The study finds criteria for discreteness in quaternionic hyperbolic space.
problem Discreteness of subgroups in quaternionic hyperbolic space.
method Using test maps to establish discreteness criteria for Zariski-dense subgroups.
result Discreteness criteria for quaternionic hyperbolic subgroups.
Improved recommendations using latent embeddings from user reviews.
problem Lack of consideration for latent embeddings in multi-criteria recommender systems.
method Utilized variational autoencoders to map user reviews into latent embeddings, which are then compressed into discrete vectors for multi-criteria recommendation.
result The proposed method significantly outperforms baselines across various datasets and evaluation measures.
New criteria distinguish cause from effect in data, overcoming statistical limitations.
problem Determining causal direction from statistical dependence alone.
method Intuitive criteria based on simplicity of prediction, tested on synthetic data.
result Criteria accurately distinguish cause from effect in various scenarios.
Transforms game optimization dynamics into frequency domain for precise hyperparameter analysis.
problem Analyzing convergence of hyperparameters in game optimization.
method Frequency-domain framework using High-Resolution Differential Equations (HRDEs) and Laplace transforms.
result Derives precise convergence criteria for the Lookahead algorithm.
New algorithms for risk management in incomplete markets.
problem Risk management in incomplete markets with various sources of incompleteness.
method Machine-learning-based algorithms to solve hedging problems.
result One algorithm is flexible and can use multiple risk criteria.
We present turnpike-type results for the risk tolerance function in an incomplete market setting under time-monotone forward performance criteria. We show that, contrary to the classical case, the temporal and spatial limits do not coincide. We also show that they depend directly on the left- and right-end of the suppo…
Extends Neural ODEs to model discrete changes in continuous systems.
problem Lack of explicit termination time in existing Neural ODE formulations.
method Introduces neural event functions to implicitly define termination criteria.
result Models discrete changes in continuous systems without prior knowledge.
A new method minimizes experimental design regret for various optimality criteria.
problem Optimizing experimental design points for statistical efficiency.
method Regret minimization framework for polynomial-time approximation.
result Achieves (1+ε) approximation with O(p/ε2) design points. The study finds discrete subgroups with full limit sets in higher rank Lie groups.
problem Finding discrete subgroups with full limit sets in higher rank Lie groups.
method Analyzing real semi-simple Lie groups of higher rank and providing criteria for discrete subgroups of G=SL(3,R). result Existence of discrete subgroups with full limit sets in higher rank Lie groups.
Efficiency criteria improve conformal predictors' performance.
problem Improving the performance of conformal predictors.
method Learning classifiers by minimizing observed fuzziness as a training objective function.
result Conformal predictors trained by minimizing observed fuzziness perform better than traditional ones.
A closed discrete subset A⊂C is called tame if C∖A is quasiconformally equivalent to C∖Z. By giving several criteria for A to be tame, we shall show that Z+iZ is not tame.
This paper introduces efficient approximations for fairness criteria in regression models.
problem Measuring fairness in real-valued outcomes (regression settings) is computationally challenging.
method Fast approximations of mutual information for independence, separation, and sufficiency fairness criteria.
result The method achieves state-of-the-art accuracy/fairness tradeoffs in real-world datasets.
The Shannon theorem is extended to locally compact groups.
problem Identifying the Poisson boundary of locally compact groups.
method Random walks and Shannon-McMillan-Breiman theorem.
result Generalized criteria for identifying Poisson boundaries.
We consider a discrete-time, generically incomplete market model and a behavioural investor with power-like utility and distortion functions. The existence of optimal strategies in this setting has been shown in a previous paper under certain conditions on the parameters of these power functions. In the present paper w…
A new framework for controllable generation of discrete masked models.
problem Efficient controllable generation of discrete data models.
method Plug-and-play framework based on importance sampling.
result Demonstrates versatility across multiple domains, including protein design.
Community detection is one of the fundamental problems of network analysis, for which a number of methods have been proposed. Most model-based or criteria-based methods have to solve an optimization problem over a discrete set of labels to find communities, which is computationally infeasible. Some fast spectral algori…
A natural approach to analyze interaction data of form "what-connects-to-what-when" is to create a time-series (or rather a sequence) of graphs through temporal discretization (bandwidth selection) and spatial discretization (vertex contraction). Such discretization together with non-negative factorization techniques c…
This paper presents the R package gRapHD for efficient selection of high-dimensional undirected graphical models. The package provides tools for selecting trees, forests and decomposable models minimizing information criteria such as AIC or BIC, and for displaying the independence graphs of the models. It has also some…
This work tackles the exploration-exploitation dilemma in RL by developing optimal policies that are inherently exploration-conscious.
problem The exploration-exploitation tradeoff in Reinforcement Learning, where policies need to balance new action exploration with past experience exploitation.
method Developed exploration-conscious criteria that result in optimal policies, solving these criteria by solving a surrogate Markov Decision Process.
result Demonstrated superior performance of exploration-conscious RL algorithms compared to non-exploration-conscious counterparts in both discrete and continuous action spaces.
The paper proves inequalities for isometries in loxodromic Kleinian groups.
problem Discreteness criteria for subgroups of PSL2(C). method Generalization of discreteness criteria, using trace inequalities and optimization problems.
result Inequalities involving traces and hyperbolic displacements for loxodromic Kleinian groups.
Poincaré's Polyhedron Theorem is a widely known valuable tool in constructing manifolds endowed with a prescribed geometric structure. It is one of the few criteria providing discreteness of groups of isometries. This work contains a version of Poincaré's Polyhedron Theorem that is applicable to constructing fibre bund…
The paper analyzes how behavioral investors make portfolio decisions using Markowitz Stochastic Dominance criteria.
problem Understanding how behavioral investors make portfolio decisions.
method Developed stochastic optimization problems and MILP models to capture subjective decision weights and probability weighting functions.
result The developed models can be used to formulate computationally tractable portfolio analysis problems.
Study polynomial trace identities in $SL(2,\IC)$ using quaternion algebras.
problem Understanding polynomial trace identities in $SL(2,\IC)$ and their applications.
method Use quaternion algebras over indefinites and their units to study discrete subgroups of $SL(2,\IC)$.
result Obtained structure theorems for quaternion algebras and new polynomial trace identities.
New JSA autoencoders tackle discrete latent variable models for semi-supervised learning.
problem Handling discrete observations and latent codes in deep generative models.
method Joint-stochastic-approximation (JSA) autoencoders that directly maximize data log-likelihood and minimize KL divergence.
result JSA autoencoders achieve comparable performance to continuous latent space models in semi-supervised tasks.
The study explores loss functions for learning distributions, finding the log loss and others are sufficient under certain conditions.
problem Understanding loss functions for distribution learning and density estimation.
method An axiomatic approach to design loss functions, proposing criteria and showing that no single loss function satisfies all criteria.
result No loss function satisfies all criteria, but the log loss and others do under the condition of candidate distributions being calibrated.
Paper introduces scalable neural architecture for solving NP-hard problems.
problem Solving NP-hard reasoning problems from natural inputs.
method Scalable neural architecture and loss function for discrete Graphical Models.
result Empirically shows efficient learning of NP-hard problems.
This work is motivated by two problems: 1) The approach of manifolds and spaces by triangulations. 2) The complexity growth in sequences of polyhedra. Considering both problems as related, new criteria and methods for approximating smooth manifolds are deduced. When the sequences of polyhedra are obtained by the action…
The paper addresses misspecification in econometric models of discrete unobserved heterogeneity.
problem Misspecification in econometric models of discrete unobserved heterogeneity.
method Generalizing previous approaches to allow multiple latent variables, developing inference results for a k-means style estimator, and proposing information criteria for model selection.
result Over-fitting can be severe in k-means style estimators when the number of clusters is over-specified.
Maximal correlation framework improves fairness in machine learning algorithms.
problem Ensuring fairness in machine learning algorithms.
method Introducing maximal correlation framework for fairness constraints and deriving regularizers.
result The approach provides smooth performance-fairness tradeoff curves and competitive performance.
This article gives an up-to-date account of the theory of discrete group actions on non-Riemannian homogeneous spaces. As an introduction of the motifs of this article, we begin by reviewing the current knowledge of possible global forms of pseudo-Riemannian manifolds with constant curvatures, and discuss what kind of …
The study explores deformations of standard locally homogeneous spaces.
problem Understanding how discrete subgroups can be deformed while preserving proper discontinuity.
method Classification results for standard quotients, including local rigidity, deformation criteria, and Zariski-closure conditions.
result Conditions for local rigidity, deformation into nonstandard quotients, and maximal Zariski-closure of discontinuous groups.
The conformal invariance and universality results of Chelkak-Smirnov on the two-dimensional Ising model hold for isoradial planar graphs with critical weights. Motivated by the problem of extending these results to a wider class of graphs, we define a generalized notion of s-holomorphicity for functions on arbitrary we…
Study on Euler-discretized Hull-White model with volatility and asset price asymptotics.
problem Analyzing properties of the Hull-White model under time discretization.
method Discretization using Euler-Maruyama scheme, study of asymptotics in large time steps limit.
result Explicit expressions for growth rates of asset price moments, phase transition criteria.
This paper uses Bayesian ARD to automatically determine utility functions for discrete choice models.
problem Challenging and time-consuming task in identifying optimal utility function specifications.
method Bayesian framework and automatic relevance determination (ARD) for data-driven utility function specification.
result The proposed DCM-ARD model accurately recovers true utility function specifications and outperforms previous methods.
Bayesian active learning improves holistic educational assessments.
problem Gap between holistic CJ and criterion-based rubrics in education.
method Extends Bayesian CJ to handle multiple LO components, using entropy-based active learning.
result Enhanced predictive rankings with uncertainty estimates and quantified assessor agreement.
Researchers analyze a new neural network training method.
problem Training robust configurations in discrete weight neural networks.
method Replicated simulated annealing combining physics and classical simulated annealing.
result Explicit criteria for algorithm convergence and successful sampling.
Optimal experiments tighten causal effect bounds efficiently.
problem Selecting experiments to tighten causal effect bounds from observational data.
method Formalized as max-potency problem, NP-hard. Polynomial-programming framework with graphical pruning criteria.
result Pruning criteria reduce search space significantly, enabling efficient experiment selection.
We consider non-elementary representations of two generator free groups in PSL(2,C), not necessarily discrete or free, G=<A,B>. A word in A and B, W(A,B), is a palindrome if it reads the same forwards and backwards. A word in a free group is {\sl primitive} if it is part of a minimal generating …
Criteria ensure manifold triangulation without differentiable structure.
problem Ensuring a manifold can be triangulated without differentiable structure.
method Local coordinate chart criteria for homeomorphism verification.
result Criteria guarantee triangulation of manifolds without Delaunay property.
A method for learning fair representations for kernel models.
problem Ensuring fairness in machine learning models.
method Using Sufficient Dimension Reduction (SDR) in the context of kernel-based models to construct fair representations in the reproducing kernel Hilbert space (RKHS).
result Demonstrates the effectiveness of model-aware fair representations for kernel models, including support for multiple fairness criteria and continuous/discrete data.
We give some general criteria of being a homeomorphism for continuous mappings of topological manifolds, as well as criteria of being a diffeomorphism for smooth mappings of smooth manifolds. As an illustration, we apply these criteria to the problems arising in two- and three-dimensional grid generation.
The study reveals flaws in pruning criteria and proposes a new assumption for better filter selection.
problem Flaws in existing pruning criteria for CNNs.
method Empirical experiments and Convolutional Weight Distribution Assumption.
result The Convolutional Weight Distribution Assumption improves filter selection in pruning.
New method finds optimal hyperparameters for multiple tasks and criteria.
problem Finding optimal hyperparameters for multiple tasks and criteria.
method Multi-Task Multi Criteria (MTMC) method that provides Pareto-optimal solutions.
result The method selects optimal hyperparameters based on given criteria significance coefficients.
New Morse theory applied to Vietoris-Rips complexes for topological data analysis and geometric group theory.
problem Understanding homotopy types of Vietoris-Rips complexes for metric spaces.
method Generalization of Bestvina-Brady discrete Morse theory applied to Vietoris-Rips complexes.
result Metric criteria (Morse and Link) to deduce homotopy types of VRt(X). New criteria for Heegaard splittings ensure strong irreducibility and finite Goeritz groups.
problem Determining strong irreducibility and finite Goeritz groups of Heegaard splittings.
method Two diagrammatic criteria for Heegaard splittings, accepting arbitrary disk systems.
result Criteria ensure strong irreducibility and finite Goeritz groups for Heegaard splittings.
Develops scenario theory for multi-criteria decision making.
problem Need for robustness assessment with multiple criteria and datasets.
method Collectively treats risks associated with individual criteria for multi-criteria decision problems.
result More accurate robustness certificates and sharper quantification of simultaneous criterion satisfaction.
We consider the problem of identifying patterns in a data set that exhibit anomalous behavior, often referred to as anomaly detection. In most anomaly detection algorithms, the dissimilarity between data samples is calculated by a single criterion, such as Euclidean distance. However, in many cases there may not exist …
The paper evaluates criteria for selecting cryptocurrencies based on historical data.
problem High risk of cryptocurrencies due to volatility.
method Characterized returns and risks using historical data in short time windows (7 and 15 days). Analyzed the importance of criteria using various methods.
result Importance of criteria for selecting cryptocurrencies is analyzed and evaluated.