Examines manifold cardinality and compares it to structure set.
problem Cardinality of manifold sets and structure sets.
method Study of homotopy equivalence and comparison of cardinalities.
result Cardinality of manifold sets is compared to structure sets.
New method solves portfolio optimization with cardinality constraints efficiently.
problem Real-world portfolio constraints like transaction costs and client preferences.
method Continuous relaxation method for NP-hard problems, extending Markowitz and CVaR models.
result Efficient algorithms find near-optimal portfolios for cardinality-constrained problems.
Study improves top-k set prediction with low cardinality.
problem Improving top-k set prediction accuracy with low cardinality.
method Introduces new target loss function and surrogate losses.
result Demonstrates effectiveness of cardinality-aware algorithms.
Paper solves NP-hard projection for three-view cardinality constraints.
problem NP-hard projection onto cardinality constraint sets.
method Formulates projection as linear programming with TVCS.
result Linear programming solution matches original projection.
Cardinality of augmentation category for Legendrian links determined by ruling polynomial.
problem Counting augmentations of Legendrian links.
method Introducing homotopy cardinality as an invariant, proving it equals ruling polynomial.
result Homotopy cardinality of augmentation category is determined by ruling polynomial.
Paper proposes a new machine learning-based approach to improve DBMS performance.
problem Improving cardinality estimation for better query optimization.
method Adaptive cardinality estimation using query execution statistics.
result Significantly increases DBMS performance for some queries.
Study on loops on non-orientable surfaces, determining cardinality and order.
problem Determining the cardinality and order of maximal complete 1-systems of loops on non-orientable surfaces.
method Proved the cardinality of maximal systems of arcs pairwise-intersecting at most once on a non-orientable surface is 2∣χ∣(∣χ∣+1), and used this to determine the cardinality of maximal complete 1-systems of loops. result Exact cardinality of maximal complete 1-systems of loops on punctured projective planes is determined.
Improves probability estimation for high-cardinality data using graphical models and count sketches.
problem Estimating probabilities in high-cardinality data with structured models.
method Combining graphical models and count-min sketches with random projections.
result Significantly improved error bounds and computational efficiency over existing methods.
EFDM models spatial point processes with variable cardinality using existence variables.
problem Challenges in extending diffusion models to variable-cardinality spatial point processes.
method Existence-field diffusion model (EFDM) that jointly models spatial locations and cardinality without discrete transitions.
result EFDM achieves improved modeling capability on datasets with varying cardinality.
Paper solves high-order portfolio optimization with cardinality constraint.
problem Solving non-convex cardinality constrained high-order portfolio optimization.
method Transformed cardinality constraint into penalty term, proposed pDCA, pDCAe, and SCA algorithms.
result Proposed algorithms achieve high utility and sparse solutions efficiently.
This study compares machine learning methods for high-cardinality categorical variables.
problem Machine learning struggles with high-cardinality categorical variables.
method Empirical comparison of tree-boosting, deep neural networks, and linear mixed effects models.
result Tree-boosting with random effects outperforms deep neural networks with random effects.
Learning rule consistency tied to non-existence of real-valued measurable cardinals.
problem Consistency of k-NN learning rule in metric spaces.
method Analyzing separable subspaces and density conditions.
result The k-NN classifier's consistency depends on the absence of real-valued measurable cardinals.
Quantum computing tackles non-convex portfolio optimization with cardinality constraints.
problem Non-convex portfolio optimization problems in asset management.
method Application of quantum annealing with non-linear cardinality constraints.
result Quantum portfolio optimization yields smaller, more profitable portfolios.
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.
problem Learning complexities of high-cardinality categorical features in tabular data.
method Substitutes one-hot encoding with regularized dual encoder-decoder embedding layers.
result Generates high-quality synthetic data with a smaller parameter space.
Homotopy cardinality counts augmentations of Legendrian knots.
problem Counting augmentations of Legendrian knots.
method Assigning ruling polynomials and proving homotopy cardinality results.
result Homotopy cardinality of representation categories is a multiple of ruling polynomials.
The paper optimizes asset selection for index trackers and enhanced trackers with varying cardinality constraints.
problem Optimizing asset selection for index trackers and enhanced trackers with cardinality constraints.
method Divided into two steps: asset pre-selection and asset weight estimation. Used eight pre-selection procedures with different combinations of selection methods and regression types.
result Out-of-sample tracking errors are roughly proportional to 1/sqrt(cardinality). OLS is more effective than LAD, BE marginally more effective than FS, and (n) marginally more effective than (c).
Improved clustering with outlier detection using cardinality constraints.
problem Outlier sensitivity and unbalanced clusters in K-means.
method Formulates a joint outlier detection and clustering problem as a mixed-integer linear program (MILP) with cardinality constraints.
result Proves the optimality of solutions under certain conditions.
Proposes new models to solve portfolio selection with cardinality constraints using factor models.
problem Solving portfolio selection with cardinality constraints using factor models.
method Developed 0-1 linear models and a minimum edge-weighted clique problem to solve the cardinality constrained portfolio problem.
result Piecewise linear approximation reduces computation time for solving the quadratic problem.
The aim of this paper is a characterization of great antipodal sets of complex Grassmannian manifolds as certain designs with the smallest cardinalities.
Paper uses deep learning for accurate, monotonic cardinality estimation.
problem Accurate and monotonic cardinality estimation for similarity selection.
method Feature extraction to Hamming space, followed by deep learning regression.
result Demonstrates improved query optimizer performance.
Max arcs on spheres intersecting twice, proven.
problem Maximizing arcs on spheres with intersection constraints.
method Proved maximal cardinality of arcs intersecting at most twice.
result Maximal cardinality of arcs intersecting at most twice is |X|(|X| + 1)(|X| + 2).
Paper challenges the usefulness of cardinal scores without simplifying assumptions on miscalibration.
problem Handling arbitrary miscalibrations in ratings.
method Designing estimators for cardinal scores with arbitrary miscalibrations, consistent with induced ranking.
result Strict and uniform outperformance of estimators over all possible ranking-based estimators.
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.
problem Inadequate encoding methods for high-cardinality categorical features in actuarial data.
method Generalised Linear Mixed Model Neural Network (GLMMNet) integrating a generalised linear mixed model in a deep learning framework.
result GLMMNet often outperforms or performs comparably with entity embedded neural networks, providing transparency.
Study on top-k classification with new loss functions and algorithms.
problem Improving multi-class classification accuracy and cardinality trade-off.
method Introducing cardinality-aware loss functions and deriving their consistency bounds.
result New cardinality-aware algorithms for top-k classification. Random shuffle method boosts HF dataset size 10-21 times.
problem Narrow dataset cardinality in HF clinical studies.
method Random shuffle method to enhance dataset size.
result Enhanced HF dataset size 10-21 times.
CPA models improve GNNs by preserving node cardinality.
problem Limited understanding of attention-based GNNs' discriminative power.
method Theoretical analysis and CPA models to preserve cardinality information.
result CPA models can improve GNNs' performance in node and graph classification.
MMbeddings reduces categorical embeddings by treating them as latent effects, significantly decreasing parameters and mitigating overfitting.
problem Large cardinalities in categorical embeddings lead to high parameter counts and overfitting.
method MMbeddings treats embeddings as latent random effects in a variational autoencoder framework, reducing parameter count and mitigating overfitting.
result MMbeddings consistently outperforms traditional embeddings across various tasks, demonstrating its potential in machine learning applications.
This work restricts hidden cardinality in causal models to infer causal relations.
problem Causal relations between variables with a common unobserved cause cannot be directly inferred.
method Derive inequality constraints from d-separation in causal models with known cardinalities of unobserved variables.
result Inference of causal relations is possible with additional assumptions about cardinalities.
Develops a new model for RLHF accounting for partially observed states and intermediate feedback.
problem Lack of models for partially observed states and intermediate feedback in RLHF.
method PORRL model with cardinal and dueling feedback methods.
result Demonstrates improved learning and alignment with new model-based and model-free methods.
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 methods encode high-cardinality string variables efficiently.
problem Efficient encoding of high-cardinality string categorical variables.
method Two approaches: Gamma-Poisson matrix factorization and min-hash encoder.
result Improves supervised learning with high-cardinality categorical variables.
New algorithm solves large cardinality-constrained clustering problems.
problem Optimizing clustering with cardinality constraints.
method Branch-and-cut technique with SDP relaxation and polyhedral cuts.
result Solves real-world instances 10 times larger than previous methods.
The knot quandle of twist-spun trefoils is studied, revealing finite cardinality for small twists.
problem Understanding the knot quandle of twist-spun trefoils.
method Analyzing the quandle structure of 3- to 5-twist-spun trefoils and the relationship with regular tessellations. result The cardinality of the knot quandle of m-twist-spun trefoils is finite if and only if 1≤m≤5. Solves portfolio optimization with cardinality constraints using column generation.
problem Portfolio optimization with cardinality constraints.
method Column generation method applied to a subset of assets in a master convex quadratic problem, using dual information to propose new assets.
result Solves portfolio optimization problems efficiently with cardinality constraints.
Study on RL from human bandit feedback for sequence-to-sequence learning, showing reliability and learnability.
problem Reliability and learnability of human bandit feedback for RL from sequence-to-sequence learning.
method Investigated reliability of human bandit feedback, analyzed influence on reward estimator learnability, and tested improvements with regression-based reward estimator.
result Improvements of over 1 BLEU can be achieved by integrating a regression-based reward estimator trained on cardinal feedback into RL for NMT.
Paper proposes a uniqueness Shapley measure to compare variable importance.
problem Comparing the importance of different variables in identifying subjects.
method Uses Shapley value to combine reductions in log cardinality due to revealing variables.
result Demonstrates speedup in calculating variable importance.
New approach to sparse optimal transport for matching tokens with experts.
problem Sparse matching of tokens with experts in neural networks.
method Sparsity-constrained optimal transport with cardinality constraints.
result Solves nonconvex cardinality constraints with gradient methods.
The paper describes a cover of strata of k-differentials with a formula for fiber cardinality.
problem Understanding the ramification locus and cardinality of fibers in strata of k-differentials.
method Intersection calculations on multi-scale compactification and flat geometry.
result A formula for the cardinality of each fiber involving the k-factorial function.
HAMD optimizes cubic portfolios without quadratization, achieving better results.
problem Optimizing higher-order portfolio models with reduced distortion.
method Hybrid pipeline combining continuous Hamiltonian search, cardinality-preserving projection, and iterated local search.
result HAMD achieves significantly lower native cubic objective values than classical heuristics.
Paper tackles P vs NP problem in portfolio optimization with cardinality constraints and Black-Scholes derivatives.
problem Operationalizing the P vs NP problem in cardinality-constrained portfolio selection.
method Mixed-integer quadratic program with genetic algorithms, Monte Carlo sampling, and greedy screening.
result Cardinality constraint reshapes efficient frontier, highlighting trade-offs between stability and computational cost.
A new penalty-free method optimizes portfolios without quantum annealing penalties.
problem Optimizing portfolios with quantum annealing penalties.
method Removing the penalty term and using a classical feasibility projector.
result Significant reduction in chain-break fractions and post-processed regret.
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…
Unified clustering model handles both pairwise and cardinality constraints for better performance.
problem Clustering with specific constraints (pairwise and cardinality) to improve clustering quality.
method Unified integer programming formulation, binary and quadratic constraints, reformulated as continuous constraints, solved using ADMM.
result Unified model outperforms single category constraints and achieves better clustering performance.
Constructs Nöbeling manifolds of arbitrary weight for any cardinal κ.
problem Creating Nöbeling manifolds of arbitrary weight for any cardinal κ.
method Constructs a space ν^n_κ(K) and a map π such that ν^n_κ(K) is a complete metric n-dimensional space of weight κ.
result Constructs Nöbeling manifolds of arbitrary weight for any cardinal κ.
Proposes a new DNN framework for count data with high-cardinality features.
problem Real-world data often have correlations and high-cardinality categorical features that traditional DNNs overlook.
method Introduces a hierarchical likelihood learning framework with gamma random effects for Poisson DNNs.
result Improves prediction performance by capturing nonlinear effects and subject-specific cluster effects.