Paper extends Enami-Ozeki-Yamaguchi's work on planar quadrangulations.
problem Finding the maximum number of colors for proper anti-rainbow colorings on planar quadrangulations.
method Introducing half-monochromatic colorings for plane graphs with even polygonal faces and providing an upper bound in terms of the independence number.
result An upper bound on the maximum number of colors for half-monochromatic colorings is given in terms of the independence number.
The number of functionally independent scalar invariants of arbitrary order of a generic pseudo--Riemannian metric on an n--dimensional manifold is determined.
New algorithm reduces conditional independence tests needed for causal discovery.
problem Efficiently infer causal relations from observational data.
method Established an algorithm with complexity pO(s) tests. result Achieves exponent-optimality up to a logarithmic factor in terms of conditional independence tests.
We give a covering number bound for deep learning networks that is independent of the size of the network. The key for the simple analysis is that for linear classifiers, rotating the data doesn't affect the covering number. Thus, we can ignore the rotation part of each layer's linear transformation, and get the coveri…
Paper solves a metric-independent problem on almost Kähler 4-manifolds.
problem Find a metric-independent generalization of Bott-Chern and Aeppli numbers.
method Introduced a new approach to generalize Bott-Chern and Aeppli numbers.
result Found a solution valid on almost Kähler 4-manifolds.
Representing distributions over permutations can be a daunting task due to the fact that the number of permutations of n objects scales factorially in n. One recent way that has been used to reduce storage complexity has been to exploit probabilistic independence, but as we argue, full independence assumptions impo…
IMA addresses non-identifiability in nonlinear ICA by assuming orthogonal Jacobian columns.
problem Non-identifiability in nonlinear ICA.
method IMA assumes orthogonal Jacobian columns and extends to manifold settings.
result IMA circumvents non-identifiability issues and can be beneficial for higher-dimensional observations.
Study subgroup growth in RAAGs and RAAGs with Coxeter relations.
problem Understanding subgroup growth in RAAGs and RAAGs with Coxeter relations.
method Analyzing the independence number of defining graphs for RAAGs and conjecturing for RAAGs with Coxeter relations.
result Subgroup growth rate depends on the independence number of the defining graph for RAAGs and a conjecture for RAAGs with Coxeter relations.
Study on Volterra Cox-Ingersoll-Ross process, proving asymptotic independence and ergodicity.
problem Analyzing the Volterra Cox-Ingersoll-Ross process and its properties.
method Fine asymptotic analysis of Volterra Riccati equation, affine transformation formula.
result Proves asymptotic independence and ergodicity of the process.
Algorithm learns causal structures from low-order conditional independencies.
problem Estimating high-order conditional independencies from data is challenging.
method Proposes an algorithm to compute a faithful graphical representation from low-order conditional independencies.
result Algorithm successfully learns causal structures from zero- and first-order conditional independencies.
Optimal transport is #P-hard when components are independent, even with approximate solutions.
problem Computational complexity of optimal transport with independent marginals.
method Proved #P-hardness and developed a pseudo-polynomial time approximation algorithm.
result Optimal transport is #P-hard even with independent components and approximate solutions.
Embedded ensembles improve neural network performance efficiently.
problem Improving neural network performance with fewer resources.
method Analyzing the wide network limit of gradient descent dynamics using Neural-Tangent-Kernel.
result Embedded ensembles exhibit two regimes: independent and collective, affecting performance.
A new DRL scheme optimizes solving large graphs' maximum independent set problem.
problem Efficiently solving maximum independent set problems on large graphs.
method Learning what to defer (LwD) to adaptively control the number of stages.
result Significantly outperforms state-of-the-art DRL and conventional solvers.
The tail of the distribution of a sum of a random number of independent and identically distributed nonnegative random variables depends on the tails of the number of terms and of the terms themselves. This situation is of interest in the collective risk model, where the total claim size in a portfolio is the sum of a …
A theorem of Jorgensen and Thurston implies that the volume of a hyperbolic 3-manifold is bounded below by a linear function of its Heegaard genus. Heegaard surfaces and bridge surfaces often exhibit similar topological behavior; thus it is natural to extend this comparison to ask whether a (g,b)-bridge surface for a…
New framework relaxes independence assumption for graph-mixing dependencies.
problem Tackles limitations of existing generalization results for graph-mixing dependencies.
method Proposes a framework where dependencies decay with graph distance, derives generalization bounds leveraging online-to-PAC framework.
result Derives high-probability generalization guarantees that depend on mixing rate and graph's chromatic number.
Proves a conjecture about graph complexes without specific cycle lengths.
problem Graph complexes without specific cycle lengths.
method Proves stronger statements about independence complexes being contractible or homotopy equivalent to spheres.
result Independence complexes are either contractible or homotopy equivalent to spheres.
Greedy selection works well in a toy model of independent increments.
problem Iterative selection of maximum-value processes from i.i.d. stochastic processes.
method Fixed greedy selection at each stage.
result Optimal strategy is greedy selection under independent increments.
We classify the dispersive Poisson brackets with one dependent variable and two independent variables, with leading order of hydrodynamic type, up to Miura transformations. We show that, in contrast to the case of a single independent variable for which a well known triviality result exists, the Miura equivalence class…
The paper offers generalization bounds for Transformers that ignore sequence length.
problem Developing generalization bounds for Transformers that are independent of sequence length.
method Covering number approach to upper bound Rademacher complexity of bounded linear transformations.
result Theoretical bounds for Transformer generalization are independent of sequence length.
New statistics improve kernel independence testing efficiency.
problem Improving efficiency in kernel independence testing.
method Adapting martingale MMD construction to joint independence problem.
result Two new statistics achieve finite-sample consistency with linear per-test cost.
Let M be a pseudo-Riemannian spin manifold of dimension n and signature s and denote by N the rank of the real spinor bundle. We prove that M is locally homogeneous if it admits more than 3/4N independent Killing spinors with the same Killing number, unless n≡1(mod4) and s≡3(mod4). We …
The paper explores how semantic independence can be captured in text embeddings using partial orthogonality.
problem Capturing semantic independence in text embeddings.
method Developed a theory and methods based on partial orthogonality to demonstrate semantic independence.
result Partial orthogonality captures semantic independence in text embeddings.
A concentration graph associated with a random vector is an undirected graph where each vertex corresponds to one random variable in the vector. The absence of an edge between any pair of vertices (or variables) is equivalent to full conditional independence between these two variables given all the other variables. In…
This paper tackles target-dependent label complexity gap in active learning.
problem Target-dependent label complexity gap in Agnostic Active Learning.
method Introduces a novel distribution-splitting strategy based on number density to reduce label complexity and error rate.
result Provides theoretical guarantees and practical advantages for reducing label complexity and error rate.
New approach tackles nonidentifiability in nonlinear blind source separation.
problem Nonidentifiability in nonlinear blind source separation.
method Independent mechanism analysis, incorporating causal assumptions.
result Empirical and theoretical evidence shows improved identifiability.
New method tests causal association using noise contrastive backdoor adjustment.
problem Testing causal association in complex settings with many confounders.
method Backdoor-HSIC (bd-HSIC) using HSIC for independence testing.
result Calibrated and powerful for binary and continuous treatments with many confounders.
The paper extends SARMA models by relaxing independence assumptions on error terms.
problem Testing adequacy of SARMA models with non-independent errors.
method Study of asymptotic distributions of residual and normalized residual empirical autocovariances and autocorrelations under weak noise assumptions.
result Established asymptotic behavior of portmanteau tests for SARMA models.
Study algebraic relations of Vassiliev invariants for families of knots.
problem Understanding algebraic structure of Vassiliev invariants for knot families.
method Analyzing algebraic relations and generating sets of Vassiliev invariants in 3D Chern-Simons theory.
result For 1-parametric knot families, Vassiliev invariants are finitely generated. For more parameters, there can be an infinite number of generators.
We show that the error probability of reconstructing kernel matrices from Random Fourier Features for the Gaussian kernel function is at most O(R2/3exp(−D)), where D is the number of random features and R is the diameter of the data domain. We also provide an information-theoretic method-independen…
GraphITE estimates individual effects of graph-structured treatments.
problem Estimating individual effects of complex treatment structures.
method Graph neural networks and Hilbert-Schmidt Independence Criterion regularization.
result GraphITE outperforms baselines in estimating treatment effects for large numbers of treatments.
To each unit complex number with positive imaginary part there is defined a Tristram-Levine knot signature function. The set of all such signature functions is linearly independent as a set of functions defined on the set of all knots. The set of averaged signature functions forms a linearly independent set of homomoro…
Satellite operations with winding number ≠ 1 are not homomorphisms.
problem Characterizing homomorphisms in satellite operations.
method Using d-invariants of branched covers and Torelli group properties. result Satellite operations with winding number ≠ 1 are not homomorphisms.
Estimates marginal independence structure of Bayesian networks from data.
problem Learning the marginal independence structure of Bayesian networks from observational data.
method Using Gröbner basis and MCMC method (GrUES) to connect and recover the true structure.
result GrUES recovers the true marginal independence structure at a higher rate than simple independence tests.
The emph{securities market} is the fundamental theoretical framework in economics and finance for resource allocation under uncertainty. Securities serve both to reallocate risk and to disseminate probabilistic information. emph{Complete} securities markets - which contain one security for every possible state of natur…
Study confirms a knot's crosscap number equals its splice-unknotting number for alternating knots.
problem Determining the crosscap number of alternating knots.
method Using a splice-unknotting number defined by Ito-Takimura, and computing through Gauss codes.
result Crosscap numbers of all prime alternating knots up to 13 crossings are computed.
Improved bounds on geodesic intersections on hyperbolic surfaces.
problem Finding the shortest geodesic with a specific number of intersections.
method Proved a new formula for minimal length of geodesics with self-intersection number k.
result Improved the threshold for the existence of geodesics with self-intersection number k.
Develops correlation number for specific potentials and Hitchin representations.
problem Analyzing correlation numbers for potentials with entropy gaps and Hitchin representations.
method Defines a correlation number for pairs of cusped Hitchin representations and explores its connection to the Manhattan curve.
result Establishes a connection between the correlation number and the Manhattan curve, revealing rigidity properties.
New method tests causal relationships from data without needing to learn the entire graph.
problem Testing if a causal graph belongs to a specific Markov equivalence class from observational data.
method Established bounds on the number of independence tests required and provided an algorithm that matches these bounds.
result Testing requires exponentially less independence tests compared to learning, especially in graphs with high in-degrees and small clique sizes.
The difficulty of multi-class classification generally increases with the number of classes. Using data from a subset of the classes, can we predict how well a classifier will scale with an increased number of classes? Under the assumptions that the classes are sampled identically and independently from a population, a…
Independent component analysis (ICA) decomposes multivariate data into mutually independent components (ICs). The ICA model is subject to a constraint that at most one of these components is Gaussian, which is required for model identifiability. Linear non-Gaussian component analysis (LNGCA) generalizes the ICA model t…
Novel tests for genetic independence in high-dimensional data.
problem Testing independence in genetics studies with many variables.
method Defining premetric structures on genetic data support spaces.
result Solid theoretical framework and computationally-efficient implementations.
New algorithms learn simple staged trees from data, improving model fit.
problem Complex conditional independences in categorical data vectors.
method Structural learning algorithms for simple staged trees, coalescing the underlying tree.
result Data-learned simple staged trees often outperform Bayesian networks in model fit.
Modeling data as being sampled from a union of independent subspaces has been widely applied to a number of real world applications. However, dimensionality reduction approaches that theoretically preserve this independence assumption have not been well studied. Our key contribution is to show that 2K projection vect…
FMCIT accelerates CI tests for causal discovery, maintaining power and efficiency.
problem High computational complexity in CI tests limits practical applicability of causal discovery methods.
method Flow Matching-based Conditional Independence Test (FMCIT) that leverages flow matching for fast CI tests.
result FMCIT effectively controls type-I error and maintains high testing power under the alternative hypothesis.
We propose a streaming algorithm for the binary classification of data based on crowdsourcing. The algorithm learns the competence of each labeller by comparing her labels to those of other labellers on the same tasks and uses this information to minimize the prediction error rate on each task. We provide performance g…
New bounds for KRR condition number reveal overfitting phenomena.
problem Characterizing overfitting in KRR with varying kernel spectral decay.
method Derived new bounds for kernel matrices, enhanced test error bounds, and identified feature independence role.
result Identified tempered and catastrophic overfitting phenomena.
A new non parametric approach to the problem of testing the independence of two random process is developed. The test statistic is the Hilbert Schmidt Independence Criterion (HSIC), which was used previously in testing independence for i.i.d pairs of variables. The asymptotic behaviour of HSIC is established when compu…