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.
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…
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…
Fast algorithms developed for adaptive and fully adaptive submodular maximization problems.
problem Maximizing submodular functions subject to constraints in linear time.
method Developed linear-time algorithms for two submodular maximization problems: adaptive and fully adaptive.
result Achieved (1−1/e−ε) approximation ratio for adaptive submodular maximization and $ rac{1-1/e-ε}{4-2/e-2ε}$ for fully adaptive submodular maximization. Submodular functions are a broad class of set functions, which naturally arise in diverse areas. Many algorithms have been suggested for the maximization of these functions. Unfortunately, once the function deviates from submodularity, the known algorithms may perform arbitrarily poorly. Amending this issue, by obtaini…
Concerning the set of exceptional surgery slopes for a hyperbolic knot, Lackenby and Meyerhoff proved that the maximal cardinality is 10 and the maximal diameter is 8. Their proof is computer-aided in part, and both bounds are achieved simultaneously. In this note, it is observed that the diameter bound 8 implies the m…
New framework for online influencer selection considering cost constraints.
problem Real-world social advertising budget limitations and cost variability of influencers.
method Introduces a budgeted framework for online influence maximization using an algorithm with semi-bandit feedback.
result Improves the state of the art regret bound for cardinality constraint setting.
The study classifies and characterizes totally symmetric sets in the general linear group.
problem Understanding the structure and properties of totally symmetric sets in the general linear group.
method Formulated a notion of irreducibility for totally symmetric sets in the general linear group and classified them.
result Classification of irreducible totally symmetric sets and those of maximal cardinality.
We prove that on a punctured oriented surface with Euler characteristic chi < 0, the maximal cardinality of a set of essential simple arcs that are pairwise non-homotopic and intersecting at most once is 2|chi|(|chi|+1). This gives a cubic estimate in |chi| for a set of curves pairwise intersecting at most once on a cl…
New algorithm maximizes non-monotone adaptive submodular functions in linear time.
problem Maximizing non-monotone adaptive submodular functions subject to a cardinality constraint.
method Developed a linear-time algorithm for non-monotone adaptive submodular maximization.
result Achieved a 1/e−ε approximation ratio with O(nε−2logε−1) value oracle queries. New guarantees for adaptive combinatorial maximization with various objectives.
problem Maximizing under cardinality constraints and minimum cost coverage in adaptive settings.
method Bayesian approach with comprehensive approximation guarantees for various utility functions.
result Maximal gain ratio is a new parameter that provides stronger approximation guarantees than greedy policies.
Proves conjectures about maximal antipodal sets in symmetric and generalised symmetric spaces.
problem Cohomological descriptions of maximal antipodal sets in symmetric spaces.
method Equivariant cohomology theory.
result Proves several long-standing conjectures by Chen--Nagano and extends them to generalised symmetric spaces.
New framework for consistent submodular maximization with insertions and deletions.
problem Maintaining near-optimal solutions in a dynamic setting with insertions and deletions.
method Developed a general framework for fully dynamic submodular maximization, instantiated for cardinality and rank-k matroid constraints.
result First constant-factor approximations with sublinear consistency for both cardinality and rank-k matroid constraints.
Dynamic submodular maximization with consistency constraints.
problem Maximizing submodular functions in a streaming environment with limited changes.
method Algorithms with trade-offs between consistency and approximation quality.
result Effective algorithms for real-world applications.
Differentially private algorithms for submodular maximization under various constraints.
problem Maximizing decomposable submodular functions under constraints while preserving privacy.
method Designing differentially private algorithms for both monotone and non-monotone decomposable submodular maximization under general matroid constraints.
result Improved utility guarantees and competitive performance compared to non-private algorithms.
A new algorithm tackles submodular bandit problems with multiple constraints.
problem Addressing diversified retrieval and online learning with budget constraints.
method Non-greedy algorithm focusing on upper-confidence bounds.
result High-probability upper bound of an approximation regret matching fast offline algorithm's ratio.
We consider the problem of multi-objective maximization of monotone submodular functions subject to cardinality constraint, often formulated as max∣A∣=kmini∈{1,…,m}fi(A). While it is widely known that greedy methods work well for a single objective, the problem becomes much harder with multiple objec…
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.
We study the problem of maximizing a monotone submodular function subject to a cardinality constraint k, with the added twist that a number of items τ from the returned set may be removed. We focus on the worst-case setting considered in (Orlin et al., 2016), in which a constant-factor approximation guarantee was g…
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.
The study counts 23 maximal 1-systems on a torus with 2 punctures.
problem Counting maximal 1-systems on a torus with punctures.
method Defined and analyzed 1-systems, generalized results to surfaces with boundary.
result There are exactly 23 maximal 1-systems on a torus with 2 punctures.
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…
We address the problem of maximizing an unknown submodular function that can only be accessed via noisy evaluations. Our work is motivated by the task of summarizing content, e.g., image collections, by leveraging users' feedback in form of clicks or ratings. For summarization tasks with the goal of maximizing coverage…
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.
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.
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).
Let k be a number field and B be a central simple algebra over k of dimension p2 where p is prime. In the case that p=2 we assume that B is not totally definite. In this paper we study sets of pairwise nonisomorphic maximal orders of B with the property that a Ok-order of rank p embeds i…
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.
Robust optimization is becoming increasingly important in machine learning applications. In this paper, we study a unified framework of robust submodular optimization. We study this problem both from a minimization and maximization perspective (previous work has only focused on variants of robust submodular maximizatio…
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.
We study the classical problem of maximizing a monotone submodular function subject to a cardinality constraint k, with two additional twists: (i) elements arrive in a streaming fashion, and (ii) m items from the algorithm's memory are removed after the stream is finished. We develop a robust submodular algorithm STAR-…
In this paper we describe a new algorithm called Fast Adaptive Sequencing Technique (FAST) for maximizing a monotone submodular function under a cardinality constraint k whose approximation ratio is arbitrarily close to 1−1/e, is O(log(n)log2(logk)) adaptive, and uses a total of O(nloglog(k)) queries. …
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. The standard greedy algorithm has been recently shown to enjoy approximation guarantees for constrained non-submodular nondecreasing set function maximization. While these recent results allow to better characterize the empirical success of the greedy algorithm, they are only applicable to simple cardinality constraint…
The study counts geodesics on special manifolds without focusing points.
problem Counting geodesics on specific types of manifolds.
method Margulis-type asymptotic estimates and analysis of geodesic flow.
result The geodesic flow on these manifolds has a unique measure of maximal entropy with the Bernoulli property.
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.
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.
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,…