Efficient adjustment sets found for cost-minimized causal estimations.
problem Estimating interventional means with minimum cost in causal graphical models.
method Defined cost-adjustment sets, constructed flow networks, and used maximum flow algorithms.
result Minimum cost optimal adjustment sets exist and can be found efficiently.
Paper links network Lasso to network flow optimization.
problem Joint clustering and optimization of networked data.
method Exploration of duality between network Lasso and network flow optimization.
result nLasso is equivalent to a minimum-cost flow problem on the data network structure.
Paper computes Kantorovich-Wasserstein distances on d d d -dimensional histograms efficiently.
problem Computing exact Kantorovich-Wasserstein distances between d d d -dimensional histograms. method Uses ( d + 1 ) (d+1) ( d + 1 ) -partite graph to solve as uncapacitated minimum cost flow problem. result Approach is competitive with state-of-the-art optimal transport algorithms.
New method improves MAP inference for CGMs on path graphs, avoiding approximation and maintaining integrality.
problem Improving MAP inference for aggregated count data in CGMs with small values.
method Formulated as a minimum cost flow problem, solved using DCA with efficient subroutines.
result Outputs higher quality solutions than conventional methods.
Gradient descent with geometrically adapted metrics drives L 2 \mathcal{L}^2 L 2 cost to global minimum at uniform rate.
problem Minimizing L 2 \mathcal{L}^2 L 2 cost in deep learning networks. method Adapting gradient descent to output layer metric in deep learning.
result Uniform exponential convergence to global minimum in L 2 \mathcal{L}^2 L 2 cost. Fair clustering ensures equal representation for protected classes.
problem Ensuring equal representation for protected classes in clustering.
method Introducing fairlets, decomposing fair clustering into finding good fairlets and traditional clustering.
result Efficient approximation algorithms for finding good fairlets using minimum cost flow.
Method approximates Wasserstein distance between 2D histograms using min cost flow.
problem Computing Wasserstein distance between 2D histograms efficiently.
method Transforms the problem into an uncapacitated min cost flow problem.
result Approximates optimal solution with reduced network size O ( n ) O(n) O ( n ) . Designs interventions to learn causal graphs with minimum cost.
problem Learning causal graphs with minimum intervention cost.
method Prove NP-hardness, develop greedy and constrained algorithms.
result Achieve nearly optimal intervention design for sparse graphs.
Framework learns linear programs from optimal decisions.
problem Learning linear programs from optimal decisions is challenging.
method Gradient-based framework for learning linear programs from optimal decisions.
result Successfully learns linear programs and multi-commodity flow instances.
Many important optimization problems, such as the minimum spanning tree and minimum-cost flow, can be solved optimally by a greedy method. In this work, we study a learning variant of these problems, where the model of the problem is unknown and has to be learned by interacting repeatedly with the environment in the ba…
Gradient flow in parameters equals linear interpolation in outputs.
problem Understanding and optimizing training algorithms in deep learning.
method Proving equivalence between gradient flow in parameter space and linear interpolation in output space, and deriving formulas for global minima.
result Gradient flow in parameters can be transformed into linear interpolation in outputs, leading to global minima.
Improved community detection in heterogeneous SBM with side information.
problem Misclassification in community detection with noisy labels.
method Optimal weighted message passing and minimum energy flow.
result Optimal weighting improves misclassification rate in heterogeneous SBM.
MPF method improves parameter estimation in probabilistic models.
problem Difficulty in fitting probabilistic models due to intractable partition function.
method Minimum Probability Flow (MPF) method for parameter estimation.
result MPF outperforms existing techniques in convergence time and accuracy.
The economic life of an asset is the optimum length of its usefulness, which is the moment that the asset's expenses are minimum. In this paper, the economic life of physical assets, such as industry machine and equipment, can be interpreted as the moment that the minimum is reached by its equivalent property cost func…
The paper constructs upper bounds for cost minimization in shallow neural networks.
problem Cost minimization in underparametrized shallow ReLU networks.
method Explicit construction of upper bounds based on the geometric structure of classification data.
result An upper bound on the minimum of the cost function of order O ( δ P ) O(δ_P) O ( δ P ) , with exact degenerate local minimum in the special case M = Q M=Q M = Q . New index for evaluating cash flow processes over a fixed horizon.
problem Evaluating performance of cash flow processes over a fixed investment horizon.
method Extended acceptability indices to càdlàg processes, providing a new index based on Average Value-at-Risk and running minimum.
result Suggested index represents a RAROC-type model for performance evaluation.
New algorithm tests model calibration in nearly-linear time.
problem Testing model calibration from samples efficiently.
method Reformulated as minimum-cost flow, solved with dynamic programming.
result Optimal testing problem solved in nearly-linear time.
This paper provides formulas for minimum cost super-hedging in a multi-asset binomial market.
problem Finding minimum cost super-hedging strategies in a multi-asset, incomplete market model.
method Explicit formulas for minimum cost super-hedging strategies for various European type multi-asset contingent claims.
result Explicit formulas for non-negative local residuals of super-hedging strategies.
A new scheme reduces global search cost by a square root factor.
problem Challenges in finding global minimum of cost functions.
method Gradient descent combined with a biased crossover of two good solutions.
result Quadratic speedup of global search efficiency.
Study shows unusual non-monotonic risk behavior in minimum-norm interpolants for various data scaling.
problem Understanding the risk behavior of minimum-norm interpolants in RKHS for different data scaling.
method Analysis of spectral properties of the random kernel matrix restricted to eigen-spaces of the population covariance operator.
result Minimum-norm interpolants in RKHS exhibit multiple descent in risk for d = n α d = n^α d = n α with α ∈ ( 0 , 1 ) α\in(0,1) α ∈ ( 0 , 1 ) . This study explains gradient flow dynamics in neural networks for small initialisation.
problem Understanding the training dynamics of neural networks for small initialisation.
method Analysis of gradient flow dynamics for one-hidden layer ReLU networks with orthogonal inputs.
result Gradient flow converges to zero loss and characterizes implicit bias towards minimum variation norm.
The paper uses optimal transport to find the minimum loss in adversarial classification.
problem Understanding the robustness of machine learning classifiers to adversarial attacks.
method Optimal transport to characterize minimum possible loss in adversarial classification scenarios.
result The minimum transportation cost between class distributions provides a lower bound on classification performance.
Improved portfolio optimization method yields better risk-adjusted returns.
problem Optimizing global minimum variance portfolios with reduced risk.
method k-fold boosted k − k- k − BAHC covariance cleaning procedure for correlation matrices. result Our method outperforms other filtering methods in Sharpe ratios, despite higher turnover.
New insights into matrix factorization show strict saddles have bounded eigenvalues.
problem Understanding the nature of critical points in matrix factorization.
method Analyzing orbits of critical points under the general linear group and identifying canonical points.
result Minimum eigenvalue of strict saddles is not uniformly bounded below zero.
Cost-sensitive learning improves predictive maintenance by reducing costs.
problem Predictive maintenance models often lead to higher costs than expected.
method Propose selecting models based on economic costs rather than traditional metrics.
result Cost reduction and fault-tolerant policies achieved through cost-sensitive learning.
Using transfer entropy, we observed the strength and direction of information flow between stock indices. We uncovered that the biggest source of information flow is America. In contrast, the Asia/Pacific region the biggest is receives the most information. According to the minimum spanning tree, the GSPC is located at…
Study rigidity of Hamiltonians near a minimum in symplectic and magnetic settings.
problem Rigidity of Hamiltonians near a minimum in symplectic and magnetic settings.
method Analyzing Hamiltonian systems near a compact symplectic Morse-Bott minimum, focusing on Zoll flows and magnetic forms.
result A constant curvature quantity characterizes complex space forms among Kähler manifolds.
New proof of energy functional monotonicity via geodesics in measure space.
problem Proving monotonicity of energy functional in generalized Ricci flow.
method Defining adapted cost functional, geodesics, and entropy functional.
result Monotonicity of cost along backwards heat flow and energy functional along generalized Ricci flow.
New algorithm reduces regret in stochastic shortest path problems.
problem Planning and control in environments with unknown dynamics and variable episode lengths.
method Developed an algorithm with a new regret bound of O ( B ⋆ ∣ S ∣ ∣ A ∣ K ) O(B_\star |S| \sqrt{|A| K}) O ( B ⋆ ∣ S ∣ ∣ A ∣ K ) . result Guaranteed a significant reduction in regret compared to previous methods.
In this paper, we mainly study the mean curvature flow in Kähler surfaces with positive holomorphic sectional curvatures. We prove that if the ratio of the maximum and the minimum of the holomorphic sectional curvatures is less than 2, then there exists a positive constant δ δ δ depending on the ratio such that $\cosα\ge…
We present an approach to market-consistent multi-period valuation of insurance liability cash flows based on a two-stage valuation procedure. First, a portfolio of traded financial instrument aimed at replicating the liability cash flow is fixed. Then the residual cash flow is managed by repeated one-period replicatio…
The study examines how shallow neural nets converge to training samples or manifold points during diffusion.
problem Understanding when and how shallow neural nets converge to training samples or manifold points during diffusion.
method Analysis of shallow ReLU neural network denoisers trained with minimal ℓ 2 \ell^2 ℓ 2 norm, comparing score flow and diffusion flow. result Probability flow converges to training points, sums of training points, or manifold points, depending on the diffusion time scheduler.
Study weak super Ricci flow through neckpinch in metric measure spaces.
problem Understanding Ricci flow behavior at singularities.
method Introduce weak super Ricci flow and show conditions for continuation.
result Weak super Ricci flow properties at singularities.
The paper constructs minimizers for deep learning networks and analyzes their geometric structure.
problem Underparametrized deep learning networks and their minimizers.
method Direct construction of minimizers without gradient descent, considering specific settings.
result Explicit family of minimizers for the global minimum and a set of degenerate local minima.
New method uses parallel Monte Carlo for nonconvex optimization without gradients.
problem Optimizing complex functions with many components.
method Parallel sequential Monte Carlo for zeroth-order optimization.
result Converges to global minimum of cost function almost surely.
Deep linear networks can closely approximate interpolants without improving risk.
problem Understanding the risk bounds of deep linear networks compared to minimum ℓ 2 \ell_2 ℓ 2 -norm solutions. method Bounding excess risk of interpolating deep linear networks trained using gradient flow.
result Deep linear networks can closely approximate or match minimum ℓ 2 \ell_2 ℓ 2 -norm solutions in terms of risk. Study shows mean field games can have multiple solutions under certain conditions.
problem Analysis of mean field games with anti-monotone running costs.
method Examined an N + 1 N+1 N + 1 -player game and mean field game with state space {0,1}, considering a minimum jumping rate. result Mean field game equation may have multiple solutions if a specific condition is met.
Gradient flow converges to a minimal convex structure.
problem Finding the minimal convex structure in hyperbolic manifolds.
method Weil-Petersson gradient vector field of renormalized volume.
result The flow converges to the structure with minimum convex core volume.
A new method for optimal transport using neural ODEs that preserves marginal constraints.
problem Optimal transport between two continuous distributions with specific cost functions.
method Iterative construction of neural ODEs to minimize transport cost while preserving marginal constraints.
result Monotonic interior approach that decreases transport cost efficiently.
Regulations impose idiosyncratic capital and funding costs for holding derivatives. Capital requirements are costly because derivatives desks are risky businesses; funding is costly in part because regulations increase the minimum funding tenor. Idiosyncratic costs mean no single measure makes derivatives martingales f…
Optimal student loan repayment strategies vary based on loan size.
problem Finding the most cost-effective repayment strategy for federal student loans.
method Analyzing the impact of different repayment strategies on total cost for varying loan sizes.
result Optimal repayment strategies depend on the loan balance, with different approaches for small, large, and intermediate balances.
Paper studies fundamental limits of communication in distributed learning.
problem Communication efficiency in model aggregation for distributed learning.
method Rate-Distortion approach to model aggregation as a vector Gaussian CEO problem.
result Derives rate region bound and sum-rate-distortion function for model aggregation.
FMOPF generates diverse near-optimal power flow solutions.
problem Generating diverse near-optimal power flow solutions for risk quantification.
method Decouples compression from generation through latent flow matching and explicitly models load-state coupling.
result FMOPF provides the most effective Newton-Raphson warm starts and lowest tail risk.
Enhances generative models by improving expressivity without high computational cost.
problem Improving expressivity in generative models without increasing computational complexity.
method Proposes a new family of generative flows on an augmented data space, proving they can approximate a Hamiltonian ODE as a universal transport map.
result Demonstrates state-of-the-art performance on flow-based generative modeling benchmarks.
The article analyzes the stability of a curve shortening flow for planar networks.
problem Stability analysis of anisotropic curve shortening flow for planar networks.
method Used Lojasiewicz-Simon gradient inequality to derive stability results.
result For initial data close to an energy minimizer, the flow exists globally and converges to a different energy minimum.
Paper proposes quantum methods for optimizing machine learning functions.
problem Machine learning optimization problem
method Average approach and Partial Swap Test Cut-off method (PSTC)
result Potential to improve PSTC to O ( ∣ Θ ∣ ⋅ s u b l i n e a r N ) O(\sqrt{|Θ|} \cdot sublinear \ N) O ( ∣Θ∣ ⋅ s u b l in e a r N ) Analyzes how order flow affects price formation in financial markets.
problem Understanding how prices are formed by order flow in financial markets.
method Critical discussion of modeling approaches and empirical observations, focusing on market impact and transaction costs.
result Algorithmic trading impacts the quality and cost of trading.
New method improves MMD estimation without convexity assumptions.
problem Lack of theoretical guarantees for MMD estimation algorithms.
method Preconditioned gradient descent (PGD) scheme for MMD optimization.
result PGD scheme converges globally under specific conditions.