arXiv research

Study improves top-k set prediction with low cardinality.

A cardinality-constrained portfolio caps the number of stocks to be traded across and within groups or sectors. These limitations arise from real-world scenarios faced by fund managers, who are constrained by transaction costs and client preferences as they seek to maximize return and limit risk. We develop a new appro…

We study the cardinality of the set of manifolds homotopy equivalent to a given manifold M and compare it to the cardinality of the structure set of M.

Study on loops on non-orientable surfaces, determining cardinality and order.

In this paper we address cardinality estimation problem which is an important subproblem in query optimization. Query optimization is a part of every relational DBMS responsible for finding the best way of the execution for the given query. These ways are called plans. The execution time of different plans may differ b…

The cardinality constraint is an intrinsic way to restrict the solution structure in many domains, for example, sparse learning, feature selection, and compressed sensing. To solve a cardinality constrained problem, the key challenge is to solve the projection onto the cardinality constraint set, which is NP-hard in ge…

Paper solves high-order portfolio optimization with cardinality constraint.

This study compares machine learning methods for high-cardinality categorical variables.

Learning rule consistency tied to non-existence of real-valued measurable cardinals.

Quantum computing tackles non-convex portfolio optimization with cardinality constraints.

Cardinality potentials are a generally useful class of high order potential that affect probabilities based on how many of D binary variables are active. Maximum a posteriori (MAP) inference for cardinality potential models is well-understood, with efficient computations taking O(DlogD) time. Yet efficient marginalizat…

CardiCat generates synthetic data for high-cardinality tabular datasets.

Homotopy cardinality counts augmentations of Legendrian knots.

Structured high-cardinality data arises in many domains, and poses a major challenge for both modeling and inference. Graphical models are a popular approach to modeling structured data but they are unsuitable for high-cardinality variables. The count-min (CM) sketch is a popular approach to estimating probabilities in…

The paper optimizes asset selection for index trackers and enhanced trackers with varying cardinality constraints.

We introduce a notion of cardinality for the augmentation category associated to a Legendrian knot or link in standard contact R^3. This `homotopy cardinality' is an invariant of the category and allows for a weighted count of augmentations, which we prove to be determined by the ruling polynomial of the link. We prese…

The aim of this paper is a characterization of great antipodal sets of complex Grassmannian manifolds as certain designs with the smallest cardinalities.

Quandles can be regarded as generalizations of symmetric spaces. Among symmetric spaces, two-point homogeneous Riemannian manifolds would be the most fundamental ones. In this paper, we define two-point homogeneous quandles analogously, and classify those with prime cardinality.

Novel GLMMNet model tackles high-cardinality categorical features in actuarial applications.

Study on top-$k$ classification with new loss functions and algorithms.

Random shuffle method boosts HF dataset size 10-21 times.

MMbeddings reduces categorical embeddings by treating them as latent effects, significantly decreasing parameters and mitigating overfitting.

We present a study on reinforcement learning (RL) from human bandit feedback for sequence-to-sequence learning, exemplified by the task of bandit neural machine translation (NMT). We investigate the reliability of human bandit feedback, and analyze the influence of reliability on the learnability of a reward estimator,…

This work restricts hidden cardinality in causal models to infer causal relations.

In this paper we propose and discuss different 0-1 linear models in order to solve the cardinality constrained portfolio problem by using factor models. Factor models are used to build portfolios to track indexes, together with other objectives, also need a smaller number of parameters to estimate than the classical Ma…

Develops a new model for RLHF accounting for partially observed states and intermediate feedback.

We introduce the notion of a positive opetope and positive opetopic cardinals as certain finite combinatorial structures. The positive opetopic cardinals to positive-to-one polygraphs are like simple graphs to free omega-categories over omega-graphs, c.f. [MZ]. In particular, they allow us to give an explicit combinato…

We study and classify topologically invariant $σ$-ideals with a Borel base on the Hilbert cube and evaluate their cardinal characteristics. One of the results of this paper solves (positively) a known problem whether the minimal cardinalities of the families of Cantor sets covering the unit interval and the Hilbert cub…

New algorithm solves large cardinality-constrained clustering problems.

Plain vanilla K-means clustering has proven to be successful in practice, yet it suffers from outlier sensitivity and may produce highly unbalanced clusters. To mitigate both shortcomings, we formulate a joint outlier detection and clustering problem, which assigns a prescribed number of datapoints to an auxiliary outl…

Paper proposes a uniqueness Shapley measure to compare variable importance.

New approach to sparse optimal transport for matching tokens with experts.

Due to the outstanding capability of capturing underlying data distributions, deep learning techniques have been recently utilized for a series of traditional database problems. In this paper, we investigate the possibilities of utilizing deep learning for cardinality estimation of similarity selection. Answering this …

Let p be a puncture of a punctured sphere, and let Q be the set of all other punctures. We prove that the maximal cardinality of a set of arcs pairwise intersecting at most once, which start at p and end in Q, is |X|(|X| + 1). We deduce that the maximal cardinality of a set of arcs with arbitrary endpoints pairwise int…

The paper describes a cover of strata of k-differentials with a formula for fiber cardinality.

HAMD optimizes cubic portfolios without quadratization, achieving better results.

Paper tackles P vs NP problem in portfolio optimization with cardinality constraints and Black-Scholes derivatives.

Cardinal scores (numeric ratings) collected from people are well known to suffer from miscalibrations. A popular approach to address this issue is to assume simplistic models of miscalibration (such as linear biases) to de-bias the scores. This approach, however, often fares poorly because people's miscalibrations are …

A new penalty-free method optimizes portfolios without quantum annealing penalties.

Reweighted l1-algorithms have attracted a lot of attention in the field of applied mathematics. A unified framework of such algorithms has been recently proposed by Zhao and Li. In this paper we construct a few new examples of reweighted l1-methods. These functions are certain concave approximations of the l0-norm func…

Proposes a new DNN framework for count data with high-cardinality features.

Regularized target encoding beats traditional methods for high cardinality features in ML.

Analysis of DPPs and k-DPPs via spectral decomposition reveals identifiable parameters and non-identifiability gaps.

Improved bounds on acylindricity for right-angled Artin groups.

Enhanced evolutionary algorithms solve NP-hard portfolio optimization with cardinality constraints.

We show that the asymptotic growth rate for the minimal cardinality of a set of simple closed curves on a closed surface of genus $g$ which fill and pairwise intersect at most $K\ge 1$ times is $2\sqrt{g}/\sqrt{K}$ as $g \to \infty$ . We then bound from below the cardinality of a filling set of systoles by $g/\log(g)$.…

When eliciting judgements from humans for an unknown quantity, one often has the choice of making direct-scoring (cardinal) or comparative (ordinal) measurements. In this paper we study the relative merits of either choice, providing empirical and theoretical guidelines for the selection of a measurement scheme. We pro…

A subgroup of a Kac-Moody group is called bounded if it is contained in the intersection of two finite type parabolic subgroups of opposite signs. In this paper, we study the isomorphisms between Kac-Moody groups over arbitrary fields of cardinality at least 4, which preserve the set of bounded subgroups. We show that …