Study clarifies variance of stratification estimators for causal effects.
problem Estimating average causal effects with discrete covariates.
method Combines insights from potential outcomes, causal diagrams, and structural models.
result Derives expressions for the variance of stratification estimators.
We define transit clusters to simplify causal diagrams and preserve their essential properties.
problem Clustering variables in causal diagrams can alter essential properties of causal effects.
method We define transit clusters and provide an algorithm to find them, ensuring they preserve causal effect identifiability.
result Transit clusters simplify causal effect identification and maintain their essential properties.
Causal diagrams based on do intervention are useful tools to formalize, process and understand causal relationship among variables. However, the do intervention has controversial interpretation of causal questions for non-manipulable variables, and it also lacks the power to check the conditions related to counterfactu…
The paper develops methods to bound causal effects using Partial Ancestral Graphs.
problem Bounding causal effects from observational data when true causal diagrams are unknown.
method Proposes a method using Partial Ancestral Graphs to derive bounds on causal effects from observational data.
result Demonstrates the effectiveness of the method with synthetic and real data examples.
Efficient algorithms decide algebraic constraints of causal graphs.
problem Distinguish causal graphs with latent confounders.
method Study algebraic constraints and propose efficient algorithms.
result Decide equivalence or subset of algebraic constraints.
D2D converts CLDs into SDMs to explore leverage points under uncertainty.
problem Limited dynamic analysis of CLDs for intervention strategies.
method Minimal user input protocol to convert CLDs into SDMs, simulating interventions.
result D2D helps distinguish leverage points and provides uncertainty estimates.
Enhanced symplectic quandle colorings detect causal structure in spacetime diagrams.
problem Detecting causal structure in spacetime diagrams using polynomial invariants.
method Comparing symplectic quandle colorings of different diagrams representing spacetime connections.
result Enhanced symplectic quandle colorings consistently distinguish between causally unrelated and related spacetime configurations.
The causal assumptions, the study design and the data are the elements required for scientific inference in empirical research. The research is adequately communicated only if all of these elements and their relations are described precisely. Causal models with design describe the study design and the missing data mech…
Paper introduces v-CMC linking causality and utility.
problem Linking causality and utility for value theory.
method Developed a new causal independence principle (v-CMC) and proved its equivalence.
result Equivalence of local, global, and decomposition versions of v-CMC.
New method estimates causal effects in complex spaces using topological structures.
problem Challenges in estimating causal effects in non-Euclidean spaces.
method Developed a topological causal inference framework using power-weighted silhouette functions of persistence diagrams.
result Successfully quantifies topological treatment effects across various complex outcomes.
A new approach to rationalization identifies true rationales by considering causal relationships.
problem Existing rationalization methods struggle with spuriousness, where snippets with similar contributions are hard to distinguish.
method The method leverages causal inference to identify non-spurious rationales, defining probabilities of causation based on a structural causal model.
result The proposed causal rationalization outperforms existing methods on real-world datasets.
Classical supervised learning produces unreliable models when training and target distributions differ, with most existing solutions requiring samples from the target domain. We propose a proactive approach which learns a relationship in the training domain that will generalize to the target domain by incorporating pri…
Paper introduces md-vtrees for efficient probabilistic and causal inference.
problem Efficient inference in complex probabilistic models.
method Introduces md-vtrees to generalize tractability conditions for advanced inference queries.
result Derives first polytime algorithms for causal inference queries.
AR CI framework handles complex confounders and sequential actions.
problem Low-dimensional confounders and singleton actions in causal inference.
method Sequencification to transform data into sequences, enabling CI with complex confounders and sequential actions.
result AR model can estimate multiple causal quantities using a single model, simplifying inference and improving outcome prediction.
We consider the problem of structure learning for bow-free acyclic path diagrams (BAPs). BAPs can be viewed as a generalization of linear Gaussian DAG models that allow for certain hidden variables. We present a first method for this problem using a greedy score-based search algorithm. We also prove some necessary and …
Framework trains safe agents avoiding deceptive behavior.
problem Training safe agents from unsafe incentives.
method Formal settings, causal influence analysis, maximizing non-mediated effects.
result Agents avoid manipulating delicate state for rewards.
Separation of the sources and analysis of their connectivity have been an important topic in EEG/MEG analysis. To solve this problem in an automatic manner, we propose a two-layer model, in which the sources are conditionally uncorrelated from each other, but not independent; the dependence is caused by the causality i…
Paper develops methods to estimate generalization error across domains.
problem Uncertainty in predicting unseen data distributions.
method Partial identification and transportability theory, Neural Causal Models.
result First general estimation technique for transportability problems.
The paper analyzes the crash of stock and commodity markets during COVID-19 using Topological Data Analysis.
problem Identifying and understanding the dynamics and interdependence of stock and commodity markets during the COVID-19 crash.
method Topological Data Analysis (TDA) and Wasserstein Distance (WD) to identify crashes and compare market dynamics.
result Significant topological differences and interdependence between stock and commodity markets during the crash period.
The paper develops personalized DAG models for web user behavior.
problem Understanding user behavior transitions between websites with user heterogeneity and network dependency.
method Personalized Binomial DAG models with network-structured covariates, embedding network structure into a dimension-reduced covariate, learning node neighborhoods, and exploring variance-mean relation.
result The proposed algorithm outperforms state-of-the-art competitors in heterogeneous data.
Automated prediction of public speaking performance enables novel systems for tutoring public speaking skills. We use the largest open repository---TED Talks---to predict the ratings provided by the online viewers. The dataset contains over 2200 talk transcripts and the associated meta information including over 5.5 mi…
In many settings (e.g., robotics) demonstrations provide a natural way to specify tasks; however, most methods for learning from demonstrations either do not provide guarantees that the artifacts learned for the tasks, such as rewards or policies, can be safely composed and/or do not explicitly capture history dependen…
The paper refines transformations of lattice diagrams and introduces dotted diagrams.
problem Investigating transformations and deformations of lattice diagrams and their associated dotted diagrams.
method Introducing dotted diagrams and investigating deformations of these diagrams, relating them to transformations of lattice diagrams.
result Refined results on the relation between deformations of admissible dotted diagrams and transformations of lattice diagrams.
Current high-throughput data acquisition technologies probe dynamical systems with different imaging modalities, generating massive data sets at different spatial and temporal resolutions posing challenging problems in multimodal data fusion. A case in point is the attempt to parse out the brain structures and networks…
This note explains how to transform Heegaard diagrams into framed link diagrams.
problem No specific problem stated; transformation of diagrams is the focus.
method Explains a procedure to transform Heegaard diagrams into framed link diagrams.
result Demonstrates a method to transform Heegaard diagrams into framed link diagrams.
New minimal link diagrams found, including torus links and homogeneous ones.
problem Finding minimal link diagrams with new classes.
method Morton-Franks-Williams inequality approach.
result New classes of minimal link diagrams, including previously unproven ones.
Algorithm converts Kirby diagrams to trisection diagrams for 4-manifolds.
problem Creating efficient trisection diagrams for 4-manifolds.
method Algorithm converting Kirby diagrams to trisection diagrams.
result Provides examples of trisection diagrams for 4-manifolds.
Kernelized Taylor diagram visualizes data populations with fewer assumptions.
problem Limitations of Taylor diagram in capturing non-linear relationships and sensitivity to outliers.
method Proposes a kernelized version of the Taylor diagram that uses maximum mean discrepancy and kernel mean embedding.
result Kernelized Taylor diagram visualizes data populations with minimal assumptions of data distributions.
A virtual link diagram is called normal if the associated abstract link diagram is checkerboard colorable, and a virtual link is normal if it has a normal diagram as a representative.In this paper, we introduce a method of converting a virtual link diagram to a normal virtual link diagram by use of the double covering …
Study categorizes knots and links as rigid or shaky based on Reidemeister moves.
problem Classifying knots and links as rigid or shaky based on adaptability to Reidemeister moves.
method Categorization of hard diagrams as rigid or shaky, investigation of rigid and shaky hard diagrams for specific knots and links.
result Every link has a rigid hard diagram, and there is an upper limit for the number of crossings in such diagrams.
Twisted graph diagrams are virtual graph diagrams with bars on edges. A bijection between abstract graph diagrams and twisted graph diagrams is constructed. Then a polynomial invariant of Yamada-type is developed which provides a lower bound for the virtual crossing number of virtual graph diagrams.
A virtual link diagram is called normal if the associated abstract link diagram is checkerboard colorable, and a virtual link is normal if it has a normal diagram as a representative. Normal virtual links have some properties similar to classical links.In this paper, we introduce a method of converting a virtual link d…
Persistence diagrams are important descriptors in Topological Data Analysis. Due to the nonlinearity of the space of persistence diagrams equipped with their {\em diagram distances}, most of the recent attempts at using persistence diagrams in machine learning have been done through kernel methods, i.e., embeddings of …
Problems on region choices for knot and link diagrams solved using Alexander numbering.
problem Existence of solutions for region choice problems on knot and link diagrams.
method Alexander numbering for regions, alternative proofs, necessary and sufficient conditions.
result Existence of solutions for region choice problems on link diagrams.
Table of symmetric diagrams for knots up to 10 crossings.
problem Finding symmetric diagrams for strongly invertible knots.
method Compilation of symmetric diagrams for knots up to 10 crossings.
result Similarity of transversal diagrams to symmetric union diagrams for strongly invertible knots.
The presence of slipknots in configurations of proteins and DNA has been shown to affect their functionality, or alter it entirely. Historically, polymers are modeled as polygonal chains in space. As an alternative to space curves, we provide a framework for working with subknots inside of knot diagrams via knotoid dia…
Proves minimal crossing diagrams for specific spatial graphs.
problem Proving minimal crossing diagrams for spatial graphs.
method Analyzing adequate diagrams and replacing vertices and edges.
result All 1-vertex spatial graphs with adequate diagrams have minimal crossing number.
Rectangular diagrams help analyze foliations in 3-sphere.
problem Analyzing foliations in 3-sphere complements.
method Introduced rectangular diagrams for foliations and links.
result Any co-orientable finite depth foliation can be presented by a compatible rectangular diagram.
Bankwitz characterized an alternating diagram representing the trivial knot. A non-alternating diagram is called almost alternating if one crossing change makes the diagram alternating. We characterize an almost alternaing diagram representing the trivial knot. As a corollary we determine an unknotting number one alter…
The paper explores when specific knot operations simplify diagrams.
problem Understanding when arc crossing changes simplify knot diagrams.
method Examined two types of arc crossing changes on link diagrams and determined when they are unknotting operations.
result Any two crossing points in an alternating knot diagram are arc crossing change admissible.
Gauss diagrams' properties can change with Hamiltonian cycle choice.
problem The impact of Hamiltonian cycle choice on Gauss diagrams.
method Examined realizable and unrealizable Gauss diagrams, and proved preservation of realizability under certain Hamiltonian cycle changes.
result Properties of Gauss diagrams can vary with Hamiltonian cycle choice.
New estimate of semimeander complexity for knots with more than 10 crossings.
problem Estimating the complexity of semimeander diagrams of knots.
method Proved a new upper bound on the number of crossings for semimeander diagrams of knots with more than 10 crossings.
result For knots with more than 10 crossings, semimeander diagrams have no more than 0.31⋅1.558cr(K) crossings. Paper proves link diagrams can be realized for some but not all types of links.
problem Realizing link diagrams for different types of links.
method Analyzing link diagrams for welded and virtual links.
result Similar results hold for welded links but not for virtual links.
GridPyM handles grid diagrams for knot theory.
problem Handling grid diagrams for knot theory.
method Generates and simplifies grids, models local transformations.
result Models local transformations between grid diagrams.
There is a well-known way to describe a link diagram as a (signed) plane graph, called its Tait graph. This concept was recently extended, providing a way to associate a set of embedded graphs (or ribbon graphs) to a link diagram. While every plane graph arises as a Tait graph of a unique link diagram, not every embedd…
The study improves inequalities for link diagrams and introduces weak rectangular diagrams.
problem Improving inequalities for link diagrams and understanding their properties.
method Introducing weak rectangular diagrams and proving new inequalities.
result Generalizes and subsumes many known inequalities related to multi-crossing numbers.
In this paper, a link diagram is said to be minimal if no Reidemeister move I or II can be applied to it to reduce the number of crossings. We show that for an arbitrary diagram D of a link without a trivial split component, a minimal diagram obtained by applying Reidemeister moves I and II to D is unique. The proof al…
By using the cohomology theory of quandles, quandle cocycle invariants and shadow quandle cocycle invariants are defined for oriented links and surface-links via broken surface diagrams. By using symmetric quandles, symmetric quandle cocycle invariants are also defined for unoriented links and surface-links via broken …