The study connects minimal and maximal surfaces in 3D and 3-L space.
problem Describing correspondences between minimal and maximal surfaces in different spaces.
method Weierstrass representation and asymptotic analysis.
result Established criteria for singularity types and moduli spaces.
Maximizes probability of completing investment schedules with optimal portfolio weights.
problem Optimizing probability of completing investment schedules with optimal portfolio weights.
method Computing maximum probability and optimal portfolio weight functions for various rebalancing schedules.
result Noticeable improvements in probability to complete schedules with optimal portfolio weights.
The paper proves Calabi-Bernstein type results for minimal and maximal surfaces in 3D and 3D-L spacetime.
problem Characterizing minimal and maximal surfaces in 3D and 3D-L spacetime.
method Analyzing surfaces with specific properties and using geometric and functional methods.
result Calabi-Bernstein type results for critical points of a weighted area functional in R3 and L3. The paper predicts survival functions using random survival trees and concordance maximization.
problem Predicting conditional survival functions in right-censored data.
method The approach combines regression strategies with random survival trees and maximizes concordance.
result The proposed weighted predictor outperforms the usual survival cobra in terms of concordance.
The paper computes characteristic classes for Lie group representations.
problem Computing characteristic classes for Lie group representations.
method The paper outlines a procedure to compute characteristic classes of irreducible representations of Lie groups, expressing them as polynomial functions in the highest weight.
result The paper expresses characteristic classes of Lie group representations as polynomial functions in the highest weight.
RWR converges to global optimum in certain settings.
problem Proving convergence of RWR to optimal policy.
method Iterative learning with return-weighted log-likelihood.
result RWR converges to global optimum under certain conditions.
Paper develops a framework to optimize neural networks using weighted metrics.
problem Discrepancy between maximizing weighted classification scores and minimizing loss function.
method Formalizes weighted classification metrics and constructs corresponding losses.
result Framework includes well-established approaches like cost-sensitive learning and weighted cross entropy.
The paper defines function spaces on manifolds with bounded or singular geometries.
problem Defining function spaces on manifolds with various geometries.
method Introduces and analyzes Sobolev, Besov, and Bessel potential spaces on uniformly regular and singular Riemannian manifolds.
result Demonstrates maximal regularity for a linear parabolic problem on singular manifolds.
We study geometry of complete Riemannian manifolds endowed with a weighted measure, where the weight function is of quadratic growth. Assuming the associated Bakry-Emery curvature is bounded from below, we derive a new Laplacian comparison theorem and establish various sharp volume upper and lower bounds. We also obtai…
In this work an iterative algorithm based on unsupervised learning is presented, specifically on a Restricted Boltzmann Machine (RBM) to solve a perfect matching problem on a bipartite weighted graph. Iteratively is calculated the weights wij and the bias parameters θ=(ai,bj) that maximize the energy funct…
A new method for clustering functional data outperforms existing methods.
problem Clustering heterogeneous functional linear regression data.
method funWeightClust, a family of parsimonious models based on cluster weighted models.
result funWeightClust outperforms existing methods in simulations and real-world traffic analysis.
Optimizes portfolios using CPT utility via convex optimization.
problem Maximizing CPT utility in portfolio selection.
method Minorization-maximization (MM) algorithm and convex-concave (CC) procedure.
result Problems can be solved globally and efficiently.
A weighted random survival forest is presented in the paper. It can be regarded as a modification of the random forest improving its performance. The main idea underlying the proposed model is to replace the standard procedure of averaging used for estimation of the random survival forest hazard function by weighted av…
We prove that if a geodesic metric measure space satisfies a comparison condition for isoperimetric profile and if the observable variance is maximal, then the space is foliated by minimal geodesics, where the observable variance is defined to be the supremum of the variance of 1-Lipschitz functions on the space. Our r…
A new clustering method for functional data using skewed distributions.
problem Clustering functional data with skewed distributions.
method Mixtures of functional linear regression models and three skewed multivariate distributions (variance-gamma, skew-t, normal-inverse Gaussian).
result The proposed method funWeightClustSkew performs well on simulated and real data.
The paper integrates behavioral distortions into portfolio optimization using implied probability weighting functions.
problem Behavioral distortions in probability weighting affect portfolio optimization under different return distributions.
method Developed a unified framework to extract probability weighting functions from optimal portfolios modeled under Gaussian and NIG distributions.
result Increasing tail fatness amplifies behavioral distortions, and shifts in risk-free rates alter the curvature of these distortions.
This paper examines MEV attacks in dynamic AMMs and proposes new protections.
problem Dynamic AMMs introduce new MEV attack vectors due to inter-block weight changes.
method Analyzed inter-block weight changes as analogous to trades, conducted simulations.
result New inter-block protections are required to guard against multi-block MEV attacks.
Networks are a convenient way to represent complex systems of interacting entities. Many networks contain "communities" of nodes that are more densely connected to each other than to nodes in the rest of the network. In this paper, we investigate the detection of communities in temporal networks represented as multilay…
Submodular functions have many applications. Matchings have many applications. The bitext word alignment problem can be modeled as the problem of maximizing a nonnegative, monotone, submodular function constrained to matchings in a complete bipartite graph where each vertex corresponds to a word in the two input senten…
Investment strategy optimizes risk using a specific risk measure.
problem Optimizing investment with risk controlled by a weighted entropic risk measure.
method Investigation of expected utility maximization and risk minimization problems with solutions provided iteratively.
result Explicit characterization of solutions to optimization problems.
The study examines the independence of GKM manifolds and symmetric spaces.
problem Understanding the independence of isotropy weights in GKM manifolds.
method Using weighted graphs and properties of symmetric spaces, the study analyzes the independence of isotropy weights.
result The maximal independence of G/H is 2, 3, or n=dimT, corresponding to symmetric spaces of rank >2. We introduce a principled method for the signed clustering problem, where the goal is to partition a graph whose edge weights take both positive and negative values, such that edges within the same cluster are mostly positive, while edges spanning across clusters are mostly negative. Our method relies on a graph-based …
Maximizing withdrawal success in a pooled annuity fund with multiple annuitants.
problem Optimizing withdrawal success in a pooled annuity fund with homogeneous annuitants.
method Maximizing the probability of completing withdrawals until death over portfolio weight functions.
result Increasing the number of annuitants can significantly increase the maximum probability of withdrawal success.
The study examines Nash equilibria in utility maximization games with multiplicative performance criteria.
problem Existence and uniqueness of Nash equilibria in multiplicative performance criteria games.
method General characterization of Nash equilibria for a large class of utility functions.
result Existence and uniqueness of Nash equilibria for arbitrary initial wealth vectors.
The study examines correlations of logarithms of integers at different scalings.
problem Analyzing pair correlations of logarithms of integers at various scalings.
method Examined correlations of logarithms of positive integers at different scalings, proving the existence of pair correlation functions.
result Level repulsion at linear scaling, total loss of mass at superlinear scalings, and Poissonian behavior at sublinear scalings.
A new approach optimizes weights in DLP for better risk-adjusted performance.
problem Optimizing time-varying weights in Double Linear Policy (DLP) for better risk-adjusted performance.
method Stochastic Model Predictive Control (SMPC) framework to maximize risk-adjusted returns while enforcing constraints.
result Empirical results show improved risk-adjusted performance and drawdown control.
Variational Bayesian neural networks (BNNs) perform variational inference over weights, but it is difficult to specify meaningful priors and approximate posteriors in a high-dimensional weight space. We introduce functional variational Bayesian neural networks (fBNNs), which maximize an Evidence Lower BOund (ELBO) defi…
Estimates Gaussian mixtures from weighted samples efficiently.
problem Estimating Gaussian mixtures from weighted samples with correct weight treatment.
method Density interpretation and expectation-maximization method considering weights.
result Correctly estimates Gaussian mixtures with weighted samples.
Paper proposes a new method for estimating conditional densities using logistic regressions.
problem Estimating conditional densities for complex distributions.
method Parametric conditional density estimation via weighted logistic regressions.
result Maximum likelihood estimates can be obtained efficiently via a block-wise alternating maximization scheme and local case-control sampling.
This work explores maximum likelihood optimization of neural networks through hypernetworks. A hypernetwork initializes the weights of another network, which in turn can be employed for typical functional tasks such as regression and classification. We optimize hypernetworks to directly maximize the conditional likelih…
In this paper, we study the problem of robust influence maximization in the independent cascade model under a hyperparametric assumption. In social networks users influence and are influenced by individuals with similar characteristics and as such, they are associated with some features. A recent surging research direc…
Let (Mn,g,e−fdv) be a smooth metric measure space of dimensional n. Suppose that v is a positive weighted p-eigenfunctions associated to the eigenvalues λ1,p on M, namely efdiv(e−f∣∇v∣p−2∇v)=−λ1,pvp−1. in the distribution sense. We first give a local gradient estimat…
The paper proposes effective margin regularization to improve adversarial robustness in deep neural networks.
problem Adversarial vulnerability of deep neural networks (DNNs).
method Regularization of effective weight norm during training to maximize effective margins.
result Effective margin regularization (EMR) boosts adversarial robustness in both standard and adversarial training.
Reducing the precision of weights and activation functions in neural network training, with minimal impact on performance, is essential for the deployment of these models in resource-constrained environments. We apply mean-field techniques to networks with quantized activations in order to evaluate the degree to which …
We consider the M-ary classification problem via crowdsourcing, where crowd workers respond to simple binary questions and the answers are aggregated via decision fusion. The workers have a reject option to skip answering a question when they do not have the expertise, or when the confidence of answering that questio…
A new trading model uses deep reinforcement learning to optimize portfolio weights.
problem Optimizing portfolio weights with risk and return considerations.
method Improved deep reinforcement learning with actor-critic architecture, quantile regression, and asset short selling.
result The proposed model outperforms benchmark strategies in backtesting.
New lower bounds for combinatorial multi-armed bandits for general reward functions.
problem Maximizing reward in sequential decisions with sets of arms.
method Proved tight regret lower bounds for all smooth reward functions under mild assumptions.
result Lower bounds are tight up to log-factors for monotone reward functions.
Real-world tasks are often highly structured. Hierarchical reinforcement learning (HRL) has attracted research interest as an approach for leveraging the hierarchical structure of a given task in reinforcement learning (RL). However, identifying the hierarchical policy structure that enhances the performance of RL is n…
The paper develops stability criteria for real reductive Lie groups acting on manifolds.
problem Analyzing stability of real reductive Lie group actions on manifolds.
method Introduced a gradient map and maximal weight function to characterize stability conditions.
result Characterized stability, semistability, and polystability using numerical criteria.
This paper introduces the hypervolume maximization with a single solution as an alternative to the mean loss minimization. The relationship between the two problems is proved through bounds on the cost function when an optimal solution to one of the problems is evaluated on the other, with a hyperparameter to control t…
Convolutional sparse coding (CSC) can learn representative shift-invariant patterns from multiple kinds of data. However, existing CSC methods can only model noises from Gaussian distribution, which is restrictive and unrealistic. In this paper, we propose a general CSC model capable of dealing with complicated unknown…
Investigates portfolio selection for rank-dependent utilities in incomplete markets.
problem Portfolio selection for agents with rank-dependent utility in incomplete financial markets.
method Characterizes deterministic strict equilibrium strategies for constant-coefficient and time-invariant probability weighting functions. Addresses the issue of selecting an optimal strategy from multiple equilibrium strategies for time-variant probability weighting functions.
result Characterizes deterministic strict equilibrium strategies and identifies optimal strategies from multiple equilibrium strategies.
New algorithm for optimizing statistical utilities in bandits.
problem Optimizing statistical functionals of long-run reward distributions.
method Influence-function calculus for stochastic gradient estimation, entropic mirror-ascent algorithm.
result Regret bounds that separate optimization and estimation errors.
In this paper we study the steepest descent L2-gradient flow of the functional $\SW_{λ_1,λ_2}$, which is the the sum of the Willmore energy, λ1-weighted surface area, and λ2-weighted enclosed volume, for surfaces immersed in R3. This coincides with the Helfrich functional with zero `spontaneous curvature'.…
We study the problem of finding the maximum of a function defined on the nodes of a connected graph. The goal is to identify a node where the function obtains its maximum. We focus on local iterative algorithms, which traverse the nodes of the graph along a path, and the next iterate is chosen from the neighbors of the…
The standard interpretation of importance-weighted autoencoders is that they maximize a tighter lower bound on the marginal likelihood than the standard evidence lower bound. We give an alternate interpretation of this procedure: that it optimizes the standard variational lower bound, but using a more complex distribut…
Improved SAC with AWMP for better control tasks.
problem Discontinuous and non-smooth optimal policies in reinforcement learning.
method Advantage Weighted Mixture Policy (AWMP) for SAC, learning state-specific weights.
result SAC with AWMP outperforms SAC in four control tasks.
Wide neural networks learn features under μP, identifying weights and decomposing support.
problem Feature learning in wide neural networks under μP. method Proving mean-field limit, characterizing identifiability, sparse-dictionary decomposition, and feature-learning-error decomposition.
result The triple (w∗,Dorb∗,S∗) identifies the natural learning cell of the architecture-data pair (σ,ρ).