This paper improves parameter estimation for autonomous systems with unmodeled dynamics.
problem Accurate parameter estimation for risk-aware autonomous systems with unmodeled dynamics.
method Spectral lines-based approach for estimating parameters of dynamic models, allowing deterministic unmodeled dynamics.
result The proposed method leads to non-asymptotic bounds on parameter estimation error, robust to unmodeled dynamics, and matches existing literature in ideal conditions.
This paper examines limitations of machine learning models in social systems.
problem Understanding and addressing the shortcomings of machine learning models in social applications.
method Structured overview of conceptual, procedural, and statistical limitations.
result Identification of failure points and ways to address them.
A semi-parametric, non-linear regression model in the presence of latent variables is introduced. These latent variables can correspond to unmodeled phenomena or unmeasured agents in a complex networked system. This new formulation allows joint estimation of certain non-linearities in the system, the direct interaction…
Successful human-robot cooperation hinges on each agent's ability to process and exchange information about the shared environment and the task at hand. Human communication is primarily based on symbolic abstractions of object properties, rather than precise quantitative measures. A comprehensive robotic framework thus…
This work presents a methodology to design trajectory tracking feedback control laws, which embed non-parametric statistical models, such as Gaussian Processes (GPs). The aim is to minimize unmodeled dynamics such as undesired slippages. The proposed approach has the benefit of avoiding complex terramechanics analysis …
Paper presents a robust Kalman filter for state estimation.
problem Robust state estimation under process and measurement noise.
method Generalized Bayesian approach to a Weighted Observation Likelihood Filter (WoLF) framework.
result Achieved robust state estimation against both process and measurement noise.
New SigSwap model for path-dependent financial risk.
problem Managing complex, path-dependent financial risks.
method Geometry-based approach using path-signature and Signature Expected Shortfall.
result Path-dependent risks can be converted into transparent risk factors.
Framework corrects model form errors in structural dynamics predictions.
problem Model form errors in parametric models of structural dynamics.
method Gaussian Process Latent Force Model (GPLFM) for non-parametric discrepancy representation, linear Bayesian filtering for state and discrepancy estimation, modal reduction for computational tractability.
result Significant reduction of displacement and rotation prediction errors under unseen excitations.
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.
A semi-parametric, non-linear regression model in the presence of latent variables is applied towards learning network graph structure. These latent variables can correspond to unmodeled phenomena or unmeasured agents in a complex system of interacting entities. This formulation jointly estimates non-linearities in the…
We address challenges of active learning under scarce informational resources in non-stationary environments. In real-world settings, data labeled and integrated into a predictive model may become invalid over time. However, the data can become informative again with switches in context and such changes may indicate un…
A novel model learns from limited data using physics constraints and GPVAE to generate realistic samples.
problem Limited data for effective generative AI training.
method Physics-informed Gaussian Process Variational Autoencoder (PIGPVAE) incorporating physical models and discrepancy terms.
result Achieves state-of-the-art performance on indoor temperature data.
An intervention may have an effect on units other than those to which it was administered. This phenomenon is called interference and it usually goes unmodeled. In this paper, we propose to combine Lauritzen-Wermuth-Frydenberg and Andersson-Madigan-Perlman chain graphs to create a new class of causal models that can re…
A common goal in statistics and machine learning is to learn models that can perform well against distributional shifts, such as latent heterogeneous subpopulations, unknown covariate shifts, or unmodeled temporal effects. We develop and analyze a distributionally robust stochastic optimization (DRO) framework that lea…
The Vector AutoRegressive (VAR) model is fundamental to the study of multivariate time series. Although VAR models are intensively investigated by many researchers, practitioners often show more interest in analyzing VARX models that incorporate the impact of unmodeled exogenous variables (X) into the VAR. However, sin…
New method for uncertainty analysis in TabPFN, a state-of-the-art tabular transformer.
problem No method for uncertainty decomposition in TabPFN.
method Casted as a Bayesian predictive inference problem, derived variance estimators using predictive CLT.
result Fast to compute credible bands that target epistemic uncertainty and achieve near-nominal frequentist coverage.
UDA improves ABI robustness but fails under certain prior misspecifications.
problem Robustness of ABI in noisy real-world data.
method Systematic evaluation of UDA across various misspecification scenarios.
result UDA aligns summary spaces but can fail under prior misspecifications.
A new framework for optimizing interventions with limited data.
problem Small data, default intervention data, unmodeled objectives, unforeseen consequences.
method Bandit data-driven optimization combining online bandit learning and offline predictive analytics.
result PROOF algorithm achieves no-regret and superior performance in simulations and real-world application.
Modern applications of machine learning (ML) deal with increasingly heterogeneous datasets comprised of data collected from overlapping latent subpopulations. As a result, traditional models trained over large datasets may fail to recognize highly predictive localized effects in favour of weakly predictive global patte…
New framework uses OR to ensure AI systems make safe decisions.
problem Ensuring generative AI systems make safe decisions as they gain autonomy.
method Developed a conceptual framework combining flow-based models and adversarial robustness.
result Increased autonomy requires new OR approaches for feasibility, robustness, and stress testing.
MF-GLaM models improve stochastic simulator emulation with multifidelity data.
problem Challenging to emulate stochastic simulators' full conditional probability distribution.
method Proposes MF-GLaMs to efficiently emulate HF stochastic simulators using LF data.
result MF-GLaMs achieve improved accuracy or comparable performance at reduced cost.
Data-driven control of robotic systems using Koopman operators with error bounds.
problem Real-time control of nonlinear robotic systems with unknown dynamics.
method Constructing a Koopman operator-based linear representation using higher-order derivatives of nonlinear dynamics, with error bounds derived from Taylor series accuracy analysis.
result The Koopman model provides marginally better performance than competing nonlinear modeling methods and can be efficiently controlled using linear control design tools.
GP-CATE calibrates CATE intervals in few-placebo trials with Gaussian processes.
problem Calibrating uncertainty intervals for CATE in small-arm trials.
method GP-CATE uses Gaussian processes to model each arm's outcome surface directly.
result GP-CATE achieves calibrated coverage where other methods fail.
New tail dependence measures for stock indices.
problem Measuring tail dependence between financial variables.
method Introducing a new stochastic order and studying monotone tail dependence measures.
result Advantage of new tail dependence measures over classical ones.
Proposes a new dependency function for measuring non-linear relationships.
problem Need for a general-purpose measure of dependency between random variables.
method Revision of ideal properties and proposal of a new dependency function.
result Proposes a new dependency function that meets all desired properties.
The paper explores the relationship between joint mixability and negative dependence structures.
problem Understanding the connection between joint mixability and various negative dependence concepts.
method Analyzes the properties of joint mixes and their relation to negative dependence structures.
result Derives necessary and sufficient conditions for a joint mix to be negatively dependent.
Extend classical theory of affine processes to path-dependent setting
problem Path-dependent affine processes
method Introduce path-dependent coefficients and provide analytic formulas for their Fourier--Laplace transform
result Define path-dependent affine processes through their exponential-affine Fourier--Laplace transform and establish a characterization theorem
Extremal dependence between international stock markets is of particular interest in today's global financial landscape. However, previous studies have shown this dependence is not necessarily stationary over time. We concern ourselves with modeling extreme value dependence when that dependence is changing over time, o…
Predicts financial asset dependencies using spatiotemporal patterns.
problem Complex dependency structures in financial assets for risk mitigation.
method Proposes Asset Dependency Matrix (ADM) and Asset Dependency Neural Network (ADNN) with ConvLSTM for spatiotemporal asset dependency prediction.
result ADNN outperforms baselines in predicting asset dependencies and their applications.
The paper develops methods to price and hedge options in path-dependent stock models.
problem Pricing and hedging options under complex stock models.
method Develops a path-dependent PDE for option pricing and differentiability of path-dependent SDE solutions.
result Provides formulas for option Greeks and differentiability of path-dependent SDE solutions.
Survey on learning with graph-dependent data, deriving new generalization bounds.
problem Traditional i.i.d. data assumption fails in many real-life applications.
method Collect and analyze graph-dependent concentration bounds, derive generalization bounds.
result New generalization bounds for graph-dependent data.
Paper tackles instance-dependent label noise by approximating it with part-dependent noise.
problem Learning with instance-dependent label noise is challenging.
method Approximate instance-dependent label noise with part-dependent noise. Use transition matrices for parts to model noise.
result Method outperforms state-of-the-art approaches for instance-dependent label noise.
Estimating the strength of dependency between two variables is fundamental for exploratory analysis and many other applications in data mining. For example: non-linear dependencies between two continuous variables can be explored with the Maximal Information Coefficient (MIC); and categorical variables that are depende…
In data science, it is often required to estimate dependencies between different data sources. These dependencies are typically calculated using Pearson's correlation, distance correlation, and/or mutual information. However, none of these measures satisfy all the Granger's axioms for an "ideal measure". One such ideal…
Deep signature algorithm for pricing path-dependent options.
problem Pricing path-dependent options with complex payoff functions.
method Extended backward scheme for state-dependent FBSDEs with reflections, incorporating signature layer for path-dependent FBSDEs.
result Convergence analysis of the algorithm with explicit dependence on truncation order and neural network approximation errors.
Study on pairwise counter-monotonicity, a type of negative dependence.
problem Understanding and quantifying extremal negative dependence structures.
method Established stochastic representation and invariance property; showed implications and connections.
result Pairwise counter-monotonicity implies negative association and joint mix dependence.
This paper presents a new methodology for clustering multivariate time series leveraging optimal transport between copulas. Copulas are used to encode both (i) intra-dependence of a multivariate time series, and (ii) inter-dependence between two time series. Then, optimal copula transport allows us to define two distan…
New measures capture tail dependence and non-exchangeability in financial data.
problem Underestimation of tail dependence and inability to capture non-exchangeable tail dependence.
method Tail copulas and novel tail dependence measures (MTCM, ATCM) are proposed.
result Captures non-exchangeable tail dependence and provides analytical forms for various copulas.
Study nearest-neighbor radii under dependent sampling, finding they remain informative.
problem Analyzing nearest-neighbor radii under dependent sampling.
method Consider strong mixing dependent observations, establish distribution-free almost sure convergence and sharp non-asymptotic moment bounds.
result Nearest-neighbor geometry remains informative under dependence sampling.
Study of time-dependent metrics and connections in geometry.
problem Understanding geodesics and connections in time-dependent Riemannian manifolds.
method Examine connections on product manifolds, explore parallel transport, geodesics, and torsion.
result Define the derivative of a one-parameter family of connections.
A crucial assumption in most statistical learning theory is that samples are independently and identically distributed (i.i.d.). However, for many real applications, the i.i.d. assumption does not hold. We consider learning problems in which examples are dependent and their dependency relation is characterized by a gra…
Estimating the dependency of variables is a fundamental task in data analysis. Identifying the relevant attributes in databases leads to better data understanding and also improves the performance of learning algorithms, both in terms of runtime and quality. In data streams, dependency monitoring provides key insights …
Estimates binary labels from dependent data using Markov Random Fields.
problem Statistical estimation from dependent data across spatial, temporal, and social domains.
method Modeling dependencies as Markov Random Fields and providing efficient estimation algorithms.
result Statistically efficient estimation rates for Ising models from a single sample.
Develops a numerical scheme for solving path-dependent FBSDEs and PDEs.
problem Solving path-dependent FBSDEs and PDEs numerically.
method Picard iteration method for FBSDEs, concentration inequality for estimator, supervised learning with neural networks for PDEs.
result Proves convergence and rate of convergence for the Picard iteration method.
We consider the problem of risk diversification of α-stable heavy tailed risks. We study the behaviour of the aggregated Value-at-Risk, with particular reference to the impact of different tail dependence structures on the limits to diversification. We confirm the large evidence of sub-additivity violations, particul…
Flow prediction (e.g., crowd flow, traffic flow) with features of spatial-temporal is increasingly investigated in AI research field. It is very challenging due to the complicated spatial dependencies between different locations and dynamic temporal dependencies among different time intervals. Although measurements of …
This paper improves tail dependence analysis by introducing a path-based approach.
problem The classical tail dependence coefficient fails to capture non-exchangeable features of tail dependence.
method The paper introduces a path-based maximal tail dependence approach to capture the most pronounced feature of dependence over all possible paths.
result The paper proves the existence and provides an explicit characterization of the path-based maximal TDC, improving analytical and computational tractability.
Proposes DR-ACI for causal effect intervals with temporal dependence.
problem Causal effect intervals under temporal dependence.
method Doubly robust adaptive conformal inference (DR-ACI).
result Constructs prediction intervals for causal effects.