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.
A method for estimating the median of gradients in stochastic optimization.
Recently, there is a growing interest in the study of median-based algorithms for distributed non-convex optimization. Two prominent such algorithms include signSGD with majority vote, an effective approach for communication reduction via 1-bit compression on the local gradients, and medianSGD, an algorithm recently pr…
Paper shows how to use geometric median for robust SGD in high dimensions.
Distributed model training is vulnerable to byzantine system failures and adversarial compute nodes, i.e., nodes that use malicious updates to corrupt the global model stored at a parameter server (PS). To guarantee some form of robustness, recent work suggests using variants of the geometric median as an aggregation r…
This paper investigates the phase retrieval problem, which aims to recover a signal from the magnitudes of its linear measurements. We develop statistically and computationally efficient algorithms for the situation when the measurements are corrupted by sparse outliers that can take arbitrary values. We propose a nove…
We investigate existence and uniqueness of p-means and the median of a probability measure on a Finsler manifold, in relation with the convexity of the support of the measure. We prove that the p-mean is the limit point of a continuous time gradient flow. Under some additional condition which is always satisfied for la…
New methods validate a hypothesis explaining how neural nets generalize well.
Paper explores using bootstrap methods to improve SGD's stability and robustness.
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…
This paper deals with distributed finite-sum optimization for learning over networks in the presence of malicious Byzantine attacks. To cope with such attacks, most resilient approaches so far combine stochastic gradient descent (SGD) with different robust aggregation rules. However, the sizeable SGD-induced stochastic…
Three methods for tuning HMC diagonal scale matrices compared.
We introduce a new sub-linear space sketch---the Weight-Median Sketch---for learning compressed linear classifiers over data streams while supporting the efficient recovery of large-magnitude weights in the model. This enables memory-limited execution of several statistical analyses over streams, including online featu…
New concept of coarse medians for higher rank symmetric spaces.
Unique median structures found in hyperbolic spaces.
Study on median algebra structures on Euclidean spaces and manifolds with local CAT(0) cubulation.
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 …
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…
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 …
Convex cores found for group actions on median spaces.
In large-scale distributed learning, security issues have become increasingly important. Particularly in a decentralized environment, some computing units may behave abnormally, or even exhibit Byzantine failures -- arbitrary and potentially adversarial behavior. In this paper, we develop distributed learning algorithm…
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…
Novel algorithm resists Byzantine attacks in federated learning for PCA and LRCS.
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…
This paper introduces online algorithms to estimate robust geometric median in large data streams.
The study finds that maximizing median returns is the only viable strategy in portfolio selection.
New graph properties inherited by Frechet mean and median.
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…
In high dimensions, the mean and geometric median are nearly identical.
New subspace prototype flag median improves clustering on noisy data.
Improved median of means estimator with tighter bounds.
Empirical median performs well in estimating location with varying scales.
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…
New estimator for symmetric kernel expectations, robust to missing data.
Median-of-means sampling outperforms mean-of-means for large sample sizes in numerical integration.
Upper bound for Hausdorff distance between hyperbolic space and its medianization.
Paper proposes a novel method to improve matrix completion with median loss for large datasets.
Stochastic gradient descent's long-term fluctuations are described by a diffusion limit.
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 …
In this work, we consider the resilience of distributed algorithms based on stochastic gradient descent (SGD) in distributed learning with potentially Byzantine attackers, who could send arbitrary information to the parameter server to disrupt the training process. Toward this end, we propose a new Lipschitz-inspired c…
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 …
Study shows Roller compactification's median graph has limited asymptotic dimension.
Extends graph factor system to quasi-median graphs.
Clustering with fast algorithms large samples of high dimensional data is an important challenge in computational statistics. Borrowing ideas from MacQueen (1967) who introduced a sequential version of the -means algorithm, a new class of recursive stochastic gradient algorithms designed for the -medians loss cri…
A new depth measure and median defined on Hadamard manifolds.
Improved private geometric median estimation with nearly-linear time complexity.
Optimal benchmark design varies based on costs in financial manipulation.
New method explains survival analysis models using median-SHAP.