arXiv research

The paper tackles sampling biases by ensuring minority groups are adequately represented in training data.

Finding an informative subset of a large collection of data points or models is at the center of many problems in computer vision, recommender systems, bio/health informatics as well as image and natural language processing. Given pairwise dissimilarities between the elements of a `source set' and a `target set,' we co…

This paper aims at justifying LWF and AMP chain graphs by showing that they do not represent arbitrary independence models. Specifically, we show that every chain graph is inclusion optimal wrt the intersection of the independence models represented by a set of directed and acyclic graphs under conditioning. This impli…

For $SU(2)$ (or $SO(3)$) Donaldson theory on a 4-manifold $X$, we construct a simple geometric representative for $μ$ of a point. Let $p$ be a generic point in $X$. Then the set $\{ [A] | F_A^-(p)$ is reducible $\}$, with coefficient -1/4 and appropriate orientation, is our desired geometric representative.

Venn diagrams are a graphical way to represent a set system. Each of the n sets is represented by a simple closed curve. The n curves subdivide the plane into 2^n open connected regions, each of which represents the intersection of its containing curves' sets. For example, two overlapping circles can divide the plane i…

The age of big data has produced data sets that are computationally expensive to analyze and store. Algorithmic leveraging proposes that we sample observations from the original data set to generate a representative data set and then perform analysis on the representative data set. In this paper, we present efficient a…

Simplifies large action space bandits by selecting representative actions.

Locally adaptive clustering for tree delineation.

A marked graph diagram is a link diagram possibly with marked $4$-valent vertices. S. J. Lomonaco, Jr. and K. Yoshikawa introduced a method of representing surface-links by marked graph diagrams. Specially, K. Yoshikawa gave local moves on marked graph diagrams, nowadays called Yoshikawa moves. It is now known that two…

New set-valued star-shaped risk measures introduced for better risk assessment.

Optimizes sample weights for representative data averages.

There is a well-known way to describe a link diagram as a (signed) plane graph, called its Tait graph. This concept was recently extended, providing a way to associate a set of embedded graphs (or ribbon graphs) to a link diagram. While every plane graph arises as a Tait graph of a unique link diagram, not every embedd…

Paper proves corner connection tiles can represent knots with fewer tiles.

Incremental clustering approaches have been proposed for handling large data when given data set is too large to be stored. The key idea of these approaches is to find representatives to represent each cluster in each data chunk and final data analysis is carried out based on those identified representatives from all t…

Let $M$ be a closed manifold of Sasaki type. A polarization of $M$ is defined by a Reeb vector field, and for one such, we consider the set of all Sasakian metrics compatible with it. On this space, we study the functional given by the squared $L^2$-norm of the scalar curvature. We prove that its critical points, or ca…

With the growing interest on Network Analysis, Relational Data Mining is becoming an emphasized domain of Data Mining. This paper addresses the problem of extracting representative elements from a relational dataset. After defining the notion of degree of representativeness, computed using the Borda aggregation procedu…

This study optimizes cycle representatives in persistent homology using linear programming.

Labeling each instance in a large dataset is extremely labor- and time- consuming . One way to alleviate this problem is active learning, which aims to which discover the most valuable instances for labeling to construct a powerful classifier. Considering both informativeness and representativeness provides a promising…

The paper introduces group-representative clustering to ensure fair representation of different groups in clusters.

Researchers develop multi-utility representations for incomplete preferences linked to risk measures.

Consider a set represented by an inequality. An interesting phenomenon which occurs in various settings in mathematics is that the interior of this set is the subset where strict inequality holds, the boundary is the subset where equality holds, and the closure of the set is the closure of its interior. This paper disc…

Reducing neural network training time by using smaller, representative datasets.

Simple algorithm for computing link polynomials using skein relations.

RepSet neural network handles set representations for improved performance.

Recognizing group activities is challenging due to the difficulties in isolating individual entities, finding the respective roles played by the individuals and representing the complex interactions among the participants. Individual actions and group activities in videos can be represented in a common framework as the…

Global Chern currents and Baum Bott currents defined on arbitrary complex manifolds.

Bayesian hyperbolic MDS improves tree-like data representation.

We consider a setting where an agent's uncertainty is represented by a set of probability measures, rather than a single measure. Measure-bymeasure updating of such a set of measures upon acquiring new information is well-known to suffer from problems; agents are not always able to learn appropriately. To deal with the…

I consider unsupervised extensions of the fast stepwise linear regression algorithm \cite{efroymson1960multiple}. These extensions allow one to efficiently identify highly-representative feature variable subsets within a given set of jointly distributed variables. This in turn allows for the efficient dimensional reduc…

A new deep learning framework selects representative samples for unsupervised learning.

In this article, we address the question of how non-knowledge about future events that influence economic agents' decisions in choice settings has been formally represented in economic theory up to date. To position our discussion within the ongoing debate on uncertainty, we provide a brief review of historical develop…

Big data sets must be carefully partitioned into statistically similar data subsets that can be used as representative samples for big data analysis tasks. In this paper, we propose the random sample partition (RSP) data model to represent a big data set as a set of non-overlapping data subsets, called RSP data blocks,…

Deep learning identifies space objects from uncorrelated observations.

Extends Carathéodory's theorem to multidimensional domains with constant curvature.

Graphs represent knot adjacency for n crossings.

In the paper, we prove that a Moran set is homeomorphic to the hyperbolic boundary of the representing symbolic space in the sense of Gromov, which generalizes the results of Lau and Wang [Indiana U. Math. J. {\bf 58} (2009), 1777-1795]. Moreover, by making use of this, we establish the Lipschitz equivalence of a class…

We prove that the norm of the Euler class E for flat vector bundles is $2^{-n}$ (in even dimension $n$, since it vanishes in odd dimension). This shows that the Sullivan--Smillie bound considered by Gromov and Ivanov--Turaev is sharp. We construct a new cocycle representing E and taking only the two values $\pm 2^{-n}$…

Apricot selects subsets from large data sets efficiently using submodular optimization.

We study the Sasaki cone of a CR structure of Sasaki type on a given closed manifold. We introduce an energy functional over the cone, and use its critical points to single out the strongly extremal Reeb vectors fields. Should one such vector field be a member of the extremal set, the scalar curvature of a Sasaki extre…

The paper classifies orbits of semisimple elements in real semisimple Lie algebras.

Every link in R^3 can be represented by a one-vertex ribbon graph. We prove a Markov type theorem on this subset of link diagrams.

An online convex matrix factorization algorithm with interpretable bases.

Study counterfactuals in combinatorial choice using a representative agent model.

Paper discusses optimal CP for second-order predictions.

In this paper we present some bounds of Hausdorff measures of objects definable in o-minimal structures: sets, fibers of maps, inverse images of curves of maps, etc. Moreover, we also give some explicit bounds for semi-algebraic or semi-Pfaffian cases, which depend only on the combinatoric data representing the objects…

We prove a partial generalization of Bonahon's tameness result to surfaces inside irreducible 3-manifolds with hyperbolic fundamental group. Bonahon's result states that geometrically infinite ends of freely indecomposable hyperbolic 3-manifolds are simply degenerate. It is easy to see that a geometrically infinite end…

This paper investigates dynamics that persist under isotopy in classes of orientation-preserving homeomorphisms of orientable surfaces. The persistence of periodic points with respect to periodic and strong Nielsen equivalence is studied. The existence of a dynamically minimal representative with respect to these relat…

This paper solves Yang-Baxter cohomology for cyclic biquandles.