FDR criterion simplifies complex causal graphs to a standard front-door setting.
problem Complex causal graphs make identification of causal effects difficult and computationally infeasible.
method Front-door reducibility (FDR) criterion and FDR-TID algorithm.
result Many graphs can be simplified to a standard front-door setting, making causal effect identification simpler and more interpretable.
New methods estimate causal effects using front-door criterion in presence of unmeasured confounders.
problem Estimating causal effects in observational studies with unmeasured confounders.
method Developed novel one-step and targeted minimum loss-based estimators for front-door assumptions.
result Established conditions for root-n consistency and asymptotic linearity.
New method estimates causal effects without knowing graph structure.
problem Estimating causal effects when graph structure is unknown.
method Testable conditional independence statements for front-door adjustment.
result Effect estimation without Markov equivalence class knowledge.
Extends causal inference to hidden mediators with proxies.
problem Identifying causal effects with hidden mediators and error-prone proxies.
method Established causal hidden mediation analysis and hidden front-door criterion.
result Identification of population intervention indirect effect possible with hidden mediators.
Debiased learners estimate heterogeneous treatment effects in observational studies.
problem Estimating heterogeneous treatment effects in observational studies with unmeasured confounders.
method Debiased Front-Door (FD) learners, FD-DR-Learner and FD-R-Learner, under specific assumptions.
result Debiased learners satisfy error bounds and stage-error decompositions, delivering reliable HTE estimates.
Unified framework for estimating indirect effects in observational studies with unmeasured confounding.
problem Challenges in evaluating indirect effects due to unmeasured confounding and unethical exposures.
method Developed a unified identification and estimation framework using proximal causal inference.
result Unified identification and estimation of PIIE and causal effect of an intervening variable in settings with pervasive unmeasured confounding.
New estimators for causal effects in DAGs with hidden variables, addressing computational and statistical challenges.
problem Estimating causal effects in DAGs with hidden variables beyond traditional criteria.
method Introduces novel one-step corrected plug-in and targeted minimum loss-based estimators for causal effects in DAGs with hidden variables.
result Root-n consistent causal effect estimates with desirable statistical properties.
Adaptive algorithm reduces regret in causal bandits.
problem Minimize regret in causal bandits with unknown d-separators.
method Adaptive algorithm exploiting d-separators without prior knowledge.
result Significantly smaller regret than previous methods.
New method verifies formulas for causal interventional distributions.
problem Deciding if a given formula correctly identifies an interventional distribution.
method Proposed a falsifier to check if a formula is identifying.
result Falsifier can induce an almost-surely correct verifier for certain models.
Study tackles causal structure learning in linear models with unobserved variables and measurement error.
problem Challenges of unobserved common causes and measurement error in causal structure learning.
method Introduces LV-SEM-ME model with four types of variables and characterizes identifiability under separability condition.
result Establishes form of identification robustness for target effect in broader LV-SEM-ME model.
A new causal graph framework identifies treatment effects without adjusting for confounders.
problem Invalid identification of causal effects due to unmeasured confounders.
method Developed the Napkin graph to identify causal effects through a ratio of g-formulas, using influence-function-based estimators.
result Demonstrated substantial efficiency gains in estimating causal effects using the Napkin graph.
New methods for estimating causal effects in hidden variable DAGs.
problem Estimating causal effects in models with hidden variables.
method Influence function based estimators for causal effects in hidden variable DAGs.
result Achieves semiparametric efficiency bounds for identifiable effects.
PESCAL uses mediators to learn from confounded offline data.
problem Learning from confounded observational data in reinforcement learning.
method PESCAL uses mediator variables and the pessimistic principle to address confounding bias and distributional shift.
result It is sufficient to learn a lower bound of the mediator distribution function to mitigate distributional shift.
Estimates long-term effects from short-term experiments and observational data with unobserved confounders.
problem Estimating long-term causal effects from short-term experiments and long-term observational data with unobserved confounding.
method Combining regression residuals with short-term experimental outcomes to create an instrumental variable for estimating long-term causal effects.
result The estimator is unbiased and its variance is analytically studied.
Temporal Causal Prior-Data Fitted Networks (TCPFN) for industrial time series causal discovery
problem Estimating causal effects in industrial time series
method Temporal Causal Prior-Data Fitted Networks
result Zero-shot causal discovery with explicit reliability signals
In this paper, we study a class of Finsler metrics which contains the class of P-reducible metrics. Finsler metrics in this class are called generalized P-reducible metrics. We consider generalized P-reducible metrics with scalar flag curvature and find a condition under which these metrics reduce to C-reducible metric…
We introduce the notion of directed diagrammatic reducibility which is a relative version of diagrammatic reducibility. Directed diagrammatic reducibility has strong group theoretic and topological consequences. A multi-relator version of the Freiheitssatz in the presence of directed diagrammatic reducibility is given.…
Reduces weak reducing pairs to spheres in 3-sphere Heegaard surfaces.
problem Finding reducing spheres for weak reducing pairs in Heegaard surfaces.
method Proves existence of reducing spheres for weak reducing pairs in 3-sphere Heegaard surfaces.
result Reduction of weak reducing pairs to spheres if genus is at most 3.
In this paper, we study one of the open problems in Finsler geometry which presented by Matsumoto-Shimada about the existence of P-reducible metric which is not C-reducible. For this aim, we study a class of Finsler metrics called generalized P-reducible metrics that contains the class of P-reducible metrics. We prove …
Reduces connectivity problem for genus-4 Heegaard surface in 3-sphere.
problem Connectivity problem in reducing sphere complex for genus-4 Heegaard surface.
method Presented a sufficient condition for a non-separating weak reducing pair to be separated by a reducing sphere.
result Reduced connectivity problem to showing disjointness of representative reducing spheres from a fixed disk.
This paper studies properties of weak reducing pairs in critical Heegaard splittings.
problem Characterize weak reducing pairs in critical Heegaard splittings.
method Analyze the properties of weak reducing pairs in critical Heegaard splittings.
result Provide a necessary condition for a Heegaard surface to be critical.
Study on reducing surgeries on knots, developing thickness and genus bounds.
problem Understanding reducible surgeries on knots in S3. method Developed thickness bounds for L-space knots and lower bounds on slice genus; used d-invariants and mapping cone formula from Heegaard Floer homology. result Provided new upper bounds on reducing slopes for fibered, hyperbolic slice knots and on multiple reducing slopes for slice knots; verified the Cabling Conjecture for thin knots.
Proves curvature bounds for close to 1 Perelman's reduced volume.
problem Curvature bounds for Ricci flow with close to 1 reduced volume.
method ε-regularity theorem for Perelman's reduced volume.
result Curvature radius cannot be too small if reduced volume is close to 1.
The paper provides examples of keen weakly reducible bridge spheres for links in b-bridge position.
problem Characterizing and finding examples of keen weakly reducible bridge spheres.
method Analyzing bridge spheres and their properties in terms of compressing disks and width complex.
result Infinitely many examples of keen weakly reducible bridge spheres for links in b-bridge position.
Study on equivariant Heegaard genus of reducible 3-manifolds with group actions.
problem Understanding the equivariant Heegaard genus of reducible 3-manifolds with group actions.
method Thin position theory for 3-dimensional orbifolds to establish bounds on equivariant Heegaard genus.
result Sharp bounds on equivariant Heegaard genus of reducible manifolds, similar to tunnel number results.
Algorithm constructs reducing spheres for genus-2 Heegaard splitting of S^3.
problem Finite generation of Goeritz group G2. method Algorithm to construct reducing spheres from a standard reducing sphere.
result Alternate proof of finite generation of G2. The paper shows how reducible complexes affect local indicability.
problem The local indicability of subcomplexes in reducible complexes.
method Characterization of diagrammatic reducibility and application to local indicability.
result Injective labeled oriented trees are locally indicable if reducible of degree 2.
Killing tensors on reducible spaces are reducible, except for special cases.
problem Characterizing Killing tensors on reducible spaces.
method Analyzing Killing tensors on product manifolds and their lifts.
result Killing tensors on product manifolds are reducible, except for specific cases.
In this paper, we first introduce the weighted forward reduced volume of Ricci flow. The weighted forward reduced volume, which related to expanders of Ricci flow, is well-defined on noncompact manifolds and monotone non-increasing under Ricci flow. Moreover, we show that, just the same as the Perelman's reduced volume…
New proof of a 111-year-old result using gauge theory.
problem Proving configurations in the list of unavoidable configurations are reducible.
method Filtered 3- and 4-color homology, gauge theory, state-reducibility.
result Birkhoff diamond is reducible using gauge theory.
Characterizes Anosov reducible representations in terms of eigenvalues.
problem Understanding Anosov representations in reducible settings.
method Characterizes Anosov representations using eigenvalue magnitudes of irreducible block factors.
result Connected components of character varieties do not contain reducible representations for many non-elementary hyperbolic groups.
The scalability of submodular optimization methods is critical for their usability in practice. In this paper, we study the reducibility of submodular functions, a property that enables us to reduce the solution space of submodular optimization problems without performance loss. We introduce the concept of reducibility…
Study Anosov representations of reducible suspensions of hyperbolic groups.
problem Characterize dynamical properties of reducible suspensions of Anosov representations.
method Analyzing linear representations of non-elementary hyperbolic groups, focusing on weak unipotent actions on subspaces.
result Characterize when reducible suspensions are discrete and faithful, quasi-isometrically embedded, and Anosov.
A new proof shows a reducing sphere can be obtained from a given sphere without surgeries.
problem Finding a reducing sphere in a 3-manifold.
method Using a sequence of 1-surgeries, show a reducing sphere can be obtained without surgeries.
result A reducing sphere can be obtained from a given sphere without surgeries.
The standard taxonomy of predictive uncertainty is inconsistent with standard measures.
problem Uncertainty taxonomy and measure inconsistency
method Proof of inconsistency
result Uncertainty is not reducible to data collection
This paper studies nonholonomic constraints in Hamiltonian systems, deriving equations and theorems.
problem Analyzing nonholonomic constraints in Hamiltonian systems.
method Deriving distributional RCH systems, geometric constraint conditions, and Hamilton-Jacobi theorems.
result Derives precise geometric constraint conditions and Hamilton-Jacobi theorems for nonholonomic systems.
In this paper, we use Heegaard Floer homology to study reducible surgeries. In particular, suppose K is a non-cable knot in the three-sphere with an L-space surgery. If p-surgery on K is reducible, we show that p equals 2g(K)-1. This implies that any knot with an L-space surgery has at most one reducible surgery, a fac…
We consider a quotient space of the Bers boundary of Teichmüller space, which we call the reduced Bers boundary, by collapsing each quasi-conformal deformation space into a point. This reduced Bers boundary turns out to be independent of the basepoint, and the action of the mapping class group on the Teichmüller space …
We show that any nontrivial reduced knot projection can be obtained from a trefoil projection by a finite sequence of half-twisted splice operations and their inverses such that the result of each step in the sequence is reduced.
Study projective derivative cocycles for circle diffeomorphisms.
problem Understanding reducibility and almost reducibility in circle diffeomorphisms.
method Computing precise expressions for projective derivative cocycles and extending to 3-torus.
result Generalization of results to diagonal action on 3-torus.
Paper develops reduction theory for controlled Lagrangian systems with symmetry and momentum map.
problem Reduction of controlled Lagrangian systems with symmetry and momentum map.
method Using Legendre transformation and Euler-Lagrange vector field, the paper extends symmetric reduction theory.
result Established regular reduction theory for RCL systems with symmetry and momentum map.
New method reduces density estimation variance for multivariate data.
problem Efficient multivariate density estimation with reduced dimensionality.
method Variance-Reduced Sketching (VRS) framework for multivariate density estimation.
result VRS framework significantly improves density estimation over existing methods.
We prove that the first reduced cohomology with values in a mixing Lp-representation, p larger than 1, vanishes for a class of amenable groups including connected amenable Lie groups. In particular this solves for this class of amenable groups a conjecture of Gromov saying that every finitely generated amenable group h…
The main purpose of this paper is to present a number of analytic and geometric properties of the l-function and the reduced volume of Perelman, including in particular the monotonicity, the upper bound and the rigidities of the reduced volume.
Study 4D steady gradient Ricci solitons reducing to 3D manifolds.
problem Understanding 4D steady gradient Ricci solitons that reduce to 3D.
method Analyzing asymptotic geometry and curvature properties.
result 4D solitons either reduce to spherical space forms or the 3D Bryant soliton.
Paper uses autoencoders for efficient reduced-order modeling of eigenvalue problems.
problem Efficiently modeling eigenvalue problems in high dimensions.
method Autoencoder-based reduced-order modeling for eigenvalue problems.
result Autoencoder-based models outperform standard POD-Galerkin methods in neutron diffusion applications.
Classification extended for reducible symmetric spaces.
problem Classifying homogeneous foliations on symmetric spaces.
method Extended classification from irreducible to reducible symmetric spaces.
result Classification completed for all noncompact symmetric spaces.
If a simple 3-manifold M admits a reducible and a toroidal Dehn filling, the distance between the filling slopes is known to be bounded by three. In this paper, we classify all manifolds which admit a reducible Dehn filling and a toroidal Dehn filling with distance 3.