Study geometric flows with varying parameters and prove continuous dependence.
problem Continuous dependence of flows on parameters in geometric settings.
method Derived suitable topologies for vector fields and flows, proved new continuous dependence.
result Proved continuous dependence of flows on parameters in a general topological space.
Training-free model learns SDE dynamics without training, accelerating parameter studies.
problem High computational cost of simulating parameter-dependent SDEs.
method Training-free conditional diffusion model with joint kernel-weighted Monte Carlo estimator.
result Accurate approximation of conditional distributions across varying parameter values.
Deep learning estimates time-varying Markov model parameters.
problem Estimating time-dependent parameters in Markov models.
method Reframes parameter estimation as an optimization problem using maximum likelihood.
result Real solution close to SDE with neural network-derived parameters under specific conditions.
We study the Euler-Lagrange equations for a parameter dependent G-invariant Lagrangian on a homogeneous G-space. We consider the pullback of the parameter dependent Lagrangian to the Lie group G, emphasizing the special invariance properties of the associated Euler-Poincaré equations with advected parameters.
Mathematical models with time dependent parameters are of great interest in financial Mathematics because they capture real life scenarios in the financial market. In this study, via the Lie group technique, we analyse evolution-type equations with time dependent parameters and give the general symmetry structure of th…
FNFs model parameter-dependent densities by combining a fixed flow with a polynomial parameter-dependent transformation.
problem Learning a separate flow for every parameter configuration is intractable.
method Factorizable Normalizing Flows (FNFs) represent the parameter-dependent density as a fixed flow for a reference configuration and a learnable polynomial transformation factorized over parameters.
result FNFs enable the recovery of the combined effect of multiple parameters without sampling their joint space, providing a scalable and interpretable solution.
Develops black-box methods to estimate parameters of complex models.
problem Lack of efficient methods to produce simulations for complex statistical models.
method Pre-training deep neural networks on extensive simulated databases for well-structured likelihoods. Iterative algorithm for other complex dependencies.
result Successfully estimates and quantifies uncertainty of parameters from non-Gaussian models.
New findings on Malgrange-Galois groupoid for Painlevé VI equation parameters.
problem Understanding transformations preserving specific forms for Painlevé VI equation.
method Computed Malgrange-Galois groupoid for Painlevé VI family with all parameters.
result Solutions of Painlevé VI do not satisfy new partial differential equations.
Unified GP model optimizes hyperparameters with conditional dependence.
problem Efficient tuning of hyperparameters in neural networks.
method Unified Bayesian optimization framework based on a new Gaussian process (GP) model.
result Higher prediction accuracy and better optimization efficiency observed.
Extends Ho-Lee model for time-dependent parameters.
problem Fixes limitations of the Ho-Lee model.
method Introduces a more flexible no-arbitrage condition.
result Resolves a drawback of the Ho-Lee model.
NeuroMemFPP uses LSTM to estimate FPP parameters with high accuracy.
problem Estimating parameters of fractional Poisson process with memory and long-range dependence.
method Recurrent Neural Network (RNN), specifically Long Short-Term Memory (LSTM), for parameter estimation.
result The LSTM-based approach reduces MSE by about 55.3% compared to traditional MOM method.
Estimates matrix trace optimization with statistical learning theory.
problem Optimizing trace of parameter-dependent matrices.
method Monte Carlo estimator with bounds derived from epsilon nets and generic chaining.
result Predicts small sampling amount for matrices with small off-diagonal mass.
Estimates dependent parameters using Markovian dependence with shrinkage.
problem Estimating dependent parameters from a hidden Markov model.
method Developed a novel non-parametric shrinkage algorithm combining Tweedie-based ideas and efficient state estimation.
result Superior performance compared to non-shrinkage methods in hidden Markov models.
Path integral method calculates PDBS option prices with time-dependent parameters.
problem Pricing proportional double-barrier step options with time-dependent interest rates and volatilities.
method Path integral method applied to a quantum mechanical analogy of barrier options.
result Derivation of pricing kernel for PDBS options with time-dependent parameters.
Develops SQR models for multivariate exponential families allowing positive dependencies.
problem Lack of positive dependencies in multivariate graphical models for exponential and Poisson distributions.
method Introduces Square Root Graphical Models (SQR) derived from univariate exponential distributions, with methods for parameter estimation and likelihood approximation.
result Allows for arbitrary positive and negative dependencies in multivariate distributions without constraints on parameter values.
The paper explores how polynomial roots and operator eigenvalues change with parameters.
problem How do roots of polynomials and eigenvalues of operators vary with parameter changes?
method Analyzes parameter dependence of polynomials and linear operators, covering real analytic to differentiable of finite order.
result Definitive optimal results for perturbation theory of polynomials and linear operators, including hyperbolic polynomials.
Generative model captures complex dependence in financial data.
problem Complex dependence structure in business and financial data.
method Multivariate generative model with heterogeneous and asymmetric tail dependence.
result Novel moment learning algorithm for scalable parameter estimation.
Tensor trains speed up option pricing for multi-asset options.
problem Speeding up option pricing for multi-asset options.
method Tensor train learning algorithms to compress functions with parameter dependence.
result The proposed method outperforms Monte Carlo-based pricing in computational complexity.
Estimates parameters of high-dimensional Bernoulli autoregressive process with long-range dependence.
problem Estimating parameters of a multivariate Bernoulli process with auto-regressive feedback in high dimensions.
method Proposes and analyzes an ℓ1-regularized maximum likelihood estimator (MLE) under the assumption of approximate sparsity. result Derives precise upper bounds on mean-squared estimation error.
This paper presents a methodology to introduce time-dependent parameters for a wide family of models preserving their analytic tractability. This family includes hybrid models with stochastic volatility, stochastic interest-rates, jumps and their non-hybrid counterparts. The methodology is applied to Heston's model. A …
This letter assesses model risk in credit capital requirements and finds substantial tail risk.
problem Uncertainty in the probability of default and loss-given-default parameters in credit capital requirements.
method Models estimation risk in a simple way, analyzing two datasets and testing parameter dependency.
result Parameter dependency significantly increases tail risk in capital requirements, requiring substantial increases in regulatory capital.
Study path-dependent affine models under uncertain parameters for financial applications.
problem Valuation of path-dependent financial derivatives under parameter uncertainty.
method Developed path-dependent setting for value function, established dynamic programming principle, approximated functional derivatives with neural networks.
result Efficient numerical methods for valuation of complex financial derivatives under parameter uncertainty.
The standard intensity-based approach for modeling defaults is generalized by making the deterministic term structure of the survival probability stochastic via a common jump process. The survival copula of the vector of default times is derived and it is shown to be explicit and of the functional form as dealt with in…
A novel stepwise VI method using vine copulas for complex latent dependence.
problem Modeling complex latent dependence structures in probabilistic models.
method Stepwise estimation of vine copula parameters using Rényi divergence and a stopping criterion.
result Our method outperforms mean-field VI and is more parsimonious in complex applications.
Deformations of Dubrovin's Hurwitz Frobenius manifolds are constructed. The deformations depend on g(g+1)/2 complex parameters where g is the genus of the corresponding Riemann surface. In genus one, the flat metric of the deformed Frobenius manifold coincides with a metric associated with a one-parameter family of…
Maxout networks study gradients and propose initialization strategies.
problem Complexity in input-output Jacobian distribution complicates stable parameter initialization.
method Obtained bounds on moments of gradients and formulated initialization strategies.
result Parameter initialization strategies improve training of deep maxout networks.
Efficient semi-analytic methods for pricing double barrier options with time-dependent parameters.
problem Pricing and calibration of double barrier options with time-dependent parameters.
method Two approaches: General Integral transform method and Heat Potential method.
result Semi-analytic techniques are more efficient for pricing double barrier options than traditional numerical methods.
A defining feature of non-stationary systems is the time dependence of their statistical parameters. Measured time series may exhibit Gaussian statistics on short time horizons, due to the central limit theorem. The sample statistics for long time horizons, however, averages over the time-dependent parameters. To model…
Software aids in estimating speciation parameters using trait-dependent models.
problem Lack of robust software to estimate numerous speciation parameters.
method Approximate Bayesian Computation approach implemented in R package pcmabc.
result Software allows estimation of parameters of trait-dependent speciation processes.
SALT models combine ARHMM and SLDS for efficient, interpretable time-series analysis.
problem Efficient modeling of systems with time-varying dynamics and long-range dependencies.
method Switching autoregressive low-rank tensor models parameterized with a low-rank factorization.
result SALT models provide a balance of interpretability and efficiency, outperforming ARHMMs and SLDSs.
In this paper new analytical and numerical approaches to valuating path-dependent options of European type have been developed. The model of stochastic volatility as a basic model has been chosen. For European options we could improve the path integral method, proposed B. Baaquie, and generalized it to the case of path…
New model captures insurance risk dependencies efficiently.
problem Dependence modeling in sparse time series of insurance claims.
method Comb-Bernoulli model bridging Lévy copulas and zero-mixed models.
result Model enables tractable simulation, likelihood evaluation, and parameter estimation.
The paper models the dependence between lifetimes of married couples using copulas.
problem The independence assumption in bivariate lifetime modeling for life insurance products is often violated.
method Copula approach with age difference and gender of the elder partner as arguments of the dependence parameter. Maximum likelihood techniques for parameter estimation.
result The correlation between lifetimes decreases with age difference and is higher when the husband is older.
This work presents an exact solution to the generalized Heston model, where the model parameters are assumed to have linear time dependence The solution for the model in expressed in terms of confluent hypergeometric functions.
Paper improves Li-Yau gradient estimates for heat equation solutions.
problem Improving Li-Yau gradient estimates for heat equation solutions.
method Obtained new Li-Yau type gradient estimates with time-dependent parameters.
result Improved Li-Yau gradient estimates for heat equation solutions.
Smoothness analysis of adversarial training reveals L∞ constraints cause more non-smoothness.
problem Non-smoothness of adversarial training loss function.
method Analyzed the smoothness of adversarial training loss function using optimal attacks for model parameters.
result The L∞ constraint causes more non-smoothness than L2 constraint. Estimates system parameters from a single observation using kernel-based score.
problem Estimating parameters of a dynamical system from a high-dimensional signal.
method Kernel-based score to compare temporal dependencies between signal and model.
result Accuracy and efficiency demonstrated on chaotic systems.
Using the framework of factor models, we establish the general expression of the coefficient of tail dependence between the market and a stock (i.e., the probability that the stock incurs a large loss, assuming that the market has also undergone a large loss) as a function of the parameters of the underlying factor mod…
Bayesian methods improve tracking multiple objects through dynamic dependencies.
problem Tracking multiple objects with time-varying cardinality and unordered measurements.
method Employing Bayesian nonparametric models, specifically dependent Dirichlet and Pitman-Yor processes, for state estimation and Monte Carlo sampling for trajectory learning.
result The proposed methods outperform existing algorithms in estimating the time-varying number of objects and identifying object associations.
New analysis shows black-box methods outperform action space methods in certain scenarios.
problem Comparing black-box methods vs. action space methods in exploration.
method Theoretical analyses and empirical comparisons of simple methods on various problems.
result Complexity of exploration in parameter space depends on parameter space dimensionality, while action space complexity depends on both action space and horizon length.
Diffeomorphism freedom induces a gauge dependence in the theory of spacetime perturbations. We derive a compact formula for gauge transformations of perturbations of arbitrary order. To this end, we develop the theory of Taylor expansions for one-parameter families (not necessarily groups) of diffeomorphisms. First, we…
Atlas models are systems of Ito processes with parameters that depend on rank. We show that the parameters of a simple Atlas model can be identified by measuring the variance of the top-ranked process for different sampling intervals.
The paper studies estimation of parameters of diffusion market models from historical data. The standard definition of implied volatility for these models presents its value as an implicit function of several parameters, including the risk-free interest rate. In reality, the risk free interest rate is unknown and need …
Investigates ways to train larger models with fewer resources, finding that test loss depends only on the actual number of trainable parameters.
problem Training larger models for cheaper under hardware constraints.
method Emulates an increase in effective parameters using frozen random parameters or fast structured transforms.
result Scaling laws cannot be deceived by spurious parameters; test loss depends only on the actual number of trainable parameters.
The study improves Poincaré and log-Sobolev inequalities on hyperbolic spaces.
problem Improving Poincaré and log-Sobolev inequalities on hyperbolic spaces.
method Establishing scale-dependent Poincaré-Hardy type identities and choosing suitable parameters, potentials, and vector fields.
result Derives new versions and substantially improves existing inequalities.
Develops a bi-variate stochastic framework to model mortality and interest rates with long-range dependence.
problem Captures long-range dependence and instantaneous correlation in mortality and interest rates.
method Mixed fractional Brownian motions, analytical solutions, risk-neutral measure, sequential parameter estimation.
result Explicit pricing of zero-coupon bonds and extreme mortality bonds, practical implications for pricing and risk management.
Empirical study on hyperparameters affecting RL generalization.
problem Understanding how hyperparameters affect RL generalization across different domains.
method Empirical analysis of hyperparameters including architecture, regularization, and RL-dependent variables.
result Complex and interdependent relationships between hyperparameters and generalization performance.
Direct approach for handling contextual bandits with latent state dynamics.
problem Handling contextual bandits with latent state dynamics, especially when rewards depend on posterior probabilities of hidden states.
method Direct reduction to standard linear contextual bandits, extended analysis of HMM parameters, periodic update of reward-model parameters.
result Periodic update of reward-model parameters allows handling complex dependencies in hidden states.