Deviance Voronoi residuals improve earthquake insurance risk assessment.
problem Assessing earthquake insurance risk using spatio-temporal point process models.
method Extended Voronoi residuals and created simulation-based approach.
result Proposed formula for country-wide minimum capital test.
Deviance-style normalization for sparse, jointly overdispersed count matrices
problem Jointly overdispersed count matrices
method Dirichlet-multinomial deviance residualization
result Preserves exact sparsity, evaluates in constant time, recovers multinomial residual
Extends matrix factorization for deviance-based losses with GLM theory.
problem Improving data loss models beyond squared error.
method Adapts GLM theory to matrix factorization for deviance losses.
result Strong consistency and robustness of the proposed decomposition.
This paper aims to review the methodology behind the generalized linear models which are used in analyzing the actuarial situations instead of the ordinary multiple linear regression. We introduce how to assess the adequacy of the model which includes comparing nested models using the deviance and the scaled deviance. …
The paper addresses insurance pricing by improving machine learning models and metrics.
problem Lack of balance and confusion in insurance model performance metrics.
method Introduces autocalibration and Tweedie deviance minimization for insurance pricing models.
result Autocalibration corrects bias and ensures balance on local scales.
Discovering the causal structure among a set of variables is a fundamental problem in many areas of science. In this paper, we propose Kernel Conditional Deviance for Causal Inference (KCDC) a fully nonparametric causal discovery method based on purely observational data. From a novel interpretation of the notion of as…
Paper introduces NICc for fast cluster-based validation of prediction models.
problem Validation of prediction models on clustered data.
method Derived NICc to approximate leave-one-cluster-out deviance for standard regression models.
result NICc provides more accurate model size and variable selection, especially with strong clustering.
This paper generalizes beta divergence beyond its classical form associated with power variance functions of Tweedie models. Generalized form is represented by a compact definite integral as a function of variance function of the exponential dispersion model. This compact integral form simplifies derivations of many pr…
Bayesian model clusters brain activity time series.
problem Heterogeneous multivariate time series in brain imaging.
method Group-based Bayesian mixture of smoothing splines with covariate effects.
result Distinct brain activity patterns identified.
New method uses kernel deviance measures to discover causal relationships in heterogeneous data.
problem Discovering causal relationships in complex, heterogeneous datasets.
method KIIM-HT, a novel score measure based on heterogeneous transformations of RKHS embeddings.
result KIIM-HT outperforms previous methods in causal discovery tasks.
EGO-MDA identifies optimal spectral-bands for process discrimination.
problem Optimal spectral-bands for process discrimination.
method EGO-MDA, an unsupervised method using EGO and Mixture Discriminant Analysis.
result EGO-MDA achieves at least 70% improvement in median deviance.
Federated learning calibrates insurance indices from renewable energy producers' data.
problem Calibrating parametric insurance indices under heterogeneous renewable energy production losses.
method Federated learning framework using Tweedie GLMs and distributed optimization.
result Federated learning recovers comparable index coefficients under moderate heterogeneity.
Study optimizes CANN for actuarial tasks using RSM.
problem Optimizing hyperparameters for neural networks in actuarial science.
method Factorial design and response surface methodology (RSM).
result Reduced hyperparameter optimization from 288 to 188, achieving near-optimal performance.
Abstract: Non-residually finite hyperbolic groups imply non-residually finite rigid hyperbolic groups.
problem Existence of non-residually finite hyperbolic groups
method Direct implication
result Existence of non-residually finite rigid hyperbolic groups
Residual finiteness is known to be an important property of groups appearing in combinatorial group theory and low dimensional topology. In a recent work [2] residual finiteness of quandles was introduced, and it was proved that free quandles and knot quandles are residually finite. In this paper, we extend these resul…
In this note, residual finiteness of quandles is defined and investigated. It is proved that free quandles and knot quandles of tame knots are residually finite and Hopfian. Residual finiteness of quandles arising from residually finite groups (conjugation, core and Alexander quandles) is established. Further, residual…
Every non-trivial knot group is fully residually perfect.
problem Understanding the residual properties of knot groups.
method Analyzing the residual properties of knot groups using group theory.
result Every non-trivial knot group is fully residually perfect.
Residual flows are shown to approximate MMD well.
problem Lack of theoretical understanding of normalizing flows' expressiveness.
method Proved residual flows are universal approximators in MMD.
result Residual flows can approximate MMD with a bounded number of blocks.
Let p be a prime. In this paper, we classify the geometric 3-manifolds whose fundamental groups are virtually residually p. Let M=M3 be a virtually fibered 3-manifold. It is well-known that G=π1(M) is residually solvable and even residually finite solvable. We prove that G is always virtually residually p…
Researchers identify critical protein residues using advanced graph theory.
problem Identifying essential residues in proteins for function.
method Learning Random Geometric Graphs (RGG) with Cramer's V correlation and organic thresholding.
result Advanced RGG methods accurately identify critical residues compared to existing techniques.
Defines Wodzicki residue using groupoids and fibered distributions.
problem Defining and understanding the Wodzicki residue in noncommutative geometry.
method Using groupoid language and filtered manifolds, defining the residue and showing its properties.
result The groupoidal residue is a trace on pseudodifferential operators and matches the usual residue in certain cases.
In this work we prove a Baum-Bott type residue theorem for flags of holomorphic foliations. We prove some relations between the residues of the flag and the residues of their correspondent foliations. We define the Nash residue for flags and we give a partial answer to the Baum-Bott type rationality conjecture in this …
We revisit residual algorithms in both model-free and model-based reinforcement learning settings. We propose the bidirectional target network technique to stabilize residual algorithms, yielding a residual version of DDPG that significantly outperforms vanilla DDPG in the DeepMind Control Suite benchmark. Moreover, we…
Wide residual networks generalize well with uniform convergence to RNTK as width increases.
problem Understanding the generalization ability of wide residual networks.
method Uniform convergence of residual network kernel to residual neural tangent kernel (RNTK).
result Generalization error converges to kernel regression error with respect to RNTK.
Given a prime p, a group is called residually p if the intersection of its p-power index normal subgroups is trivial. A group is called virtually residually p if it has a finite index subgroup which is residually p. It is well-known that finitely generated linear groups over fields of characteristic zero are …
The paper studies residues of manifolds and their applications in geometry.
problem Understanding the residues of manifolds and their geometric implications.
method Analytic continuation and Möbius invariance of residues, introduction of relative and weighted residues.
result Scalar curvature, mean curvature, and Euler characteristic can be expressed in terms of residues.
We show that Out(G) is residually finite if G is a one-ended group that is hyperbolic relative to virtually polycyclic subgroups. More generally, if G is one-ended and hyperbolic relative to proper residually finite subgroups, the group of outer automorphisms preserving the peripheral structure is residually finite. We…
Simplifies residual flows to make flow-based modeling more practical.
problem Extremely high computational cost of residual flows limits their applicability.
method Introduces Quasi-Autoregressive (QuAR) approach to residual flows.
result Significantly reduces compute time and memory requirements for flow-based modeling.
Study on endomorphism and automorphism groups of specific quandles.
problem Characterizing endomorphism and automorphism groups of residually finite and profinite quandles.
method Proved properties of endomorphism monoids and automorphism groups for residually finite and profinite quandles.
result Endomorphism and automorphism groups of residually finite quandles are residually finite.
Unified ODE model explains residual and non-residual networks.
problem Unclear relationship between residual and non-residual networks.
method Introducing a damping term in an ODE model to interpolate between ResNet and CNN architectures.
result Unified framework for understanding residual and non-residual networks.
Defines and proves generalized noncommutative residue theorems for specific dimensions.
problem Defining and proving residue theorems for noncommutative geometry.
method Defined generalized noncommutative residue of Dirac operator; proved Kastler-Kalau-Walze type theorems.
result Validated Kastler-Kalau-Walze type theorems for 4D and 6D compact manifolds.
Batch normalization makes deep residual networks train faster.
problem Training deep residual networks with large depths.
method Downscaling the residual branch by a normalizing factor early in training.
result Normalized residual blocks compute functions close to the identity function early in training.
Proves Singer conjecture for graph manifolds with residually finite groups.
problem Proving the Singer conjecture for graph manifolds with specific properties.
method Used residual finiteness and graph manifold properties to prove the conjecture.
result Proved the Singer conjecture for extended graph manifolds and pure complex-hyperbolic higher graph manifolds.
Study excess logarithmic residues for foliations to bound invariant hypersurfaces and test log canonicity.
problem Bounding invariant hypersurfaces and testing log canonicity of singularities.
method Introduce excess logarithmic residues, prove residue formula, derive Poincaré-type bound, and use them to recover log discrepancies.
result Componentwise logarithmic residues of a lifted foliation along the exceptional divisor recover log discrepancies of singularities.
Fair market valuations ignore future worker profits in employee-owned firms.
problem Ignoring future worker profits in fair market valuations for employee-owned firms.
method Analyzing property rights and residual claimants in employee-owned firms.
result Fair market valuations are inappropriate for employee-owned firms.
Framework monitors insurance pricing models for drift and recalibration.
problem Maintaining predictive performance of pricing models in evolving insurance portfolios.
method Formalizes deviance loss and Murphy's score, studies Gini score, develops monitoring framework.
result Framework guides decisions on refitting or recalibrating pricing models.
We conduct mathematical analysis on the effect of batch normalization (BN) on gradient backpropogation in residual network training, which is believed to play a critical role in addressing the gradient vanishing/explosion problem, in this work. By analyzing the mean and variance behavior of the input and the gradient i…
The discovery of causal relationships is a fundamental problem in science and medicine. In recent years, many elegant approaches to discovering causal relationships between two variables from observational data have been proposed. However, most of these deal only with purely directed causal relationships and cannot det…
ResGCN detects anomalies in attributed networks by capturing sparsity and nonlinearity.
problem Detecting anomalous nodes in attributed networks.
method Attention-based deep residual modeling using Graph Convolutional Networks.
result ResGCN effectively detects anomalies in attributed networks.
Proposes a neural network method to correct residual distortions in coordinate transformations.
problem Nonlinear and spatially dependent distortions in coordinate transformation models.
method Residual-based neural network approach focusing on systematic distortions.
result The method improves accuracy and stability in challenging conditions.
Introduces Soft-SVM for binary classification bridging logistic and SVM.
problem Data separability issues in binary classification.
method Soft-SVM regression using convex relaxation of hinge loss with softness and class-separation parameters.
result Soft-SVM performs well in classification and prediction errors.
In this paper we propose the use of continuous residual modules for graph kernels in Graph Neural Networks. We show how both discrete and continuous residual layers allow for more robust training, being that continuous residual layers are those which are applied by integrating through an Ordinary Differential Equation …
We count meromorphic differentials with fixed residues and poles of fixed orders.
problem Counting meromorphic differentials with fixed residues and poles of fixed orders.
method Intersection theory on compactified moduli spaces of differentials.
result Complete solution to the problem with interesting combinatorial properties.
In this work we prove a residue formula for Morita-Futaki-Bott invariant with respect any holomorphic vector fields with isolated (possibly degenerated) singularities in terms of Grothendieck's residues.
Extends Hawkes process for flexible residual modeling in point processes.
problem Modeling high-frequency financial data with complex residual distributions.
method Introduces self and mutually exciting point process with discretely Markovian dynamics.
result Flexible residual distributions improve intensity modeling and high-frequency data estimation.
PRISMA uses PDE residuals for fast, robust, and accurate inference.
problem Slow gradient-based optimization and instability in PDE residual-based methods.
method Integrates PDE residuals directly into the model's architecture via attention mechanisms in the spectral domain.
result Competitive accuracy with significantly lower inference costs and faster speeds.
A new algorithm improves stochastic linear bandit performance using residual bootstrap.
problem Improving performance in stochastic linear bandit problems.
method Residual bootstrap exploration to estimate mean reward and pull the arm with the highest estimate.
result Proposed algorithm exttt{LinReBoot} achieves high-probability sub-linear regret under mild conditions.
The study examines discrete subgroups of Lie groups and their residual finiteness.
problem Determining when discrete subgroups of Lie groups are residually finite.
method Analyzes known results and poses open questions.
result Answers to open questions will provide a comprehensive understanding of residual finiteness in Lie groups.