Paper proposes MU+BDs score for Bayesian network structure learning.
problem Small sample sizes and sparse data cause issues with BDeu score.
method Proposes MU+BDs score with marginal uniform graph prior.
result MU+BDs score is more accurate and competitive than U+BDeu.
The paper critiques BDeu score for Bayesian network learning and proposes BDs as a better alternative.
problem Critiquing the BDeu score for Bayesian network structure learning from sparse data.
method Linking BD scores to the maximum relative entropy principle and using simulation studies.
result BDs score is recommended for sparse data as it avoids issues with BDeu.
Paper introduces a new Bayesian score for discrete networks.
problem Learning the structure of discrete Bayesian networks.
method Empirical Bayes approach with MU+BDs scoring.
result MU+BDs score outperforms U+BDeu in structure learning and prediction.
Let C and D be a pair of crumpled n-cubes and h a homeomorphism of Bd C to Bd D for which there exists a map fh:C→D such that fh∣Bd C=h and fh−1(Bd D)=Bd C. In our view the presence of such a triple (C,D,h) suggests that C is "at least as wild as" $D…
Two heuristics solve dynamic multiple travelling salesmen problems.
problem Dynamic routing with unknown customers.
method Balanced dynamic closest vehicle heuristic and balanced dynamic assignment vehicle heuristic.
result Continuous approximation models for strategic dynamic routing.
Proposes a method to prevent overfitting in deep DRE models.
problem Overfitting in deep DRE models using empirical Bregman divergence.
method Introduces a non-negative correction for empirical Bregman divergence.
result The proposed method mitigates train-loss hacking and improves performance.
Study uses interviews to automatically detect BD and BPD with good accuracy.
problem Challenges in distinguishing BD and BPD from clinical interviews.
method Developed a multi-modal dataset and used a linear classifier with selected features from interviews.
result Different sets of features characterize BD and BPD, providing insights into their differences.
CFM-BD builds interpretable fuzzy models for Big Data.
problem Maintaining accuracy and interpretability in fuzzy models for Big Data.
method Distributed learning algorithm with three stages: pre-processing, rule induction, and rule selection.
result CFM-BD constructs simpler models with fewer rules and linguistic labels, achieving competitive accuracy.
Smoothly bounded domains have special functions that are plurisubharmonic.
problem Finding smooth functions that are plurisubharmonic on bounded domains.
method Proving existence of smooth defining functions that are p-plurisubharmonic. result Smooth domains with smooth p-convex boundaries admit smooth defining functions that are p-plurisubharmonic. Let X be a quasiprojective manifold given by the complement of a divisor $\bD$ with normal crossings in a smooth projective manifold $\bX$. Using a natural compactification of X by a manifold with corners $\tX$, we describe the full asymptotic behavior at infinity of certain complete Kahler metrics of finite volume o…
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.
Let D be a link diagram with n crossings, s_A and s_B its extreme states and |s_AD| (resp. |s_BD|) the number of simple closed curves that appear when smoothing D according to s_A (resp. s_B). We give a general formula for the sum |s_AD|+|s_BD| for a k-almost alternating diagram D, for any k, characterising this sum as…
We characterize metric spaces X whose hyperspaces 2X or Bd(X) of non-empty closed (bounded) subsets, endowed with the Hausdorff metric, are absolute [neighborhood] retracts.
Diagonal complexes and symmetric complexes study surfaces with involution and punctures.
problem Understanding surfaces with involution and punctures through diagonal complexes.
method Construction and study of diagonal and symmetric diagonal complexes, their barycentric subdivisions, and homotopy equivalence.
result Symmetric diagonal complex is homotopy equivalent to a punctured symmetric surface.
The paper creates knot and braid invariants using points in R^2 and Ptolemy relations.
problem Creating invariants for braids, knots, and links.
method Dynamics of points in R^2 and Ptolemy relation application.
result Constructs invariants of braids, knots, and links.
100 years ago exactly, in 1906, Hartogs published a celebrated extension phenomenon (birth of Several Complex Variables), whose global counterpart was stated in full generality later by Osgood (1929): holomorphic functions in a connected neighborhood V(bD) of a connected boundary bD contained in C^n (n >= 2) do extend …
BHLR predicts hyperlink weights from data vectors using symmetric similarity functions and Bregman divergence.
problem Predicting hyperlink weights from data vectors in a general framework.
method BHLR learns a symmetric similarity function to minimize Bregman-divergence between hyperlink weights and estimated similarities.
result BHLR is statistically consistent and computationally tractable, providing theoretical guarantees for various methods.
Paper proposes S2ConvSCN for robust subspace clustering and classification.
problem Insufficient handling of nonlinear manifolds, data corruptions, and out-of-sample data.
method Self-supervised convolutional subspace clustering network (S2ConvSCN) with FC layer, CIM for robustness, and BD regularization. result Robust S2ConvSCN outperforms baseline on unseen data. Let K be a knot in S^3. We study the iterated Bing doubles of K, giving a new proof for the following statement: If BD_n(K) is slice for some n, then K is algebraically slice. This result was first proved by Cha and Kim using covering link calculus. We also use this tool, but our proof is substantially simpler and illu…
We consider surfaces with parallel mean curvature vector field and finite total curvature in product spaces of type Mn(c)×R, where Mn(c) is a space form, and characterize certain of these surfaces. When n=2, our results are similar to those obtained in \cite{bds} for surfaces wit…
The Rolling Ball Theorem asserts that given a convex body K in Euclidean space and having a smooth surface bd(K) with all principal curvatures not exceeding c>0 at all boundary points, K necessarily has the property that to each boundary point there exists a ball B_r of radius r=1/c, fully contained in K and touching b…
Curvature tensors can always be matched to a metric tensor under certain conditions.
problem Sectionally positive curvature tensors and their relationship to metric tensors.
method Existence and uniqueness of a metric tensor gab such that Rabcdgbd=gacλ. result A metric tensor gab can be found for sectionally positive curvature tensors, and it is unique up to a constant factor. Holomorphic connections on Calabi-Yau manifolds are flat.
problem Existence of holomorphic connections on Calabi-Yau manifolds.
method Proving the existence of flat holomorphic connections for holomorphic vector bundles.
result Holomorphic vector bundles over compact Kähler Calabi-Yau manifolds admit flat holomorphic connections.
Study on deformations of holomorphic Cartan geometries, focusing on flat cases.
problem Deformation of holomorphic Cartan geometries on complex manifolds.
method Computing infinitesimal deformations and analyzing the forgetful map.
result The forgetful map from infinitesimal deformations of a flat holomorphic Cartan geometry to the underlying flat principal bundle is an isomorphism.
Diagonal complexes generalize associahedra to surfaces, providing models for ribbon graphs and tautological bundles.
problem Generalizing associahedra to surfaces with marked points.
method Defining cell complexes and their barycentric subdivisions on surfaces, proving homotopy equivalences and contraction properties.
result Homotopy equivalence of diagonal complexes to ribbon graph spaces and tautological bundles.
Hybrid models are reinterpreted as Neuro-Symbolic AI designs to quantify uncertainty and variability.
problem Limited semantic interface for comparing hybrid models across domains.
method Reinterpret hybrid models as Neuro-Symbolic AI, translating them into explicit inference function and logic-belief decomposition.
result Metrics SVR and BD quantify uncertainty and variability in hybrid models.
In this work, we consider Corporate Governance (CG) ties among companies from a multiple network perspective. Such a structure naturally arises from the close interrelation between the Shareholding Network (SH) and the Board of Directors network (BD). In order to capture the simultaneous effects of both networks on CG,…
The paper proposes a method to integrate prior information into penalized regression.
problem Improving predictive performance in high-dimensional tasks with prior information.
method Integrating multiple sources of prior information into penalized regression.
result The method improves predictive performance, as shown by simulations and applications.
We prove that there is an algorithm which determines whether or not a given 2-polyhedron can be embedded into some integral homology 3-sphere. This is a corollary of the following main result. Let M be a compact connected orientable 3-manifold with boundary. Denote G=Z, G=Z/pZ or $G=\Q$. If H1(M;G)≅Gk…
Survey on generalized holomorphic Cartan geometries.
problem Classifying holomorphic Cartan geometries on compact Calabi-Yau manifolds.
method Introducing branched holomorphic Cartan geometries and classifying them.
result Classification of branched holomorphic Cartan geometries on compact Calabi-Yau manifolds.
The paper proves properties of surfaces with holes and ends.
problem Properties of Riemann surfaces with holes and ends.
method Analyzes Riemann surfaces with countably many ends and discs removed.
result Completes the complex structure of a minimal surface in 3D space.
In 1985, physicists Dixon, Harvey, Vafa and Witten studied string theories on Calabi-Yau orbifolds (cf. [DHVW]). An interesting discovery in their paper was the prediction that a certain physicist's Euler number of the orbifold must be equal to the Euler number of any of its crepant resolutions. This was soon related t…
Paper connects CR geometry conditions to closed range of ∂ˉ-operator.
problem Establishing closed range of the ∂ˉ-operator on CR manifolds. method Defined third and fourth order CR invariants and used them to show closed range for ∂ˉ-Laplacian. result Third and fourth order CR invariants provide sufficient conditions for closed range of ∂ˉ-operator. Paper improves deep point cloud compression techniques.
problem Efficiently compressing 3D point cloud data for various applications.
method Integrates scale hyperprior model, deeper transforms, focal loss, and optimal thresholding.
result Achieves significant BD-PSNR gains over existing methods.
New method recovers kernel and sparse inputs from convolved data efficiently.
problem Recovering kernel and sparse inputs from convolved data.
method Nonconvex optimization over the sphere using Riemannian gradient descent.
result Vanilla Riemannian gradient descent recovers kernel and signals up to a signed shift ambiguity.
For an oriented link $L \subset S^3 = \Bd\!D^4$, let χs(L) be the greatest Euler characteristic χ(F) of an oriented 2-manifold F (without closed components) smoothly embedded in D4 with boundary L. A knot K is {\it slice} if χs(K)=1. Realize D4 in $\C^2$ as {(z,w):∣z∣2+∣w∣2≤1}. It has been c…
FIRAL is a scalable active learning algorithm for multiclass classification.
problem Scalability issues with FIRAL in large datasets.
method Proposed an approximate algorithm with reduced storage and computational complexity.
result Demonstrated strong scalability and accuracy on large datasets.
Generative models' evaluation scores can be misleading, leading to inflated grades.
problem Misleading evaluation scores for generative models.
method Analyzed and compared various scores for evaluating synthetic vs. ground-truth data.
result The Eden score avoids grade inflation and better aligns with human perception.
The paper characterizes compactifications of manifolds with boundary.
problem Characterizing compactifications of manifolds with noncompact boundaries.
method Application of Siebenmann's and O'Brien's work, and new conditions for Z-compactifiability.
result A complete characterization of compactifications of manifolds with boundary.
Improves score estimation for noised targets using known clean scores.
problem Poor score estimation at low noise levels in Denoising Score Matching.
method Introduces Target Score Identity and Target Score Matching loss.
result Score estimates are more accurate at low noise levels.
This work improves likelihood of score-based diffusion ODEs using high-order denoising score matching.
problem The gap between maximum likelihood and score matching objectives for score-based diffusion ODEs.
method High-order denoising score matching to maximize likelihood.
result Score-based diffusion ODEs achieve better likelihood on synthetic and CIFAR-10 data.
Study compares multivariate scoring rules for distribution forecasts.
problem Evaluating the discrimination ability of multivariate scoring rules.
method Simulation study comparing energy and variogram scores using historical data.
result Variogram score with p=0.5 outperforms other scores.
Paper explores modern CNNs for IoT-based farms.
problem Insufficient insight from agricultural IoT data.
method Review of state-of-the-art CNN architectures and their applications.
result Benchmarking guide for selecting CNN architectures.
A new method improves data generation quality by correcting score mismatches.
problem Score mismatch issue in conditional score-based data generation methods.
method Denoising Likelihood Score Matching (DLSM) loss for classifier training.
result The proposed method outperforms previous methods on Cifar-10 and Cifar-100 benchmarks.
New scoring rules improve probabilistic classification model evaluation.
problem Traditional scoring rules misalign with the preference for correct classifications.
method Introduces Penalized Brier Score (PBS) and Penalized Logarithmic Loss (PLL) to modify proper scoring rules.
result PBS and PLL better identify optimal checkpoints and early stopping points, leading to superior F1 scores.
Paper introduces max-plus statistical leverage scores for faster approximation of conventional scores.
problem Approximating statistical leverage scores of complex matrices efficiently.
method Max-plus algebraic analogue for statistical leverage scores.
result Max-plus statistical leverage scores can approximate conventional scores quickly and accurately.
Extends denoising and score estimation to energy models via Tweedie's formula.
problem Linking denoising and score estimation for a wider range of distributions.
method Derives a fundamental identity connecting energy score derivatives and scores.
result Establishes a new identity for energy scores analogous to Tweedie's formula.
Mixed-SCORE+ improves community detection in weak signal networks.
problem Detecting communities in weak signal networks.
method Proposes Mixed-SCORE+ combining properties of Mixed-SCORE and SCORE+.
result Significantly improves detection error rates on Polblogs and weak signal networks.