New algorithm solves complex medical radiation therapy problems.
problem Optimizing radiation therapy treatment plans.
method Majorization-minimization principle applied to non-linear split feasibility problems.
result Euclidean norm in proximity function replaced by Bregman divergences.
We adapt the Douglas-Rachford (DR) splitting method to solve nonconvex feasibility problems by studying this method for a class of nonconvex optimization problem. While the convergence properties of the method for convex problems have been well studied, far less is known in the nonconvex setting. In this paper, for the…
MaxRR efficiently unlearns models by splitting and selecting core samples.
problem Efficiently unlearning models while verifying unlearning guarantees.
method Model splitting and core sample selection with a generalized unlearning metric.
result MaxRR achieves efficient unlearning with properties matching full retraining.
New method uses symmetric splitting for efficient HMC inference in large neural networks.
problem Efficient inference for Bayesian neural networks with large datasets.
method Introduces a symmetric integration scheme for Hamiltonian Monte Carlo (HMC) that does not rely on stochastic gradients.
result Symmetric splitting leads to more efficient HMC inference over large data sets.
New approach for distributed learning of Gaussian mixtures.
problem Large datasets distributed across different centers.
method Split-and-conquer approach with MM algorithm.
result New estimator is consistent and retains root-n consistency.
In modern scientific research, massive datasets with huge numbers of observations are frequently encountered. To facilitate the computational process, a divide-and-conquer scheme is often used for the analysis of big data. In such a strategy, a full dataset is first split into several manageable segments; the final out…
Paper models ultra-high dimensional data using Gaussian and vine copulas.
problem Modeling ultra-high dimensional non-Gaussian data.
method Divide-and-conquer approach: Gaussian methods for subsets, vine copulas for reconciled model.
result Feasibility and estimation in thousands of dimensions demonstrated.
New method selects best HTE estimator without ground-truth treatment effects.
problem Selecting best HTE estimator from multiple candidates.
method Cross-fitted, exponentially weighted test statistic with two-way sample splitting.
result Empirically, reliable error control and reduced false selections.
Spatio-temporal data is intrinsically high dimensional, so unsupervised modeling is only feasible if we can exploit structure in the process. When the dynamics are local in both space and time, this structure can be exploited by splitting the global field into many lower-dimensional "light cones". We review light cone …
This paper explains CART random forests using stochastic control theory.
problem Understanding the inner workings of CART random forests.
method Developed a stochastic-control perspective on CART random forests, interpreting feature subsampling as a random feasible action set and the split rule as a policy.
result Established that the CART policy is locally stabilizing but globally suboptimal for the forest objective.
Proposes a method to predict responses from covariates over time.
problem Predicting responses from covariates with changing conditional distributions over time.
method Invariant Subspace Decomposition (ISD) framework that splits the conditional distribution into time-invariant and time-dependent components.
result The decomposition can be used for zero-shot and time-adaptation prediction tasks.
Improved Bayesian learning for deep models using efficient integrators.
problem Scalable learning and inference in deep models with uncertainty.
method High-order stochastic gradient thermostats with an efficient symmetric splitting integrator.
result The proposed scheme improves general Bayesian posterior sampling, especially for deep models.
In this paper, we extend Meek's conjecture (Meek 1997) from directed and acyclic graphs to chain graphs, and prove that the extended conjecture is true. Specifically, we prove that if a chain graph H is an independence map of the independence model induced by another chain graph G, then (i) G can be transformed into H …
New method boosts GANs by creating new classes from clustering, improving sample quality.
problem Improving GAN sample quality with class information.
method Clustering representations learned by GAN to create new classes, enhancing conditional GANs.
result Generated samples reach state-of-the-art Inception scores for CIFAR-10 and STL-10 datasets.
Paper addresses feasibility of counterfactual explanations in ML models, especially for critical domains.
problem Feasibility of counterfactual examples in ML models, especially in healthcare and finance.
method Uses partial structural causal models and modified variational autoencoder loss to generate counterfactuals that satisfy feasibility constraints.
result Generated counterfactuals better satisfy feasibility constraints than existing methods.
New algorithm finds best feasible arm in grouped bandits.
problem Finding the best arm with all attributes above a threshold.
method Feasibility Constrained Successive Rejects (FCSR) algorithm.
result FCSR identifies the best feasible arm with optimal dependence on problem parameters.
Bayesian search optimizes exploration of feasible solutions under expensive constraints.
problem Identifying feasible solutions in computationally expensive constraint spaces.
method Bayesian models with an acquisition function for efficient exploration and exploitation.
result The proposed acquisition function improves the prediction of feasibility.
Develops a new framework for integrating satellite allocations in small portfolios.
problem Feasibility constraints in small portfolios, not return predictability, are the primary concerns.
method A four-layer feasibility framework: physical, economic, structural, and epistemic.
result Closed-form feasibility bounds on satellite size, turnover, and breadth without return forecasts.
AES learns feasible domains in unbounded spaces with bounded query budget.
problem Learning feasible domains in unbounded input spaces with limited query budget.
method Active Expansion Sampling (AES) progressively expands knowledge of the input space, switching between learning decision boundaries and searching for new feasible domains.
result AES has a misclassification loss guarantee within the explored region, independent of iterations or labeled samples.
Algorithm tackles large-scale portfolio optimization with higher moments, improving computational efficiency.
problem Optimizing portfolios with higher moments (variance, skewness, kurtosis) for large asset universes is computationally infeasible.
method Developed a structure-exploiting algorithm based on Yau's affine-normal descent, working directly with return matrix.
result Algorithm avoids explicit higher-order tensors and exploits quartic structure for efficient computation.
Enhances OTA FL algorithms by defining inverse feasibility for linear models.
problem Improving security and privacy in over-the-air federated learning.
method Defines inverse feasibility as an upper bound on condition number, analyzes existing model, proposes new model.
result Proposes a new OTA FL model with enhanced characteristics.
SFLS method finds feasible solutions faster with less data.
problem Efficiently solving SOECs with near-feasibility and near-optimality.
method SFLS method that emphasizes feasibility before convergence.
result SFLS maintains high-probability feasibility at each iteration.
New algorithm exploits curvature of feasible sets for fast online convex optimization.
problem Online convex optimization with fast rates.
method Adapting FTL algorithm to curvature of feasible sets.
result Achieves logarithmic regret bound of O(ρlogT) in stochastic environments. FACE generates actionable counterfactuals that are feasible and coherent with data.
problem Counterfactual explanations can be unachievable and offensive.
method FACE proposes a new approach to generate counterfactuals that are coherent with the data and feasible.
result FACE generates counterfactuals that are coherent with the data and feasible.
Comonotonic allocations are restored under certain constraints, improving risk-sharing.
problem Feasibility constraints can distort optimal risk-sharing allocations.
method Identified componentwise convex-order solidity as a sufficient condition to restore comonotonic allocations.
result Componentwise convex-order solidity ensures comonotonic improvements under feasible constraints.
Introduces CCR for constructing confidence regions from conformal predictions.
problem Challenges in constructing confidence regions for model parameters.
method Combines conformal prediction intervals for model outputs to establish confidence regions for parameters under minimal assumptions.
result Valid coverage guarantees for finite sample regime, applicable to various model types.
The paper studies SDP feasibility and sos ranks for specific polynomials.
problem Characterizing sos representations of nonnegative polynomials.
method Explicit SDP formulation based on Clifford systems.
result Quantitative rank bounds for sos representations, with rigidity.
Paper addresses quadratic feasibility problems and their sample complexity.
problem Recovering complex vectors from quadratic measurements.
method Analyzes conditions for identifiability and explores optimization landscape.
result Gradient algorithms can converge to globally optimal solutions with high probability.
Bayesian framework proves thresholds for multi-graph alignment feasibility.
problem Determining when multi-graph alignment is statistically possible.
method Developed a Bayesian estimation framework over metric spaces.
result Identified thresholds for Gaussian and sparse Erdős-Rényi models.
SnareNet adds repair layers to neural networks to ensure outputs meet physical constraints.
problem Unconstrained neural network predictions violate physical or safety requirements.
method SnareNet appends a differentiable repair layer that navigates constraints to produce feasible outputs.
result SnareNet consistently improves objective quality while satisfying constraints more reliably.
DFFL tackles federated learning with heterogeneous objectives and constraints.
problem Federated learning with clients having different objectives and feasible regions.
method Derived heterogeneity bounds for cost-vector distances and support-function/shape-distance terms. Lifted pointwise bounds to local-versus-federated excess-risk comparison.
result Federation is beneficial when the statistical advantage of pooling exceeds a client-specific heterogeneity penalty.
Novel algorithm improves feasibility classification of complex simulation outcomes.
problem Determining feasible regions in complex simulation environments with binary outcomes.
method Iterative exploration using machine learning techniques (kernel support vector machines, kernel ridge regression).
result Improves feasibility classification and guides exploration towards regions of interest.
Detecting correlated trees helps align sparse graphs.
problem Detecting correlation between trees for sparse random graphs.
method MPAlign message-passing algorithm for graph alignment.
result MPAlign succeeds in polynomial time for partial alignment.
Study tests feasibility of linear programs with bandit feedback.
problem Testing feasibility of unknown linear programs with bandit feedback.
method Developed a novel test based on low-regret algorithms and a nonasymptotic law of iterated logarithms.
result Proved that the test is reliable and adapts to the signal level, with mean sample costs scaling as \( \widetilde{O}(d^2/Γ^2) \).
Reinforcement learning solves VRP efficiently.
problem Optimizing vehicle routes for delivery problems.
method Training a single model with policy gradient to find near-optimal solutions.
result Outperforms classical heuristics and OR-Tools on VRP instances.
Paper defines conditions for feasible correlation matrices from factor structures.
problem Feasibility of option implied correlation matrices in non-FX markets.
method Quantitative and economic approaches to solve the nearest correlation matrix problem.
result Introduces methods to ensure feasible correlation matrices from factor structures.
Mathematical framework for transfer learning feasibility and transfer risk.
problem Theoretical analysis of transfer learning.
method Reformulated transfer learning as an optimization problem, introduced transfer risk concept.
result Demonstrated the potential and benefits of incorporating transfer risk in transfer learning evaluation.
Unified theory of ownership concentration, overlap, and dependence.
problem Understanding the complex layers of ownership concentration, overlap, and dependence in financial markets.
method Develops a unified quadratic framework for analyzing these layers and their interactions.
result Unified framework shows that the same residual operator measures static overlap and governs linearized market transmission.
SPlit optimizes dataset splitting for better model performance.
problem Improving model performance through optimal dataset splitting.
method Adapting Support Points (SP) algorithm for subsampling and categorical variables in a sequential nearest neighbor approach.
result SPlit significantly improves worst-case testing performance compared to random splitting.
New algorithms for convex optimization with many constraints using random projections and stochastic gradient descent.
problem Optimization problems with a large number of constraints.
method Stochastic gradient descent combined with random feasibility updates on randomly selected constraint subsets.
result The proposed algorithms converge almost surely and achieve efficient performance.
Proposes a recursive MPC scheme with probabilistic safety guarantees for uncertain dynamic systems.
problem Probabilistic safety guarantees for MPC in dynamic environments with unknown stochastic agents.
method Uses conformal prediction to derive high-confidence prediction regions and gradually relax safety constraints online.
result Ensures recursive feasibility of MPC schemes by relaxing safety constraints over time.
The paper extends keenness concept to bridge splittings and finds conditions for existence.
problem Extending keenness concept to bridge splittings and finding conditions for existence.
method Extending the concept of keenness to bridge splittings and proving existence conditions.
result Existence of strongly keen (g,b)-splitting of a link with distance n for certain integers g, b, and n. Non-split almost complex supermanifolds and non-split Riemannian supermanifolds are studied. The first obstacle for a splitting is parametrized by group orbits on an infinite dimensional vector space. Further it is shown that non-split structures appear in the first case as deformations of a split reduction and in the …
Study flippable Heegaard splittings in Seifert fibered spaces.
problem Identifying flippable Heegaard splittings in Seifert fibered spaces.
method Examining isotopies that interchange Heegaard splitting sides in Seifert fibered spaces.
result Characterized which Heegaard splittings are flippable in Seifert fibered spaces.
The study examines higher-order modern portfolio theory with complex critical points and feasible portfolio variety.
problem Understanding the complex critical points and feasible portfolio variety in higher-order modern portfolio theory.
method Established genericity conditions for utility functions with higher-order cumulants, analyzed discriminant loci, and determined the dimension and degree of the feasible portfolio variety.
result The utility function has a constant number of complex critical points under genericity conditions, and the feasible portfolio variety has a determined dimension and degree.
Learning feasibility is undecidable in PAC-learning.
problem Deciding the feasibility of learning a mapping between data and labels.
method Investigating the existence of a test for PAC-learnability.
result No test for PAC-learnability exists, showing undecidability.
The paper proves infinitely many non-isotopic splitting 3-spheres for split sphere links in 4D.
problem Proving the existence of infinitely many non-isotopic splitting 3-spheres for split sphere links in 4D.
method Establishing a general sufficient condition for infinitely many topologically non-isotopic splitting 3-spheres in connected sums of 4-manifolds.
result Proves infinitely many non-isotopic splitting 3-spheres for split sphere links in 4D.
Bound on splitting number in terms of four-genus of knots.
problem Understanding the relationship between splitting number and four-genus of knots.
method Provided a bound on the splitting number in terms of the four-genus of related knots.
result Bound on splitting number in terms of four-genus.