Researchers formalize PD and PFI to relate them to data generating process.
problem Lack of theory linking PD and PFI to data generating process.
method Formalize PD and PFI as estimators of ground truth estimands, account for model variance with learner-PD and learner-PFI.
result PD and PFI estimates deviate from ground truth due to statistical biases, model variance, and Monte Carlo approximation errors.
The paper stabilizes PD term structures under forecast uncertainty using a Kalman filter with an anchored observation model.
problem Stable estimation of lifetime PDs under forecast uncertainty.
method Reformulated in state-space framework, introduced an anchored observation model.
result Asymptotic stochastic stability of error dynamics, leading to smoother projections.
A reinforcement learning framework evolves persistence diagrams on PD space for stochastic dynamics.
problem Stochastic modeling and evolution of persistence diagrams (PDs) for topological analysis.
method Reinforcement learning framework for PD space, evolving diagrams through topology-aware local edit operations.
result Established conditions for geometric ergodicity of Markov chains on PD space, yielding unique stationary laws.
Every PD3-complex bounds a PD4-pair.
problem Bounding PD3-complexes with PD4-pairs. method Constructing PD4-pairs from PD3-complexes. result Every PD3-complex bounds a PD4-pair (Z,P). Paper presents a method for estimating long-term PDs with incomplete data.
problem Estimating long-term PDs with limited and incomplete historical data.
method Single risk factor approach for simultaneous calibration of PDs across sub-portfolios.
result Method yields long-term PDs without requiring complete historical data.
PD_3-groups split as HNN extensions, revealing homology class properties.
problem Understanding PD_3-groups splitting as HNN extensions.
method Analyzing PD_3-groups splitting as HNN extensions and examining homology classes.
result The Poincaré dual of the homology class of a PD_3-group in the kernel of an epimorphism is revealed.
A new tree-based estimator, FastPD, efficiently estimates PD functions for machine learning models.
problem Efficiently estimating Partial Dependence functions for machine learning models.
method Proposes a new tree-based estimator, FastPD, to estimate PD functions.
result FastPD consistently estimates the desired population quantity and improves complexity from quadratic to linear.
The study of PD3-pairs extends results for aspherical 3-manifolds.
problem Understanding PD3-pairs with aspherical ambient spaces. method Attaching 1-handles to PD3-pairs with aspherical ambient space and π1-injective boundary. result There are only finitely many PD3-pairs with a specific group property. If the probability of default parameters (PDs) fed as input into a credit portfolio model are estimated as through-the-cycle (TTC) PDs stressed market conditions have little impact on the results of the capital calculations conducted with the model. At first glance, this is totally different if the PDs are estimated as…
Proves Tits alternative for specific PD(3) groups.
problem Tits alternative for PD(3) groups. method Proving Tits alternative for almost coherent PD(3) groups. result Almost coherent PD(3) groups contain rank 2 free groups. Study pro-p completions of orientable PD_n groups, proving best results in three cases.
problem Understanding pro-p completions of orientable PD_n groups. method Examined four cases of orientable PD_3-groups and some PD_n groups (n≤5), providing examples and proving best results in three cases.
result Best results in three out of four cases of orientable PD_3-groups.
Paper proposes a simple method for deriving lifetime PD forecasts.
problem Deriving accurate lifetime PD forecasts with minimal data.
method Classical asset-based credit portfolio model with autoregressive process for systematic factor, Bayesian methodology for macroeconomic judgments.
result Endogenous derivation of lifetime PD forecasts without exogenous macroeconomic forecasts.
A new kernel for persistence diagrams using Sliced Wasserstein distance.
problem Incorporating persistence diagrams into machine learning pipelines.
method Proposes a new kernel for persistence diagrams based on the Sliced Wasserstein approximation of the Wasserstein distance, demonstrating its stability and discriminative power.
result The proposed kernel is stable and discriminative, outperforming existing kernels on various benchmarks.
Tutorial on interpreting SPECT images for PD recognition using AI.
problem Difficulty in interpreting complex DL models for clinical use.
method Evaluation of six interpretation methods on four DCNN architectures.
result Guided backpropagation and SHAP methods are suitable for PD recognition.
Method predicts motor symptoms of Parkinson's disease from daily activities.
problem Objective monitoring of Parkinson's disease symptoms.
method Multi-layer Gaussian process models for three types of movement abnormalities.
result Strong agreement between model predictions and clinical annotations.
The paper classifies PD_4-complexes based on their fundamental group properties.
problem Understanding the structure of PD_4-complexes based on their fundamental group properties.
method Analyzing the fundamental group and its modules to classify PD_4-complexes.
result The classification of PD_4-complexes based on their fundamental group properties.
We define partial differential (PD in the following), i.e., field theoretic analogues of Hamiltonian systems on abstract symplectic manifolds and study their main properties, namely, PD Hamilton equations, PD Noether theorem, PD Poisson bracket, etc.. Unlike in standard multisymplectic approach to Hamiltonian field the…
New model forecasts stock market volatility better than existing methods.
problem Forecasting volatility in stock markets.
method Combines HAR model with path-dependent volatility models.
result HAR-PD model family outperforms basic HAR model family in volatility forecasting.
The intention with this paper is to provide all the estimation concepts and techniques that are needed to implement a two-phases approach to the parametric estimation of probability of default (PD) curves. In the first phase of this approach, a raw PD curve is estimated based on parameters that reflect discriminatory p…
In this paper we formalize a combinatorial object for describing link diagrams called a Planar Diagram Code. PD-codes are used by the KnotTheory Mathematica package developed by Bar-Natan, et al. We present the set of PD-codes as a stand alone object and discuss its relationship with link diagrams. We give an explicit …
Extends characterization of PD3-pairs with aspherical boundaries to those with spherical boundaries.
problem Characterizing fundamental triples of PD3-pairs with boundary components of different types. method Extends Turaev and Bleile's work by relaxing the π1-injectivity hypothesis and considering pairs with spherical boundary components. result Characterization of fundamental triples for PD3-pairs with spherical boundary components and c.d.π1(P)≤2. Paper exposes vulnerabilities in interpreting machine learning models using adversarial attacks on PD plots.
problem Vulnerability of permutation-based interpretation methods, particularly PD plots, to adversarial attacks.
method Adversarial framework to manipulate black-box models and produce deceptive PD plots.
result It is possible to hide discriminatory behaviors in machine learning models through interpretation tools like PD plots.
New framework for efficient PD averaging and clustering.
problem Challenges in averaging and clustering persistence diagrams.
method Reformulate PD metrics as optimal transport problems, leveraging recent computational advances.
result Scalable computations of PD barycenters and clustering on thousands of diagrams.
A model learns symptom-drug relations for PD patients.
problem Automatic prescription recommendation for Parkinson's Disease patients.
method Builds a dataset of PD symptoms and prescriptions, learns latent symptom space, uses alternating optimization.
result Effective in recommending suitable prescription drugs for new PD patients.
Unreduced PDs can perform similarly to reduced PDs in machine learning tasks.
problem Ignoring much of the information in persistence diagrams in machine learning pipelines.
method Developed methods to generate topological feature vectors from unreduced boundary matrices.
result Unreduced PDs can perform on par with, and sometimes outperform, fully-reduced PDs in machine learning tasks.
The study uses the Merton model to estimate PD and finds a phase transition affecting convergence speed.
problem Estimating the probability of default (PD) using limited historical data.
method Adopted the Merton model and analyzed phase transitions in default correlation.
result PD estimation converges slowly when temporal correlation decays by power law less than one.
Study extends Elkalla's work on subnormal subgroups to PD3-groups, but L2-Betti numbers need verification.
problem Verifying L2-Betti numbers for PD3-groups and group pairs. method Algebraic arguments extending Elkalla's work, but reliant on unproven L2-Betti number hypothesis. result Need further research on L2-Betti numbers for general PD3-groups. The risk of a credit portfolio depends crucially on correlations between the probability of default (PD) in different economic sectors. Often, PD correlations have to be estimated from relatively short time series of default rates, and the resulting estimation error hinders the detection of a signal. We present statist…
Develops a PD estimation model using Lévy-driven processes for credit risk.
problem Estimating Probability of Default under new IFRS 9 regulations.
method Lévy-driven Ornstein-Uhlenbeck process with multiple latent variables, Integral Equation and PIDE formulation.
result Existence of weak and strong solutions for PD function, numerical schemes developed.
Tutorial on estimating PD using survival analysis under IFRS 9.
problem Dynamic estimation of credit losses under IFRS 9.
method Discrete-time survival analysis for estimating PD.
result Development of a comprehensive tutorial and diagnostic measures.
We define an order relation among oriented PD4-complexes. We show that with respect to this relation, two PD4-complexes over the same complex are homotopy equivalent if and only if there is an isometry between the second homology groups. We also consider minimal objects of this relation.
Scaff-PD improves fairness and robustness in federated learning with reduced communication.
problem Improving fairness and robustness in federated learning with limited communication.
method Scaff-PD uses a family of distributionally robust objectives and an accelerated primal dual algorithm with bias-corrected steps.
result Scaff-PD achieves significant gains in communication efficiency and convergence speed while maintaining fairness and robustness.
PD curve calibration refers to the transformation of a set of rating grade level probabilities of default (PDs) to another average PD level that is determined by a change of the underlying portfolio-wide PD. This paper presents a framework that allows to explore a variety of calibration approaches and the conditions un…
Model quantifies systemic risk in financial networks using PD and contagion mechanisms.
problem Underestimation of capital needed for financial system stability.
method Dynamic PD model combining credit risk techniques and contagion mechanism on network of exposures.
result Systemic risk statistics and node contributions revealed through loss distribution.
Paper solves open question about non-positive kernels by decomposing them into PD kernels.
problem Can non-positive definite kernels be decomposed into the difference of two positive definite kernels?
method Introduced signed measure to transform positive decomposition into measure decomposition, providing a sufficient and necessary condition.
result First random features algorithm for unbiased estimation of non-positive kernels.
We show that the orientable double covering space of an indecomposable non-orientable PD3-complex has torsion free fundamental group.
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.
We show that if X is an indecomposable PD3-complex and π1(X)isthefundamentalgroupofareducedfinitegraphoffinitegroupsbutisnotvirtuallycyclicthenXisorientable,theunderlyinggraphisatree,alltheedgegroupsareZ/2Zandallbutatmostoneofthevertexgroupsisdihedraloforder2m…
A new model SIPS improves graph embedding by approximating non-PD similarities.
problem Improving neural network-based graph embedding by approximating non-positive definite similarities.
method Shifted Inner Product Similarity (SIPS) model that approximates Conditionally Positive Definite (CPD) similarities.
result SIPS significantly improves graph embedding without configuring the similarity function.
New method converts complex PDs into stable vectors for ML.
problem Complex structure of persistence diagrams makes them hard to use in ML.
method Persistence bag-of-words (BoW) for vectorizing PDs.
result Achieves state-of-the-art performance and speed in ML.
A new kernel for comparing persistence diagrams without approximation.
problem Lack of suitable kernels for comparing persistence diagrams.
method Persistence Fisher kernel based on Fisher information geometry.
result Proposes a positive definite kernel for persistence diagrams without approximation.
Intuitively, the default risk of a single borrower is higher when her or his assets and debt are denominated in different currencies. Additionally, the default dependence of borrowers with assets and debt in different currencies should be stronger than in the one-currency case. By combining well-known models by Merton …
Classifies pro-p PD2 pairs and builds a pro-p curve complex.
problem Classifying pro-p Poincaré duality pairs in dimension two. method Using classification of pro-p PD2 pairs to build a pro-p curve complex. result Established basic properties of the pro-p curve complex. Machine learning classifies Parkinson's Disease stages from walker sensors data.
problem Limited cost-effective methods for quantitatively assessing Parkinson's Disease stages.
method Machine learning applied to walker-mounted sensors data, feature selection methods compared.
result Feature selection method using ANOVA provides similar accuracy to full feature set and is clinically interpretable.
Paper proposes E/PD-Control for better neural network training.
problem Training efficiency and robustness of CNNs in online data flows.
method E/PD-Control combines feedback PD controller with exponential signal.
result Better learning efficiency and robustness demonstrated experimentally.
Machine learning aids in diagnosing Parkinson's disease with higher accuracy.
problem Subjectivity in traditional PD diagnosis methods and missed early symptoms.
method Machine learning applied to various data modalities for PD and control group classification.
result Machine learning methods show high potential for improving PD diagnosis.
A new model reduces rating transition matrix estimation errors for small portfolios.
problem Estimating rating transition matrices for small portfolios leads to unreliable and unstable predictions.
method A sparse structural model with three parameters that assumes an autoregressive mean-reverting ability-to-pay process.
result The model produces well-behaved transition probabilities, reducing statistical degrees of freedom and improving reliability.
Unified framework detects changes in complex system models.
problem Accurate identification of dynamic changes in simulation models.
method Combines machine learning and process-driven simulation modeling.
result Significantly improves change point detection accuracy.