This paper derives the non-analytic solution to the Fokker-Planck equation of fractional Brownian motion using the method of Laplace transform. Sequentially, by considering the fundamental solution of the non-analytic solution, this paper obtains the transition probability density function of the random variable that i…
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169,181 papers · 148 categories
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48 results for “Non-analytical Models”
We analyze the slope gap distribution of Veech surfaces, finding finite non-analytic points and quadratic tail decay.
problem Understanding the slope gap distribution of Veech surfaces.
method Explicit parameterization of a Poincaré section to the horocycle flow, finiteness result for the first return map.
result The limiting gap distribution of slopes of saddle connections on Veech surfaces is piecewise real-analytic with finitely many points of non-analyticity and has quadratic tail decay.
Design of Experiments for Model Discrimination Hybridising Analytical and Data-Driven Approachesstat.AP
Develops a method to discriminate between competing models using Gaussian process surrogates.
problem Discriminating between competing models when data is insufficient and models are non-analytical.
method Introduces Gaussian process surrogates to extend design of experiments methods to non-analytical models.
result Extends design of experiments methods to non-analytical models in a computationally efficient manner.
Analytic networks with bounded coefficients can't outperform polynomial approximations.
problem Approximation limits of neural networks with analytic activation functions under coefficient constraints.
method Deterministic analysis using comparison argument and Bernstein-type estimates.
result Networks with analytic activation functions and controlled coefficients cannot outperform classical polynomial approximation rates on non-analytic targets.
Tensor networks improve integration accuracy for high-dimensional problems.
problem Integration of high-dimensional functions with exponential convergence.
method Regression-free tensor network representations for integration.
result Exponential convergence achieved for non-analytic integrands.
ED-VAE improves VAEs by explicitly including entropy components in ELBO.
problem Limitations of traditional VAEs with ELBO in generating high-quality samples and interpreting latent spaces.
method Introduces ED-VAE, a re-formulation of ELBO that includes entropy and cross-entropy components.
result Significantly enhances model flexibility and improves interpretability and generative performance.
The strong unique continuation property for Einstein metrics can be concluded from the well-known fact that Einstein metrics are analytic in geodesic normal coordinates. Here we give a proof of the same result that given two Einstein metrics with the same Ricci curvature on a fixed manifold, if they agree to infinite o…
Financial Friction and Multiplicative Markov Market Gamecond-mat.stat-mech
We study long-term growth-optimal strategies on a simple market with linear proportional transaction costs. We show that several problems of this sort can be solved in closed form, and explicit the non-analytic dependance of optimal strategies and expected frictional losses of the friction parameter. We present one der…
The Local Isometric Embedding of Two-Metrics of Low Differentiability in Euclidean Three Spacemath.DG
Proves local isometric embedding of low-differentiability metrics in 3D space.
problem Isometric embedding of metrics of low differentiability in Euclidean 3-space.
method Simplified notation, geodesic and level parameters, solutions of initial value problems for first order non-linear PDEs, classical linear algebraic systems.
result Local isometric embedding exists for metrics of C1 differentiability.
Study of zeta functions for Anosov flows in 3D confirms Fried conjecture.
problem Relating Reidemeister torsion and zeta function values for Anosov flows.
method Analyzing twisted Ruelle zeta functions for smooth Anosov vector fields.
result Fried conjecture confirmed for Anosov flows in 3D and near geodesic flows.
Probabilistic Solutions to Differential Equations and their Application to Riemannian Statisticsstat.ML
We study a probabilistic numerical method for the solution of both boundary and initial value problems that returns a joint Gaussian process posterior over the solution. Such methods have concrete value in the statistics on Riemannian manifolds, where non-analytic ordinary differential equations are involved in virtual…
OccamNet finds interpretable symbolic fits to data efficiently.
problem Complex neural models extrapolate poorly and are hard to interpret.
method Samples functions, biases towards better fits, and uses cross-entropy matching.
result Outperforms state-of-the-art symbolic regression methods on real-world datasets.
Interpretable meta-learning for physical systems reduces computational costs and improves interpretability.
problem Challenges in learning from heterogeneous experimental data.
method Affine structure learning model for multi-environment generalization.
result Proves the model can identify physical parameters and demonstrates competitive performance.
We propose an analytically tractable variation of the minority game in which rational agents use probabilistic strategies. In our model, agents choose between two alternatives repeatedly, and those who are in the minority get a pay-off 1, others zero. The agents optimize the expectation value of their discounted fu…
Model explains asset price dynamics, defaults, and market crashes via non-linear dynamics.
problem Understanding asset price dynamics, defaults, and market crashes in financial markets.
method Proposes a non-equilibrium model incorporating market frictions and feedback mechanisms.
result The QED model produces non-linear dynamics, broken scale invariance, and corporate defaults.
SRF improves kernel approximation and GP regression performance.
problem Efficient kernel approximation and Bayesian kernel learning in large-scale regression problems.
method Stein variational gradient descent to generate high-quality random features and approximate spectral measure posteriors.
result SRF outperforms traditional approaches in kernel approximation and GP regression.
Fast approximate inference for non-Gaussian data.
problem Efficient inference for non-Gaussian data.
method Laplace Matching for fast approximate inference in latent Gaussian models.
result Achieves high approximation quality with low computational cost.
Dropout schedules can be optimized to significantly reduce model test loss.
problem Improving model performance in neural networks.
method Developed a mean-field theory of dropout at the edge of chaos, proposing front-loaded dropout schedules.
result Front-loaded dropout schedules reduce test loss by 18-35% over constant dropout.
The most likely common causephysics.data-an
New method identifies common cause in causal insufficiency, revealing complex phase transitions.
problem Identifying common cause in causal insufficiency with observed joint probability.
method Generalized maximum likelihood method, closely related to maximum entropy principle.
result Identifies consistent common cause that aligns with the common cause principle.
A new method combines ANN and Laplace for fast Bayesian inference in ODE models.
problem Bayesian inference for ODE systems with non-analytical solutions is computationally expensive.
method Hybrid approach using ANN for tractable likelihood and Laplace approximation.
result Effective posterior inference with improved computational cost compared to traditional methods.
Sharp threshold found for metric uniqueness in Riemannian Calderón-type problems.
problem Determining metrics uniquely from Dirichlet-to-Neumann maps in Riemannian Schrödinger problems.
method Adaptation of Lassas-Uhlmann reconstruction theorem and novel Gevrey space techniques.
result Analytic metrics uniquely determine the metric up to boundary-preserving diffeomorphisms, but non-analytic metrics are not uniquely determined.
Automatic trajectory recognition in Active Target Time Projection Chambers data by means of hierarchical clusteringphysics.ins-det
New algorithm clusters particle tracks for better trajectory recognition in noisy data.
problem Challenging automatic reconstruction of particle tracks from Active Target Time Projection Chambers data.
method Non-parametric algorithm based on hierarchical clustering of point triplets.
result Algorithm identifies and isolates non-analytical particle tracks with high recall and precision.
Compact Lorentzian manifolds embed in Ricci-flat spaces.
problem Embedding Lorentzian manifolds in Ricci-flat semi-Riemannian spaces.
method Reviewing relevant results, constructing isometric embeddings for compact Lorentzian manifolds in Ricci-flat semi-Riemannian spaces.
result Any compact Lorentzian manifold with specific Sobolev space properties admits an isometric embedding in a Ricci-flat semi-Riemannian manifold.
This paper improves the approximation of machine learning models by transforming them to better fit locally -integrable functions.
problem The approximation quality of machine learning models can degrade outside compact subsets of the domain.
method Introduces a canonical transformation to enhance the local -type universal approximation property.
result The transformed model class, , is dense in a finer topology , improving expressibility.
On Two Theorems of Darbouxmath.AP
The paper proves two theorems about solutions to certain PDE systems.
problem Finding local existence and uniqueness of solutions to specific types of first order PDE systems.
method Picard iteration for determined systems, and a proof for overdetermined systems under integrability conditions.
result Precise formulations and proofs of the theorems, addressing continuity and regularity assumptions.
Study develops time-continuous models and probabilistic descriptions for agent-based economic market models.
problem Formulating and describing agent-based economic market models in a time-continuous and probabilistic manner.
method Derived time-continuous formulations, discussed impact of time-scaling, proved stability, presented probabilistic descriptions using kinetic theory.
result Time-continuous formulations and probabilistic descriptions for agent-based economic market models.
Hybrid model combines interpretable and black-box models for better transparency and performance.
problem Balancing interpretability and predictive performance in machine learning models.
method Proposes a Hybrid Predictive Model (HPM) integrating an interpretable model with a black-box model, using principled objective functions and customized training algorithms.
result Hybrid models achieve an efficient trade-off between transparency and predictive performance.
The paper introduces BCART models for aggregate claim amount, improving frequency-severity and joint modeling.
problem Modeling aggregate claim amount with frequency-severity and joint dependencies.
method Developed three types of BCART models: frequency-severity, sequential, and joint models. Used various distributions for claim severity data.
result Weibull distribution outperforms gamma and lognormal for right-skewed, heavy-tailed claim severity data.
Boosts generative models by combining multiple meta-models.
problem Challenges in creating a single generative model that accurately represents complex data.
method Cascades multiple meta-models (like RBM and VAE) to create a stronger generative model.
result Derives a decomposable variational lower bound for training and evaluating the boosted model.
The paper uses model-based trees to create interpretable surrogate models for complex machine learning models.
problem Interpreting complex machine learning models.
method Using model-based trees to partition feature space and create interpretable models.
result Model-based trees generate optimal surrogate models that balance interpretability and performance.
Study on limits of community detection in various network models.
problem Limits of community detection in network models.
method Analysis of several network models including Stochastic Block Model, Exponential Random Graph Model, Latent Space Model, Directed Preferential Attachment Model, and Directed Small-world Model.
result Information-theoretic limits for recovery of node labels in network models.
Gauge Flow Modelscs.LG
Gauge Flow Models use a learnable Gauge Field in Generative Flow Models.
problem Improving generative model performance.
method Integrates a learnable Gauge Field into Flow ODEs.
result Gauge Flow Models outperform traditional Flow Models in Flow Matching experiments.
The study examines how model predictions hold up under model extensions.
problem Model predictions may not be robust under model extensions, limiting their applicability.
method The study uses causal ordering to assess robustness of qualitative model predictions and characterizes model extensions that preserve predictions.
result Conditions and techniques are provided to assess robustness of model predictions under model extensions.
MALC combines interpretable linear models with black-box models for better predictions and transparency.
problem Combining interpretability with black-box models for better predictions.
method Formulates MALC as a convex optimization problem and uses accelerated proximal gradient method for training.
result MALC provides an efficient frontier balancing prediction accuracy and transparency.
Revises Bayesian model averaging for foundation models.
problem Ensemble pre-trained and lightly-finetuned foundation models for improved classification performance.
method Introduces trainable linear classifiers and computationally cheaper model averaging scheme (OMA).
result Ensembled models can better predict on various datasets.
Paper introduces symmetric divergence link models for probability distributions.
problem Symmetric divergence measures for probability distributions.
method Two general classes of link models: one for survival functions and another for cumulative probability distribution functions.
result Advantages of symmetric divergence measures over asymmetric measures for model averaging and feature assessment.
The paper tests stock return models and uses LSTM to predict stock returns.
problem Validating stock return models and predicting stock returns.
method Used Fama-French three-factor, four-factor, and five-factor models; also used LSTM model.
result Fama-French five-factor model shows better validity for stock returns.
New method to handle credit portfolio model uncertainties.
problem Model risk in credit portfolio models.
method Demonstrates comprehensive yet easy-to-implement approach to uncertainty in model parameters.
result Comprehensive method to deal with model uncertainties.
A new neural network model predicts multi-symbol tokens over multiple scales.
problem Language modeling with improved flexibility and performance.
method A learned dictionary of multi-symbol tokens using BPE compression.
result The model outperforms LSTM on language modeling tasks, especially for smaller models.
Researchers review challenges in interpreting additive models, especially neural additive models.
problem Challenges in interpreting additive models, particularly neural additive models.
method Review of generalized additive models and discussion of nonidentifiability.
result Challenges in claiming interpretability or suitability for safety-critical applications of additive models.
Distill-and-Compare audits black-box models by training transparent models to mimic them.
problem Auditing proprietary, opaque black-box risk scoring models.
method Model distillation and comparison of transparent student models to black-box models.
result Identifies missing features in black-box models, improving transparency.
Proposes a decision-theoretic approach for enhancing model interpretability in Bayesian frameworks.
problem Challenges the traditional approach of restricting model structure for interpretability in Bayesian frameworks.
method Introduces an interpretability utility function and a two-step method involving a reference model and a proxy model.
result Demonstrates that the proposed method generates more accurate models with the same level of interpretability.
Novel hybrid modeling combines ML and physics for real-time diagnosis.
problem Real-time diagnosis of complex systems.
method Combines machine learning and physics-based models to create reduced-order models.
result Generated models are two orders of magnitude simpler, improving efficiency.
CRS model improves ranking data modeling with theoretical guarantees.
problem Lack of rich, multimodal models for ranking data.
method Contextual Repeated Selection (CRS) model for multimodal ranking data.
result CRS model significantly outperforms existing methods in various ranking contexts.
Sigma models linked to Gross-Neveu models via quiver varieties.
problem Understanding the relationship between sigma models and Gross-Neveu models.
method Exploring the mathematical correspondence between sigma models and Gross-Neveu models, including their geometric and trigonometric/elliptic deformations.
result Sigma models are mathematically equivalent to Gross-Neveu models under certain conditions.
Simple models are preferred over complex models, but over-simplistic models could lead to erroneous interpretations. The classical approach is to start with a simple model, whose shortcomings are assessed in residual-based model diagnostics. Eventually, one increases the complexity of this initial overly simple model a…
Matryoshka hides secret models in a carrier model, achieving high capacity and robustness.
problem Stealing functionality of private ML data by hiding models in a carrier model.
method Parameter sharing approach exploiting the learning capacity of the carrier model.
result Hides a 26x larger secret model or 8 secret models in the carrier model.
Eigen-stratified models reduce model size and improve performance.
problem Large model size in Laplacian-regularized stratified models.
method Formulate eigen-stratified models with linear combinations of bottom eigenvectors of the graph Laplacian.
result Significant reduction in model size with eigen-stratified models.