable strategy in portfolio selection.
problem Difficulties in studying optimal portfolio strategies due to discontinuity and time inconsistency in maximizing median and quantile returns.
method Used intra-personal equilibrium approach to analyze portfolio selection under median and quantile maximization.
result Median maximization is the only viable strategy, with no investment in risky assets for other quantiles.
New graph properties inherited by Frechet mean and median.
problem Characterizing the average of graph-valued samples.
method Analysis of Frechet mean and median graphs.
result Edge density is hereditary in Frechet mean and median graphs.
Paper proposes a robust method for federated ICA with geometric median aggregation.
problem Federated ICA with permutation ambiguity in client estimations.
method Geometric median aggregation with k-means clustering to resolve permutation ambiguity.
result The method provably remains effective in highly heterogeneous scenarios.
A new depth measure and median defined on Hadamard manifolds.
problem Statistical depth and median on Hadamard manifolds.
method Horospherical depth and Busemann median defined using renormalized distance functions.
result The Busemann median exists for every Borel probability measure on Hadamard manifolds.
Characterizes ends and coends of graph pairs using quasi-median graphs.
problem Understanding the number of ends and coends in graph pairs.
method Characterizes ends and coends using quasi-median graphs.
result Characterizes ends and coends of graph pairs in terms of quasi-median graphs.
Tukey median performance analyzed under TV corruptions.
problem Performance analysis of Tukey median under TV corruptions.
method Analysis of Tukey median and projection algorithm under TV corruptions.
result Breakdown point reduced to 1/4 under TV corruptions, compared to 1/3 under Huber's model.
In high dimensions, the mean and geometric median are nearly identical.
problem Understanding the relationship between mean and geometric median in high-dimensional spaces.
method Analytical derivation and simulation of the distance between mean and geometric median.
result The distance between mean and geometric median vanishes with dimensionality in high dimensions.
The Flag Median and FlagIRLSstat.ML
New subspace prototype flag median improves clustering on noisy data.
problem Finding robust prototypes for datasets of images and videos.
method Proposes flag median and introduces FlagIRLS algorithm for its calculation.
result Flag median is robust to outliers and improves cluster purity.
Improved median of means estimator with tighter bounds.
problem Improving the efficiency and reliability of median of means estimator.
method Modification of the median of means estimator with sub-Gaussian deviation bounds.
result Achieves nearly optimal constants under minimal assumptions.
Empirical median performs well in estimating location with varying scales.
problem Estimating location with varying scales in data.
method Analysis of empirical median as an estimator.
result Matching upper and lower bounds on estimation error.
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…
We propose a general framework for denoising high-dimensional measurements which requires no prior on the signal, no estimate of the noise, and no clean training data. The only assumption is that the noise exhibits statistical independence across different dimensions of the measurement, while the true signal exhibits s…
In this paper, we define the geometric median of a probability measure on a Riemannian manifold, give its characterization and a natural condition to ensure its uniqueness. In order to calculate the median in practical cases, we also propose a subgradient algorithm and prove its convergence as well as estimating the er…
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…
New estimator for symmetric kernel expectations, robust to missing data.
problem Efficient estimation of symmetric kernel expectations with missing data.
method Median-of-Incomplete-U-Statistics (MIU) estimator.
result Established finite-sample concentration rate for MIU.
Median-of-means sampling outperforms mean-of-means for large sample sizes in numerical integration.
problem Improving numerical integration accuracy in high dimensions.
method Median-of-means sampling compared to mean-of-means using RQMC methods.
result Median-of-means sampling is superior for large sample sizes, while mean-of-means is better for smaller sample sizes.
Upper bound for Hausdorff distance between hyperbolic space and its medianization.
problem Calculating the Hausdorff distance between hyperbolic space and its medianization.
method Using de Sitter space to model finite-dimensional hyperbolic space and its medianization, calculating the Hausdorff distance.
result An upper bound for the Hausdorff distance between hyperbolic space and its medianization is calculated.
Paper proposes a novel method to improve matrix completion with median loss for large datasets.
problem Matrix completion with absolute deviation loss for large-scale data.
method Proposes a refinement step using pseudo data to improve inefficient estimators of median matrix completion.
result Turns inefficient estimators into a rate (near-)optimal matrix completion procedure.
We study the sample-based k-median clustering objective under a sequential setting without substitutions. In this setting, an i.i.d. sequence of examples is observed. An example can be selected as a center only immediately after it is observed, and it cannot be substituted later. The goal is to select a set of centers …
K-bMOM robustly clusters data with outliers, improving on Lloyd-type methods.
problem Outliers in datasets disrupt traditional clustering algorithms.
method Lloyd-type iterations with robust median-of-means estimates.
result K-bMOM outperforms existing robust K-means methods.
Evolutionary algorithms (EAs) are a sort of nature-inspired metaheuristics, which have wide applications in various practical optimization problems. In these problems, objective evaluations are usually inaccurate, because noise is almost inevitable in real world, and it is a crucial issue to weaken the negative effect …
Robust Estimation in metric spaces: Achieving Exponential Concentration with a Fréchet Medianmath.ST
This work achieves exponential concentration in heavy-tailed data over CAT(κ) spaces using the Fréchet median.
problem Achieving robust estimation in heavy-tailed data distributions.
method Developing a concentration bound for the Fréchet median in CAT(κ) spaces.
result Exponential concentration of the Fréchet median in CAT(κ) spaces over heavy-tailed data.
Marine buoys aid in the battle against Illegal, Unreported and Unregulated (IUU) fishing by detecting fishing vessels in their vicinity. Marine buoys, however, may be disrupted by natural causes and buoy vandalism. In this paper, we formulate marine buoy placement as a clustering problem, and propose dropout k-means an…
In kernel methods, the median heuristic has been widely used as a way of setting the bandwidth of RBF kernels. While its empirical performances make it a safe choice under many circumstances, there is little theoretical understanding of why this is the case. Our aim in this paper is to advance our understanding of the …
Borel asymptotic dimension of the Roller boundary of finite dimensional CAT(0) cube complexesmath.GT
Study shows Roller compactification's median graph has limited asymptotic dimension.
problem Understanding the asymptotic dimension of Roller compactifications.
method Proved using finite dimensional CAT(0) cube complexes and Borel median graph.
result Borel asymptotic dimension is bounded by the complex's dimension.
Extends graph factor system to quasi-median graphs.
problem Constraint relaxation for combinatorial HHS machinery.
method Relaxing domain constraints on combinatorial HHS machinery and extending factor system to quasi-median graphs.
result Factor system applied to quasi-median graphs.
Improved private geometric median estimation with nearly-linear time complexity.
problem Estimating the geometric median of a dataset while maintaining privacy.
method Improved algorithm using subsampling and geometric aggregation, achieving nearly-linear runtime.
result Achieves the same approximation quality as previous methods but with nearly-linear runtime.
Paper improves statistical efficiency of median-of-means estimator for Byzantine robust distributed inference.
problem Byzantine robustness in distributed learning systems.
method Variance reduced median-of-means (VRMOM) estimator for Byzantine robust distributed inference.
result Achieves a fast convergence rate with only a constant number of rounds of communications.
Optimal benchmark design varies based on costs in financial manipulation.
problem Manipulation of price benchmarks in finance.
method Analyzes empirical pattern and cost structures to determine optimal benchmark design.
result The optimal benchmark depends on the relative sizes of fixed and variable costs.