Bayesian nonparametric method estimates individualized treatment-response curves from observational data.
problem Estimating individualized treatment-response curves from observational time series data.
method Developed a Bayesian nonparametric method using the G-computation formula.
result BNP method provides more accurate estimates of treatment responses than alternative approaches.
G-Net uses deep learning for complex counterfactual outcome prediction.
problem Estimating counterfactual outcomes under dynamic treatment strategies.
method G-Net is a sequential deep learning framework for G-computation.
result G-Net can handle complex temporal data and provide accurate treatment effects.
Prognostic scores improve logistic regression analysis in RCTs with binary outcomes.
problem Non-collapsibility in logistic regression analysis of RCTs with binary endpoints.
method Prognostic score adjustment using AI predictions to address non-collapsibility.
result Prognostic score adjustment increases power or reduces sample size for estimating conditional odds ratios.
G-computation improves clinical trial power with machine learning.
problem Balancing prognostic factors in randomized trials to prevent near-confounders.
method G-computation with penalized models (Lasso, Elasticnet) and algorithm-based methods (neural network, SVM, super learner).
result G-computation with Elasticnet and splines reduces variance and increases power in RCTs.
Bayesian method corrects timing misalignment in recurrent event studies.
problem Estimating differences in event rates under two treatments with timing misalignment.
method g-computation procedure with joint semiparametric Bayesian model.
result Correctly estimates average causal effects under right-censoring.
Estimates causal effects from patient trajectories using DeepACE model.
problem Estimating causal effects from observational data in medical practice.
method DeepACE model using iterative G-computation formula and sequential targeting procedure.
result DeepACE achieves state-of-the-art performance in estimating time-varying ACEs.
Proposes an efficient algorithm for identifying important features in binary classification.
problem Understanding explainability of deep neural networks in binary classification.
method Variable-importance framework combined with lazy training.
result Achieves well-controlled error rates with minimal assumptions.
Improves deep RL for partially observable environments.
problem Handling partially observable environments in deep RL.
method Action-specific Deep Recurrent Q-Network (ADRQN) architecture.
result Demonstrates effectiveness in partially observable domains.
This paper introduces an efficient method for optimizing deep learning hyperparameters.
problem The high dependency of deep learning algorithms on hyper-parameters.
method Orthogonal Array Tuning Method (OATM) for deep learning hyper-parameter tuning.
result The proposed OATM method significantly saves tuning time compared to state-of-the-art methods.
A novel bandit problem with delayed arms, showing optimal strategies and lower bounds.
problem Optimizing reward in a stochastic multi-armed bandit setting with delayed arms.
method Mapping to PINWHEEL scheduling problem, simple greedy algorithm, UCB based algorithm, lower bounds.
result Simple greedy algorithm is asymptotically ( 1 − 1 / e ) (1-1/e) ( 1 − 1/ e ) optimal and UCB based algorithm has c log T + o ( log T ) c \log T + o(\log T) c log T + o ( log T ) cumulative regret. WU-UCT parallelizes MCTS with linear speedup and limited performance loss.
problem Challenges in parallelizing Monte Carlo Tree Search (MCTS) due to its sequential nature.
method Introduces unobserved samples to track incomplete simulations and modify UCT tree policy.
result Achieves linear speedup and only limited performance loss with increasing parallel workers.
Unified framework estimates desirability of outcome ranking for benefit-risk evaluation.
problem Estimating desirability of outcome ranking in randomized and observational studies.
method Unified covariate-adjusted causal inference framework, estimating conditional ordinal distributions through sequential risk-set hazards, and deriving efficient influence function (EIF).
result CVTMLE-SL showed strongest performance across various settings.
New method uses SMC for Bayesian MABs with time-varying, nonlinear rewards.
problem Learning optimal actions in dynamic, non-stationary environments.
method Sequential Monte Carlo (SMC) for estimating statistics of unknown reward distributions.
result SMC-based Bayesian MAB policies achieve good regret performance in non-stationary, nonlinear reward scenarios.
Proposes a method to handle missing inputs in Bayesian optimization.
problem Missing values in historical data and function evaluations.
method Impute missing values using probability distributions and develop a new acquisition function.
result Improves performance of Bayesian optimization by handling missing inputs effectively.
New estimators improve causal inference in machine learning studies.
problem Improving causal inference in machine learning models.
method Doubly-robust cross-fit estimators for average causal effect.
result Doubly-robust cross-fit estimators outperform other methods in simulations.
AFS uses attention to select features efficiently.
problem Efficiently selecting features from high-dimensional data.
method AFS combines an attention module and a learning module to address feature selection challenges.
result AFS outperforms state-of-the-art feature selection algorithms in accuracy and stability.
FLANs process each feature separately for better interpretability.
problem Need for interpretable machine learning models in critical scenarios.
method Feature-wise latent representations summed for prediction.
result FLANs enhance interpretability without sacrificing performance.
Bayesian model estimates ACT impact on pediatric AML survival.
problem Estimating ACT impact on survival in AML patients with treatment timing issues.
method Generative Bayesian semi-parametric model with Gamma Process priors.
result Posterior inference for ACT efficacy under dynamic rules.
A new FFT-based method for fast rigid alignment of 2D closed curves.
problem Rigid alignment of 2D closed curves with application to shape analysis.
method FFT-based algorithm for optimal rigid alignment of closed curves with O(N log N) complexity.
result Order of magnitude speed-up in curve alignment compared to previous methods.
End-to-end CAD system for thyroid nodule classification using multimodal data and expert guidance.
problem Improving accuracy in thyroid nodule classification for clinicians.
method Knowledge-driven DenseNet framework using multimodal ultrasound data and expert cues.
result The proposed system achieves relevant performances in thyroid nodule classification.
Bayesian model for cost-effectiveness analysis with subgroup discovery.
problem Statistical challenges in cost-effectiveness analysis, especially with non-random treatment assignment and censored data.
method Developed a nonparametric Bayesian model using Dirichlet and Gamma processes to estimate cost-survival distributions and identify cost-effectiveness subgroups.
result Identified and estimated policy-relevant causal CEA estimands using a Bayesian nonparametric g-computation procedure.
The study evaluates and tests k k k -NN models in various applications.
problem The relation between parameters and accuracy of k k k -NN models is not well understood. method Developed a randomized algorithm to test the k k k -NN property with a complexity of O ( n k 2 / ε 2 ) O(\sqrt{n} k^2 / ε^2) O ( n k 2 / ε 2 ) . result The algorithm can detect k k k -NN models with bad accuracy in significantly less time than building the model. New algorithms solve DR-submodular maximization with faster convergence.
problem Maximizing monotone DR-submodular functions under convex constraints.
method Introduced strongly DR-submodular functions and proposed SDRFW and PGA algorithms.
result SDRFW achieves optimal approximation ratio after fewer iterations.
We use flip points to explain and audit deep learning models, revealing decision boundaries and improving model performance.
problem Lack of interpretability in deep learning models hinders their use in important applications.
method Flip points are used to analyze decision boundaries of deep learning models with continuous output scores.
result Flip points reveal the least changes in input that would alter a model's classification, enabling better understanding and improvement of model behavior.
Proves a general connected sum formula for families Seiberg-Witten invariants.
problem Limited connected sum formulae for families Seiberg-Witten theory.
method Develops a general connected sum formula incorporating previous results.
result Proves a new connected sum formula for Seiberg-Witten families.
Derives an integral formula for G2-structures.
problem Calculating properties of G2-structures.
method Applies an integral formula for G-structures to G2.
result Derives an integral formula relating curvatures and quadratic invariants.
Derives integral formulae on weighted manifolds.
problem No specific problem stated; focuses on mathematical derivations.
method Introduces weighted mean sigma-r curvature and uses weighted Newton transformations.
result Derives integral formulae generalizing previous work.
Paper proves a fixed point formula and applies it to a new proof of Harish-Chandra's character formula.
problem Proving a fixed point formula for equivariant indices of elliptic differential operators.
method Fixed point formula for proper actions by connected semisimple Lie groups on manifolds.
result New proof of Harish-Chandra's character formula for discrete series representations.
Unified formula for surfaces in Euclidean or Lorentzian 3-space.
problem Describe surfaces in Euclidean or Lorentzian 3-space.
method Unified Kenmotsu-type formula for surfaces in Euclidean or Lorentzian 3-space.
result Unified single equation for Kenmotsu-type formulas in Euclidean and Lorentzian 3-space.
Two tropical gluing formulas help calculate Gromov-Witten invariants.
problem Calculating Gromov-Witten invariants of symplectic manifolds.
method Tropical geometry applied to exploded manifolds.
result Generalizes existing formulas for Gromov-Witten invariants.
Paper derives trace formula for magnetic Laplacian at zero energy.
problem Trace formula for magnetic Laplacian at zero energy.
method Generalizes Gutzwiller trace formula, focuses on zero energy level.
result Derives trace formula at zero energy level.
The Gauss formula is extended to various Laplacians on submanifolds.
problem Deriving formulas for Laplacians on submanifolds.
method Extending the Gauss formula to different types of Laplacians.
result Formulas for various Laplacians on submanifolds.
The paper is devoted to the problem of finding explicit combinatorial formulae for the Pontryagin classes. We discuss two formulae, the classical Gabrielov-Gelfand-Losik formula based on investigation of configuration spaces and the local combinatorial formula obtained by the author in 2004. The latter formula is based…
Note on new cancellation formulas for manifolds.
problem Generalizing anomaly cancellation formulas to manifolds.
method Proving new (a, b) type cancellation formulas and using transgression.
result Obtained characteristic forms with modularity properties.
The study identifies types of manifolds using variational formulas and integral-differential formulas.
problem Identifying specific types of manifolds based on curvature properties.
method Established variational formulas for Ricci curvature bounds and used them to identify manifolds.
result Constant curvature, Einstein, and Ricci parallel manifolds identified with specific formulas.
The main result of the present paper is a coincidence formula for foliated manifolds. To prove this we establish Kuenneth formula, Poincare duality and intersection product in the context of tangential de Rham cohomology and homology of tangential currents. We apply the formula to get a dynamical Lefschetz formula for …
Formula calculates volume of two-bridge knots.
problem Calculating the volume of two-bridge knots.
method Derived from Hopf formula and Fox derivatives.
result Closed formula for the volume of two-bridge knots.
Formula connects surgeries to Seiberg-Witten invariants.
problem Understanding how surgeries affect Seiberg-Witten invariants.
method Proves surgery formulas for Seiberg-Witten invariants and families.
result Expresses new invariants in terms of original ones.
It has been shown that the Alvarez-Gaum e ˊ \mathrm{\acute{e}} e ˊ -Witten miraculous anomaly cancellation formula in type IIB superstring theory and its various generalizations can be derived from modularity of certain characteristic forms. In this paper, we show that the Green-Schwarz formula and the Schwarz-Witten formula i…
Introduces a universal Bochner formula for scalar curvature.
problem None explicitly stated; focuses on a new formula.
method Introduces a universal Bochner formula.
result Contains special cases like stability inequality and Schrödinger-Lichnerowicz-type formula.
Extension formulae on almost complex manifolds studied with applications.
problem Understanding almost complex manifolds through extension formulae.
method Provided extension formulae and decompositions for almost complex manifolds.
result Studied ( n , 0 ) (n,0) ( n , 0 ) -forms, ( n , 0 ) (n,0) ( n , 0 ) -Dolbeault cohomology group, and ( n , q ) (n,q) ( n , q ) -forms. Formula calculates Gromov-Witten invariants for triple products.
problem Calculating Gromov-Witten invariants for complex geometrical structures.
method Developed a gluing formula for Gromov-Witten invariants in a triple product.
result Simplified gluing formula for easy explanation.
Calculates volumes of specific cone-manifolds using Schläfli formula.
problem Calculating volumes of specific cone-manifolds.
method Using Schläfli formula.
result Volume of the 7 3 2 7_3^2 7 3 2 link cone-manifolds and its cyclic coverings. Proves a formula for a special invariant of 4-manifolds.
problem Calculating the Bauer-Furuta invariant for connected sums of 4-manifolds.
method Uses a finite dimensional approximation of the Seiberg-Witten monopole map to derive a formula for the families Bauer-Furuta invariant of a fibrewise connected sum.
result Derives a general connected sum formula for the families Bauer-Furuta invariant.
Corrected McLean's formulas for special submanifolds.
problem Incorrect formulas for calibrated submanifolds in exceptional geometries.
method Unified treatment using calibration method and Harvey-Lawson's identities.
result Corrected formulas for associative and Cayley submanifolds.
Proves a special case of the Gaussian kinematic formula using large sphere limits.
problem Proving a special case of the Gaussian kinematic formula.
method Viewing the GKF as the limit of spherical kinematic formulas for large dimension spheres.
result Proves a special case of the Gaussian kinematic formula.
New Crofton formulae derived from existing ones.
problem Generalizing Crofton formulae for products.
method Calculations in the ring of normal densities.
result Generalizations of Crofton formulae in terms of mixed Riemannian volume.
Formulae for non-symmetric connections derived from covariant derivatives.
problem Deriving commutation formulae for non-symmetric affine connections.
method Covariant derivatives of tensors with respect to symmetric and non-symmetric affine connections.
result Formulae for non-symmetric connections derived from covariant derivatives.