In this paper we consider minors of ribbon graphs (or, equivalently, cellularly embedded graphs). The theory of minors of ribbon graphs differs from that of graphs in that contracting loops is necessary and doing this can create additional vertices and components. Thus the ribbon graph minor relation is incompatible wi…
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48 results for “minors”
A new oversampling framework generates minority samples by perturbing majority classes.
problem Oversampling in imbalanced classification often neglects majority classes, leading to samples spread across the minority space.
method Introduces a counterfactual objective to generate new minority samples by perturbing majority samples.
result Generated minority samples are near the decision boundary and significantly outperform state-of-the-art methods.
Improves generation of minority samples using diffusion models.
problem Generating minority samples on low-density regions of a data manifold.
method Introduces minority guidance to focus diffusion models on minority samples.
result Significantly improves generation of high-quality minority samples.
Characterizes minor-minimal separating projective planar graphs and their generalizations.
problem Understanding projective planar graphs and their properties.
method Analyzing minors, embeddings, and specific link types.
result Partial characterization of minor-minimal separating projective planar graphs and their generalizations.
Every infinitely edge-connected graph has a minor of Farey graph or .
problem Characterizing edge-connected graphs with specific minor properties.
method Analyzing the minor structure of infinitely edge-connected graphs.
result Infinitely edge-connected graphs contain Farey graph or as a minor.
Boost-and-Skip generates minority samples without guidance, faster and more effectively.
problem Generating minority samples in low-density regions of a data manifold.
method Boost-and-Skip approach with variance-boosted initialization and timestep skipping.
result Boost-and-Skip effectively promotes the emergence of underrepresented minority features.
Paper determines Assouad-Nagata dimension for all minor-closed metrics.
problem Understanding the Assouad-Nagata dimension of minor-closed metrics.
method Using edge-weighted graphs and edge-deletion/contraction to model minor-closed metrics, determining their Assouad-Nagata dimension.
result Determined the Assouad-Nagata dimension for every minor-closed metric.
The study combines graph-minors and metric spaces, answering some questions and conjectures.
problem Whether geodesic metric spaces without a fat minor are quasi-isometric to graphs without minor.
method Combining graph-minors and coarse geometry, answering affirmatively for small .
result Affirmative answer for small in the problem statement.
In this paper we study the continuum time dynamics of a stock in a market where agents behavior is modeled by a Minority Game and a Grand Canonical Minority Game. The dynamics derived is a generalized geometric Brownian motion; from the Black & Scholes formula the calibration of both the Minority Game and the Grand Can…
This paper gives a critical account of the minority game literature. The minority game is a simple congestion game: players need to choose between two options, and those who have selected the option chosen by the minority win. The learning model proposed in this literature seems to differ markedly from the learning mod…
The complement of a non-separating planar graph contains a K_n minor.
problem Characterizing the structure of complements of planar graphs.
method Analyzing the structure of complements of non-separating planar graphs and using examples to illustrate hypotheses.
result The order 2n-3 is the lowest possible for a non-separating planar graph whose complement contains a K_n minor.
An Adaptive Oversampling Learning Method for Class-Imbalanced Fault Diagnostics and Prognosticscs.LG
Data-driven fault diagnostics and prognostics suffers from class-imbalance problem in industrial systems and it raises challenges to common machine learning algorithms as it becomes difficult to learn the features of the minority class samples. Synthetic oversampling methods are commonly used to tackle these problems b…
The paper is partially withdrawn: in its current form, Lemma 2.3 is false, so that our proof of Theorem A and Proposition B has an important gap. We were unable to fix it yet. Any help is most welcome. We prove that the restriction of surface minority to fiber surfaces of divides is a well-quasi-order. Here surface min…
Model explains periodic trading in financial markets through game theory.
problem Understanding periodic trading activities in financial markets.
method Mean-field liquidation game with major-minor players.
result Existence and uniqueness of Nash equilibrium established.
Overparameterized models can worsen minority group errors even when overall test error improves.
problem Overparameterization exacerbates spurious correlations, harming minority groups.
method Simulations and experiments on image datasets, theoretical analysis of linear models.
result Subsampling the majority group can achieve low minority error in overparameterized models.
This paper classifies chiral graphs up to size 12.
problem Understanding the chirality of simple graphs to predict molecular behavior.
method Classifying minor minimal intrinsically chiral graphs among simple graphs of size up to 12.
result Complete set of minor minimal graphs for intrinsic properties of chiral molecules.
Statistical and Multifractal Properties of the Time Series Generated by a Modified Minority Gamephysics.soc-ph
In this paper it was developed a modification of the known multiagent model Minority Game, designed to simulate the behavior of traders in financial markets and the resulting price dynamics on the abstract resource. The model was implemented in the form of software. The modified version of Minority Game was investigate…
Dynamical Minority Games in Futures Exchange Marketsphysics.soc-ph
We introduce the minority game theory for two kinds of the Korean treasury bond (KTB) in Korean futures exchange markets. Since we discuss numerically the standard deviation and the global efficiency for an arbitrary strategy, our case is found to be approximate to the majority game. Our result presented will be compar…
Well-quasi-orders proved on embedded planar graphs.
problem Proving well-quasi-orders on embedded planar graphs.
method Careful analysis and extensions of classical methods for embedded minor relations.
result Embedded minor relations are well-quasi-orders on various classes of embedded planar graphs.
We list more than 200 new examples of minor minimal intrinsically knotted graphs and describe many more that are intrinsically knotted and likely minor minimal.
We prove that every simple graph of order 12 which has minimum degree 6 contains a K_6 minor.
M2m method improves deep learning performance on class-imbalanced datasets.
problem Class imbalance in labeled training datasets causes deep neural networks to generalize poorly to minority classes.
method Augment less-frequent classes by translating samples from more-frequent classes.
result Significantly improves generalization on minority classes compared to existing methods.
AGGAN uses genetic algorithm with simulated annealing to generate minority class data.
problem Overcoming class imbalance in minority class data.
method AGGAN combines genetic algorithm and simulated annealing to train GANs on scarce minority class data.
result AGGAN effectively generates minority class data distributions from limited samples.
We show that any self-complementary graph with vertices contains a minor. We derive topological properties of self-complementary graphs.
Imbalanced data classification problem has always been a popular topic in the field of machine learning research. In order to balance the samples between majority and minority class. Oversampling algorithm is used to synthesize new minority class samples, but it could bring in noise. Pointing to the noise problems, thi…
Framework learns to transform majority to minority samples for balanced classification.
problem Imbalanced classification leading to biased predictions.
method Minimizes MMD and uses triplet loss for global alignment and boundary awareness.
result Consistent improvements over classical and generative baselines in AUROC, G-mean, F1-score, and MCC.
Price return auto-correlation and predictability in agent-based models of financial marketscond-mat.stat-mech
We demonstrate that minority mechanisms arise in the dynamics of markets because of effects of price impact; accordingly the relative importance of minority and delayed majority mechanisms depends on the frequency of trading. We then use minority games to illustrate that a vanishing price return auto-correlation functi…
Two new minor minimal intrinsically chiral graphs identified.
problem Identifying intrinsically chiral graphs in molecular structures.
method Analyzing graph symmetry and embedding properties.
result Found two new minor minimal intrinsically chiral graphs and .
Extends ML fairness to handle minority groups over time.
problem Limitations of existing fairness criteria.
method Performative Distributionally Robust Optimization.
result Improves fairness for minority groups over time.
Decision trees can be biased towards minority class, contrary to belief.
problem Bias in decision trees towards minority class in imbalanced datasets.
method Critical evaluation of past literature, specific conditions analysis, tree-fitting adjustments, and post-hoc calibration methods.
result Decision trees can be biased towards minority class under specific conditions, not always towards majority.
Model shows how diversity on corporate boards influences decision-making and innovation.
problem Understanding dynamics of diversity and innovation in corporate boards.
method Developed a dynamic model calibrated with empirical data of firm and board networks.
result Homophily and visibility biases shape the trajectory towards equality in corporate boards.
Classifiers trained with class-imbalanced data are known to perform poorly on test data of the "minor" classes, of which we have insufficient training data. In this paper, we investigate learning a ConvNet classifier under such a scenario. We found that a ConvNet significantly over-fits the minor classes, which is quit…
Exploring Deep Neural Networks via Layer-Peeled Model: Minority Collapse in Imbalanced Trainingcs.LG
New model explains neural collapse and limits on minority classes in imbalanced datasets.
problem Understanding and predicting performance limits of deep learning models on imbalanced datasets.
method Layer-Peeled Model, a nonconvex optimization program isolating top layers and applying constraints.
result Reveals a new phenomenon called Minority Collapse that limits deep learning models on minority classes.
A new sampling method balances imbalanced data using gamma distribution.
problem Imbalanced class distribution in data causes bias in classification algorithms.
method Intelligent resampling of minority class instances via gamma distribution.
result The proposed method outperforms existing techniques on 12 out of 24 datasets.
Graphs with fat minors have a limited large-scale structure.
problem Understanding the large-scale structure of graphs excluding certain minors.
method Introduced the concept of Baker-treewidth and used it to prove asymptotic dimension bounds.
result Every hereditary class of bounded-degree graphs excluding some graph as a fat minor has asymptotic dimension at most 2.
In this paper, we present a simple stock market model (the market game) which incorporates, as ab initio dynamics delayed majority dynamics, according to which agents (with heterogeneous strategies and price expectations) are rewarded if their actions at time t are the actions of the majority of agents at time t+1. We …
The Minority Game: a statistical physics perspectivecond-mat.dis-nn
A brief review is given of the minority game, an idealized model stimulated by a market of speculative agents, and its complex many-body behaviour. Particular consideration is given to analytic results for the model rather than discussions of its relevance in real-world situations.
LQG Risk-Sensitive Single-Agent and Major-Minor Mean-Field Game Systems: A Variational Frameworkmath.OC
Develops variational framework for LQG risk-sensitive MFGs with major-minor interactions.
problem Risk-sensitive optimal control in LQG systems with major-minor interactions.
method Variational approach, nonlinear necessary and sufficient condition of optimality, equivalent risk-neutral measure, Markovian closed-loop best-response strategies.
result Derives optimal control strategies for LQG risk-sensitive MFGs with major-minor interactions, establishing Nash and -Nash equilibria.
The paper analyzes how minority group imbalance affects neural network performance.
problem The impact of minority group imbalance on neural network performance.
method Formulated group imbalance problem with Gaussian Mixture Model, quantified sample complexity, convergence rate, and testing performance.
result Increasing the minority group fraction does not necessarily improve the generalization performance of the minority group.
The paper extends logistic regression for unbounded majority classes and derives asymptotic properties.
problem Infinitely imbalanced logistic regression inference.
method Derive a second order expansion for slope parameter under unbounded majority class.
result The second order term converges to a normal distribution with a variance depending only on the minority class's mean.
Real payoffs and virtual trading in agent based market modelscond-mat.stat-mech
The \$-Game was recently introduced as an extension of the Minority Game. In this paper we compare this model with the well know Minority Game and the Majority Game models. Due to the inter-temporal nature of the market payoff, we introduce a two step transaction with single and mixed group of interacting traders. When…
The Interactive Minority Game: Instructions for Expertscond-mat.dis-nn
The Interactive Minority Game (IMG) is an online version of the traditional Minority Game in which human players can enter into competition with the traditional computer-controlled agents. Through the rich (and, importantly, analytically understood) behaviour of the MG, we can explore humans' behaviour in different kin…
Study embeddability of 2-complexes in 4-space, proving Heawood family's excluded minors.
problem Whether a 2-dimensional CW complex embeds in .
method Operations preserving embeddability, constructions of non-preserving transformations, study of 4-flat graphs.
result Prove 78 graphs of Heawood family are excluded minors for 4-flat graphs.
Fewer obstructions for small graphs in knotless embedding.
problem Finite obstructions for knotless embedding of small graphs.
method Analysis of graph minor obstructions and knotless embedding.
result There are only three obstructions for size 23 graphs, significantly fewer than previously known.
Credit scores misclassify borrowers, especially minorities, leading to inequitable access.
problem Misclassification of borrowers by credit scores, particularly minorities.
method Benchmarked a widely used credit score against a machine learning model.
result Machine learning model improves predictive accuracy for low-quality data, leading to more equitable access.
We show that the 20 graph Heawood family, obtained by a combination of triangle-Y and Y-triangle moves on , is precisely the set of graphs of at most 21 edges that are minor minimal for the property not --apex. As a corollary, this gives a new proof that the 14 graphs obtained by triangle-Y moves on are t…
Conformal prediction fails to cover minority classes in imbalanced datasets, but a class-conditional fix improves coverage.
problem Conformal prediction fails to cover minority classes in imbalanced datasets, leading to poor performance on rare labels.
method Class-conditional conformal prediction to improve coverage of minority classes.
result Class-conditional conformal prediction restores minority coverage to target with a modest increase in prediction-set size.
Imbalanced datasets are ubiquitous. Classification performance on imbalanced datasets is generally poor for the minority class as the classifier cannot learn decision boundaries well. However, in sensitive applications like fraud detection, medical diagnosis, and spam identification, it is extremely important to classi…