Existence of Kähler-Einstein metrics on toric varieties proven.
problem Existence of Kähler-Einstein metrics on toric varieties.
method Characterization of K-stability using log Cox ring and universal orbifold cover.
result Every Q-factorial normal projective toric variety allows an orbifold Kähler-Einstein metric.
Enhances Cox model for survival analysis with symbolic non-linear log-risk functions.
problem Limited interpretability and non-linearity in traditional Cox models.
method Introduces GCPH model using Kolmogorov-Arnold Networks for symbolic non-linear log-risk functions.
result GCPH achieves competitive performance and superior interpretability.
Firm size data usually do not show the normality that is often assumed in statistical analysis such as regression analysis. In this study we focus on two firm size data: the number of employees and sale. Those data deviate considerably from a normal distribution. To improve the normality of those data we transform them…
New methods for time-to-event prediction are proposed by extending the Cox proportional hazards model with neural networks. Building on methodology from nested case-control studies, we propose a loss function that scales well to large data sets, and enables fitting of both proportional and non-proportional extensions o…
Active-set algorithm improves Cox regression for shape-restricted covariates.
problem Improving Cox regression for shape-restricted covariates.
method Shape-restricted inference using active-set optimization for spline basis expansion.
result Active-set algorithm produces accurate linear covariate effect estimates.
We consider the finite sample properties of the regularized high-dimensional Cox regression via lasso. Existing literature focuses on linear models or generalized linear models with Lipschitz loss functions, where the empirical risk functions are the summations of independent and identically distributed (iid) losses. T…
An accurate model of patient-specific kidney graft survival distributions can help to improve shared-decision making in the treatment and care of patients. In this paper, we propose a deep learning method that directly models the survival function instead of estimating the hazard function to predict survival times for …
Extends deep learning for nonlinear Cox regression variable selection.
problem Variable selection for nonlinear Cox regression model.
method Extends LassoNet to survival data for nonlinear Cox model.
result Valid and effective method demonstrated through simulations.
We generalize the log Gaussian Cox process (LGCP) framework to model multiple correlated point data jointly. The observations are treated as realizations of multiple LGCPs, whose log intensities are given by linear combinations of latent functions drawn from Gaussian process priors. The combination coefficients are als…
Proves finitely generated graded rings for klt singularities.
problem Understanding the structure of klt singularities.
method Analyzes graded rings associated with minimizers of normalized volume functions.
result Graded rings are finitely generated for klt singularities.
Reductive quotients preserve klt singularities in algebraic geometry.
problem Preserving klt singularities in quotients of klt singularities.
method Proving that the quotient of a klt type singularity by a reductive group is of klt type.
result The quotient of a klt variety by a reductive group results in a klt variety with a suitable boundary.
We consider structural credit modeling in the important special case where the log-leverage ratio of the firm is a time-changed Brownian motion (TCBM) with the time-change taken to be an independent increasing process. Following the approach of Black and Cox, one defines the time of default to be the first passage time…
CoxSE combines deep learning with self-explaining neural networks for survival analysis.
problem Improving predictive power of Cox Proportional Hazards model while maintaining explainability.
method Proposes CoxSE, a locally explainable Cox proportional hazards model using SENN, and CoxSENAM, a hybrid model with NAM.
result CoxSE provides more stable and consistent explanations while maintaining predictive power.
A new method clusters rows of a matrix of point processes.
problem Challenges in analyzing structured point process data.
method Mixture model of multi-level marked point processes, combined with ES algorithm and FPCA.
result An efficient method for clustering rows of a matrix of point processes.
McCullagh and Yang (2006) suggest a family of classification algorithms based on Cox processes. We further investigate the log Gaussian variant which has a number of appealing properties. Conditioned on the covariates, the distribution over labels is given by a type of conditional Markov random field. In the supervised…
Study compares Cox model and RSF for predicting patient survival, finding RSF superior in certain scenarios.
problem Comparing predictive accuracy of Cox proportional hazards model and Random Survival Forest for patient-specific survival probabilities.
method Conducted a comprehensive comparison study using simulation scenarios and real-world datasets.
result RSF outperforms Cox model in nonproportional hazards settings and with treatment-covariate interactions.
Semi-parametric survival analysis methods like the Cox Proportional Hazards (CPH) regression (Cox, 1972) are a popular approach for survival analysis. These methods involve fitting of the log-proportional hazard as a function of the covariates and are convenient as they do not require estimation of the baseline hazard …
Proves finitely generated associated graded rings for valuations on log Fano pairs.
problem Stability thresholds of log Fano pairs.
method Proves finite generation of associated graded rings for valuations.
result Log Fano pairs are uniformly K-stable if their stability threshold is less than a certain value.
New Hawkes processes model spatiotemporal events with triggering and clustering.
problem Modeling self-excitatory behavior in spatiotemporal data.
method Developed a new class of spatiotemporal Hawkes processes with efficient inference method.
result Efficiently modeled and inferred spatiotemporal events with triggering and clustering.
During the past decades, the Ising distribution has attracted interest in many applied disciplines, as the maximum entropy distribution associated to any set of correlated binary (`spin') variables with observed means and covariances. However, numerically speaking, the Ising distribution is unpractical, so alternative …
Develops asymptotic theory for deep Cox models to enable valid inference.
problem Theoretical gaps in deep neural network estimators for Cox models.
method Asymptotic distribution theory linking in-sample optimization error to population risk.
result Pointwise and multivariate asymptotic normality for subsampled ensemble estimators.
The Korányi ellipsoidal ring E of radii B and A, 0<B<A, is defined as the image of the Korányi spherical ring of the same radii and centred at the origin via a linear contact map L in the Heisenberg group. If K≥1 is the maximal distortion of L then we prove that the modulus of E i…
Proves unique degeneration of log Fano fibration germs.
problem Stable degeneration of log Fano fibration germs.
method Introduced the H-invariant for filtrations over log Fano fibration germs and used a unique quasi-monomial valuation to achieve the degeneration.
result Unique K-polystable special degeneration of log Fano fibration germs.
Given an arbitrary d>0 we construct a group G and a group ring element S in Z[G] such that the spectral measure mu of S has the property that mu((0,eps)) > C/|log(eps)|^(1+d) for small eps. In particular the Novikov-Shubin invariant of any such S is 0. The constructed examples show that the best known upper bounds on m…
This paper presents an original approach for jointly fitting survival times and classifying samples into subgroups. The Coxlogit model is a generalized linear model with a common set of selected features for both tasks. Survival times and class labels are here assumed to be conditioned by a common risk score which depe…
We study the Heston-Cox-Ingersoll-Ross++ stochastic-local volatility model in the context of foreign exchange markets and propose a Monte Carlo simulation scheme which combines the full truncation Euler scheme for the stochastic volatility component and the stochastic domestic and foreign short interest rates with the …
The method integrates survival constraints into NMF for identifying survival-associated gene clusters.
problem Understanding and interpreting high-dimensional biological data for disease markers.
method Cox proportional hazards regression integrated with NMF via proportional hazards non-negative matrix factorization.
result The method can uncover survival-associated gene clusters in cancer gene expression data.
New statistical properties for mini-batch Cox-NN optimization.
problem Optimizing deep Cox neural networks using mini-batches.
method Developed mini-batch maximum partial-likelihood estimator (mb-MPLE) for Cox-NN.
result mb-MPLE is consistent and achieves optimal convergence rate.
We develop a general theory of log spaces, in which one can make sense of the basic notions of logarithmic geometry, in the sense of Fontaine-Illusie-Kato. Many of our general constructions with log spaces are new, even in the algebraic setting. In the differentiable setting, our theory yields a framework for treating …
Improved survival analysis using square root Cox's models and neural networks.
problem Feature selection in survival analysis.
method Square root Cox's survival analysis by the fittest linear and neural networks model, directly tuning penalty parameter λ.
result Substantially improved over traditional methods, achieving phase transition in feature selection.
MEC-Cox: A Machine-Learning-Assisted Generalized Entropy Calibration Method for Estimating ATT Marginal Hazard-Ratio
problem Estimating ATT marginal hazard-ratio in externally controlled survival trials
method Machine-learning-assisted generalized entropy calibration for IPW Cox regression
result Reduces bias, increases efficiency, and improves coverage
Adapts bandit algorithms for online survival analysis under Cox PH model.
problem Online survival analysis challenges in a bandit framework.
method Adapts three bandit algorithms to balance exploration and exploitation.
result Demonstrates sublinear regret bounds and effective learning of treatment policies.
The study examines Cox models for lifetime loan default risk, addressing biased estimates by incorporating recurrent events.
problem Ignoring recurrent default events in Cox models leads to biased and inaccurate PD estimates.
method Investigates and compares different Cox models (Andersen-Gill and Prentice-Williams-Peterson) for lifetime loan default risk.
result The Andersen-Gill model underperforms compared to the Prentice-Williams-Person model and the time to first default model.
Flexible Cox model for time-dependent covariates with complex sparsity patterns.
problem Lack of flexibility in enforcing specific sparsity patterns in time-dependent Cox models.
method Proposes a flexible framework for variable selection in time-dependent Cox models, accommodating complex selection rules.
result Achieves accurate estimation with low false alarm rates for complex covariate structures.
Federated Cox model handles non-proportional hazards in siloed data.
problem Handling non-proportional hazards in federated healthcare data.
method Developed a federated Cox model that relaxes proportional hazards assumption.
result Federated model performs similarly to standard models on clinical datasets.
Interpretable survival analysis improves heart failure risk prediction.
problem Improving heart failure risk prediction using survival analysis.
method Survival stacking, ControlBurn, Explainable Boosting Machines.
result Achieves state-of-the-art performance and provides novel insights.
SurvLIME explains survival models by approximating them with Cox models.
problem Explaining complex survival models in machine learning.
method Applies Cox proportional hazards model to approximate survival model locally.
result Demonstrates efficiency through numerical experiments.
Proposes isotonic regression for calibrating Deep Cox models' survival probabilities.
problem Poor calibration of Deep Cox models' survival probabilities.
method Isotonic regression for post hoc calibration of Deep Cox models.
result Establishes favorable theoretical guarantees and demonstrates empirical effectiveness.
Study compares LSTM, Transformer, and Mamba for bladder cancer recurrence analysis.
problem Complex time-dependent data in bladder cancer recurrence analysis.
method Evaluation of LSTM, Transformer, and Mamba models using Cox proportional hazards model.
result LSTM-Cox model outperforms Transformer-Cox and Mamba-Cox models in prediction accuracy.
A new method for federated survival analysis using Cox models.
problem Non-separability of Cox PH model loss function in federated learning.
method Discrete-time Cox model, separable loss function, federated learning.
result Improved performance and communication efficiency compared to previous methods.
Abstract: Tangent categories get a Cartan calculus with scalar multiplication by a commutative ring.
problem Constructing a Cartan calculus in tangent categories.
method Define scalar multiplication by a commutative ring object R to equip tangent bundles with R-module structure. result Every object in tangent categories carries a Cartan calculus of Lie-Rinehart forms.
Proves tropical Hodge theory for smooth projective varieties, conditional on Laplacian regularity.
problem Proving log-concavity of characteristic polynomials of matroids.
method Combinatorial approach, conditional proof of Kähler package.
result Conditional proof of Kähler package for tropical cohomology.
The spectral energy distribution (SED) is a relatively easy way for astronomers to distinguish between different astronomical objects such as galaxies, black holes, and stellar objects. By comparing the observations from a source at different frequencies with template models, astronomers are able to infer the type of t…
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.
Study improves Cox model for predicting stock trading signs using Japanese market data.
problem Improving Cox model for predicting stock trading signs using Japanese market data.
method Added new covariates and used high-frequency trading data for 222 Nikkei 225 stocks.
result Cox-type model performs well in Japanese market and identifies key factors for accurate estimation.
Study adaptive sensing of Cox processes using posterior sampling and positive bases.
problem Adaptive sensing of Cox point processes with intensity function modeling.
method Model intensity function as truncated Gaussian process in positive basis, use Langevin dynamics and posterior sampling.
result Demonstrated improved sensing compared to classical Bayesian experimental design.
The Cox proportional hazards model is ubiquitous in the analysis of time-to-event data. However, when the data dimension p is comparable to the sample size N, maximum likelihood estimates for its regression parameters are known to be biased or break down entirely due to overfitting. This prompted the introduction of …
Paper extends multi-task Gaussian Cox processes for heterogeneous tasks.
problem Modeling multiple heterogeneous correlated tasks jointly.
method Data augmentation and mean-field approximation for non-conjugate Bayesian inference.
result Demonstrates improved performance and inference on synthetic and real data.