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.
New model estimates sparse transport maps for high-dimensional data.
Gradient-based clustering method for various cost functions.
New geometry for optimal transport cost based on Bregman divergences.
This work proposes the Bregman-Tweedie classification model and analyzes the domain structure of the extended exponential function, an extension of the classic generalized exponential function with additional scaling parameter, and related high-level mathematical structures, such as the Bregman-Tweedie loss function an…
The Bregman divergence (Bregman distance, Bregman measure of distance) is a certain useful substitute for a distance, obtained from a well-chosen function (the "Bregman function"). Bregman functions and divergences have been extensively investigated during the last decades and have found applications in optimization, o…
Bregman divergences play a central role in the design and analysis of a range of machine learning algorithms. This paper explores the use of Bregman divergences to establish reductions between such algorithms and their analyses. We present a new scaled isodistortion theorem involving Bregman divergences (scaled Bregman…
New Langevin Monte Carlo algorithms for sampling from nonsmooth distributions.
CDF uses centroids to split features for high-dimensional classification.
The study characterizes quadrics among affine hyperspheres based on centroid collinearity of sections.
In this work, we extend some quantities introduced in "Optimization of conditional value-at-risk" of R.T Rockafellar and S. Uryasev to the case where the proximity between real numbers is measured by using a Bregman divergence. This leads to the definition of the Bregman superquantile. Axioms of a coherent measure of r…
A new classification method using disjoint centroids and normalized distance.
Distances are fundamental primitives whose choice significantly impacts the performances of algorithms in machine learning and signal processing. However selecting the most appropriate distance for a given task is an endeavor. Instead of testing one by one the entries of an ever-expanding dictionary of {\em ad hoc} dis…
Paper introduces a new method for learning Bregman divergence from data.
This manuscript develops the theory of agglomerative clustering with Bregman divergences. Geometric smoothing techniques are developed to deal with degenerate clusters. To allow for cluster models based on exponential families with overcomplete representations, Bregman divergences are developed for nondifferentiable co…
New findings show Bregman proximal algorithms can get stuck near non-stationary points.
Ball k-means reduces point-centroid distance computations for faster k-means clustering.
New algorithm solves maximal monotone inclusion problems.
In this paper, we introduce new classes of divergences by extending the definitions of the Bregman divergence and the skew Jensen divergence. These new divergence classes (g-Bregman divergence and skew g-Jensen divergence) satisfy some properties similar to the Bregman or skew Jensen divergence. We show these g-diverge…
We define a new method to estimate centroid for text classification based on the symmetric KL-divergence between the distribution of words in training documents and their class centroids. Experiments on several standard data sets indicate that the new method achieves substantial improvements over the traditional classi…
Centroid Transformers reduce memory and computation by summarizing inputs into centroids.
New method improves structure learning on sparse graphs.
Separable Bregman divergences induce Riemannian metric spaces that are isometric to the Euclidean space after monotone embeddings. We investigate fixed rate quantization and its codebook Voronoi diagrams, and report on experimental performances of partition-based, hierarchical, and soft clustering algorithms with respe…
EKM addresses imbalanced data clustering by repelling centroids in large clusters.
Empty core found in max-loss non-centroid clustering.
Due to the success of the bag-of-word modeling paradigm, clustering histograms has become an important ingredient of modern information processing. Clustering histograms can be performed using the celebrated -means centroid-based algorithm. From the viewpoint of applications, it is usually required to deal with symm…
The paper proves a theorem linking convex body centroids and category theory.
Centroids Matching tackles catastrophic forgetting by matching feature vectors to class centroids.
Optimizes a small set of centroid points to approximate bootstrap distribution.
This paper proposes the use of an optimization algorithm, namely PSO to decide the initial centroids in K-means, to eventually get better accuracy. The vectorized notation of the optimal centroids can be thought of as entities in an optimization space, where the accuracy of K-means over a random subset of the data coul…
Text clustering method replaces centroids with summaries for interpretability and scalability.
We formally prove the connection between k-means clustering and the predictions of neural networks based on the softmax activation layer. In existing work, this connection has been analyzed empirically, but it has never before been mathematically derived. The softmax function partitions the transformed input space into…
The nearest-centroid classifier is a simple linear-time classifier based on computing the centroids of the data classes in the training phase, and then assigning a new datum to the class corresponding to its nearest centroid. Thanks to its very low computational cost, the nearest-centroid classifier is still widely use…
Proposes BMME for optimizing nonsmooth nonconvex problems with block structure.
The paper generalizes the second Pappus-Guldin theorem for calculating volumes of bodies.
Generalizes bias-variance decomposition for Bregman divergences.
Sharp Lp affine isoperimetric inequalities are established for the entire class of Lp projection bodies and the entire class of Lp centroid bodies. These new inequalities strengthen the Lp Petty projection and the Lp Busemann--Petty centroid inequality.
In a variety of research areas, the weighted bag of vectors and the histogram are widely used descriptors for complex objects. Both can be expressed as discrete distributions. D2-clustering pursues the minimum total within-cluster variation for a set of discrete distributions subject to the Kantorovich-Wasserstein metr…
A conceptually simple way to classify images is to directly compare test-set data and training-set data. The accuracy of this approach is limited by the method of comparison used, and by the extent to which the training-set data cover configuration space. Here we show that this coverage can be substantially increased u…
Bregman perspective on CART provides a unified framework for impurity measures.
The mirror descent algorithm (MDA) generalizes gradient descent by using a Bregman divergence to replace squared Euclidean distance. In this paper, we similarly generalize the alternating direction method of multipliers (ADMM) to Bregman ADMM (BADMM), which allows the choice of different Bregman divergences to exploit …
In addition to finding meaningful clusters, centroid-based clustering algorithms such as K-means or mean-shift should ideally find centroids that are valid patterns in the input space, representative of data in their cluster. This is challenging with data having a nonconvex or manifold structure, as with images or text…
Divergence functions play a key role as to measure the discrepancy between two points in the field of machine learning, statistics and signal processing. Well-known divergences are the Bregman divergences, the Jensen divergences and the f-divergences. In this paper, we show that the symmetric Bregman divergence can be …
Optimal payoff choice constrained by Bregman-Wasserstein divergence.
New analysis of annealing paths in sampling and estimation.
Develops clustering methods based on likelihood and convergence proved.
CCC clusters with controlled spread, outperforming standard methods.
Unified deep metric learning approach using neural networks.
Bregman divergences generalize measures such as the squared Euclidean distance and the KL divergence, and arise throughout many areas of machine learning. In this paper, we focus on the problem of approximating an arbitrary Bregman divergence from supervision, and we provide a well-principled approach to analyzing such…