A network of independently trained Gaussian processes (StackedGP) is introduced to obtain predictions of quantities of interest with quantified uncertainties. The main applications of the StackedGP framework are to integrate different datasets through model composition, enhance predictions of quantities of interest thr…
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48 results for “Quantities of interest”
Probabilistic numerics expands numerical tasks with black box methods.
problem Difficult conditioning of random variables in numerical tasks.
method Construct probabilistic numerical methods based on final outputs, extrapolating limiting quantities.
result Higher orders of convergence achieved in various numerical tasks.
This paper evaluates heterogeneous information fusion using multi-task Gaussian processes in the context of geological resource modeling. Specifically, it empirically demonstrates that information integration across heterogeneous information sources leads to superior estimates of all the quantities being modeled, compa…
Numerical approximation of hybrid Poisson-jump Ait-Sahalia-type interest rate model with delayq-fin.RM
This paper modifies the Ait-Sahalia model to better describe interest rate behaviors.
problem Inadequate specifications of the original Ait-Sahalia model to explain various interest rate phenomena.
method Proposes a modified hybrid Poisson-jump Ait-Sahalia model and uses truncated EM techniques for numerical approximation.
result Validates the modified model using Monte Carlo simulations for bond and barrier option payoffs.
Transaction costs: a new point of viewcond-mat.dis-nn
We consider a new approach to portfolio selection in presence of transaction costs which allows to map the problem into one without costs. The proposed approach connects all the quantities of interest to exit times and probabilities to reach barriers. This leads to analytic results in the Wiener case and to directly me…
The field of risk theory has traditionally focused on ruin-related quantities. In particular, the socalled Expected Discounted Penalty Function has been the object of a thorough study over the years. Although interesting in their own right, ruin related quantities do not seem to capture path-dependent properties of the…
Improved deep learning framework for estimating combustion variables.
problem Accurately estimating thermo-chemical state variables in turbulent combustion.
method Introducing deep ensembles to approximate posterior distribution of quantities of interest, using Flamelets or Points strategies.
result ChemTab Deep Ensembles provide more accurate representation of source energy and key species source terms.
The paper develops methods to assess and correct model uncertainties in graphical models.
problem Model uncertainty in probabilistic graphical models.
method Information-theoretic and non-parametric stress tests.
result Ranking and correcting impactful sources of uncertainty in graphical models.
A new discretisation of a doubled, i.e. BF, version of the pure abelian Chern-Simons theory is presented. It reproduces the continuum expressions for the topological quantities of interest in the theory, namely the partition function and correlation function of Wilson loops. Similarities with free spinor field theory a…
ROM-net framework applies to industrial design uncertainty quantification.
problem Uncertainty quantification in industrial design models.
method Dictionary-based ROM-net framework for reduced order modeling.
result ROM-net computes predictions in 2 hours with high accuracy.
ABCI infers causal models and queries simultaneously using Bayesian active learning.
problem Inference of causal models and effects in a two-stage process is inefficient and unnatural.
method Active Bayesian Causal Inference (ABCI) using Gaussian processes for sequentially designing experiments.
result ABCI is more data-efficient and accurate in learning causal queries from fewer samples.
A new method for experimental design focuses on predicting downstream quantities of interest.
problem Designs that maximize parameter learning may not maximize downstream quantity prediction.
method Likelihood-free goal-oriented optimal experimental design (LF-GO-OED) using ABC density ratio estimation.
result LF-GO-OED maximizes the expected information gain for downstream quantities.
We explore the possibility of using machine learning to identify interesting mathematical structures by using certain quantities that serve as fingerprints. In particular, we extract features from integer sequences using two empirical laws: Benford's law and Taylor's law and experiment with various classifiers to ident…
The Relationship Between Stock Market Parameters and Interbank Lending Market: an Empirical Evidenceq-fin.ST
The article presents calculations that prove practical importance of the earlier derived theoretical relationship between the interest rate on the interbank credit market, volume of investment and the quantity of securities tradable on the stock exchange.
for 3d theorieshep-th
Proposes a new effective central charge for 3d N=2 theories.
problem Understanding the effective central charge in 3d N=2 theories.
method Analyzes the superconformal index to propose a new quantity and discusses its properties and computation.
result Proposes a new effective central charge for 3d N=2 theories.
This paper introduces a method for efficiently inferring a high-dimensional distributed quantity from a few observations. The quantity of interest (QoI) is approximated in a basis (dictionary) learned from a training set. The coefficients associated with the approximation of the QoI in the basis are determined by minim…
LUQ learns QoI from dynamical systems for consistent observation inversion.
problem Quantifying uncertainties on model inputs corresponding to observable QoI in dynamical systems.
method LUQ framework for SIPs, including data filtering, dynamics learning, observation classification, and feature extraction.
result LUQ provides tractable solutions to SIPs for dynamical systems, enabling uncertainty quantification.
Minsky Financial Instability, Interscale Feedback, Percolation and Marshall-Walras Disequilibriumq-fin.GN
We study analytically and numerically Minsky instability as a combination of top-down, bottom-up and peer-to-peer positive feedback loops. The peer-to-peer interactions are represented by the links of a network formed by the connections between firms, contagion leading to avalanches and percolation phase transitions pr…
Study proves convergence of interest rate model approximations.
problem Investigating convergence of stochastic interest rate models.
method Developed analytical tools for true and truncated EM solutions, proving convergence in probability.
result True solution converges in probability to truncated EM solution as step size approaches zero.
In this paper, we derive the evolution equation for the first eigenvalue of the Witten-Laplace operator acting on the space of functions along the mean curvature flow on a closed oriented manifold. We show some interesting monotonic quantities under the mean curvature flow.
Automatic differentiation frameworks are optimized for exactly one thing: computing the average mini-batch gradient. Yet, other quantities such as the variance of the mini-batch gradients or many approximations to the Hessian can, in theory, be computed efficiently, and at the same time as the gradient. While these qua…
The matrix-based Renyi's α-order entropy functional was recently introduced using the normalized eigenspectrum of a Hermitian matrix of the projected data in a reproducing kernel Hilbert space (RKHS). However, the current theory in the matrix-based Renyi's α-order entropy functional only defines the entropy of a single…
We propose a general non-linear order book model that is built from the individual behaviours of the agents. Our framework encompasses Markovian and Hawkes based models. Under mild assumptions, we prove original results on the ergodicity and diffusivity of such system. Then we provide closed form formulas for various q…
New framework compresses and recovers scientific data efficiently.
problem Efficiently managing and recovering from large scientific datasets.
method Grounded in learning exponential families, preserves uncertainty and supports trade-offs.
result Preserves physical features and quantities of interest in compressed representations.
In this paper, we analyse piecewise deterministic Markov processes, as introduced in Davis (1984). Many models in insurance mathematics can be formulated in terms of the general concept of piecewise deterministic Markov processes. In this context, one is interested in computing certain quantities of interest such as th…
We develop a novel approximate Bayesian computation (ABC) framework, ABCDP, that produces differentially private (DP) and approximate posterior samples. Our framework takes advantage of the Sparse Vector Technique (SVT), widely studied in the differential privacy literature. SVT incurs the privacy cost only when a cond…
Generalized Random Forestsstat.ME
We propose generalized random forests, a method for non-parametric statistical estimation based on random forests (Breiman, 2001) that can be used to fit any quantity of interest identified as the solution to a set of local moment equations. Following the literature on local maximum likelihood estimation, our method co…
A method to improve surrogate model accuracy using multiple fidelity models.
problem Efficiently combining models of varying accuracy and computational cost.
method Multifidelity Gaussian process models and leave-one-out cross-validation.
result Reduced LOO-CV error at the highest fidelity through adaptive learning.
Algorithm selects optimal experiments in Markov chains to learn unknown quantities.
problem Designing efficient experiments in Markov chains to learn about unknown quantities.
method Proposes extsc{markov-design} algorithm for sequential policy selection.
result Algorithm provably converges to optimal measurement allocation.
We describe a method for removing the effect of confounders in order to reconstruct a latent quantity of interest. The method, referred to as half-sibling regression, is inspired by recent work in causal inference using additive noise models. We provide a theoretical justification and illustrate the potential of the me…
Many processes in science and engineering can be described by partial differential equations (PDEs). Traditionally, PDEs are derived by considering first principles of physics to derive the relations between the involved physical quantities of interest. A different approach is to measure the quantities of interest and …
Deep neural networks improve surrogate models for non-smooth quantities in uncertain geometries.
problem Building accurate surrogates for non-smooth quantities in uncertain geometries.
method Deep neural networks for point evaluation of solutions to interface problems with geometric uncertainties.
result Neural networks provide good surrogates without suffering from the curse of dimensionality.
We show that prices and shortfall risks of game (Israeli) barrier options in a sequence of binomial approximations of the Black--Scholes (BS) market converge to the corresponding quantities for similar game barrier options in the BS market with path dependent payoffs and the speed of convergence is estimated, as well. …
The paper introduces recklessness to improve recommendation quality and quantity.
problem The reliability/coverage dilemma in recommender systems limits the number of recommended items.
method Incorporates a new term (recklessness) into matrix factorization-based recommender systems to address the dilemma.
result Recklessness improves the quantity and quality of recommendations by allowing for risk regulation.
R. Cont and A. de Larrard (SIAM J. Finan. Math, 2013) introduced a tractable stochastic model for the dynamics of a limit order book, computing various quantities of interest such as the probability of a price increase or the diffusion limit of the price process. As suggested by empirical observations, we extend their …
We define On-Average KL-Privacy and present its properties and connections to differential privacy, generalization and information-theoretic quantities including max-information and mutual information. The new definition significantly weakens differential privacy, while preserving its minimalistic design features such …
Recent decades have seen an interest in prediction problems for which Bayesian methodology has been used ubiquitously. Sampling from or approximating the posterior predictive distribution in a Bayesian model allows one to make inferential statements about potentially observable random quantities given observed data. Th…
Order positions are key variables in algorithmic trading. This paper studies the limiting behavior of order positions and related queues in a limit order book. In addition to the fluid and diffusion limits for the processes, fluctuations of order positions and related queues around their fluid limits are analyzed. As a…
Modeling interest rate dynamics: an infinite-dimensional approachcond-mat.stat-mech
We present a family of models for the term structure of interest rates which describe the interest rate curve as a stochastic process in a Hilbert space. We start by decomposing the deformations of the term structure into the variations of the short rate, the long rate and the fluctuations of the curve around its avera…
The paper critiques existing uncertainty concepts and proposes a new decision-theoretic approach.
problem Incoherence in existing discussions of aleatoric and epistemic uncertainty.
method Decision-theoretic perspective that relates uncertainty, predictive performance, and statistical dispersion.
result Popular information-theoretic quantities can be poor estimators but still useful for guiding data acquisition.
The study examines cryptocurrency market activity, revealing multifractal inter-transaction times and challenging traditional statistical models.
problem Analyzing long-range autocorrelations and multifractality in cryptocurrency market activity.
method Analysis of tick-by-tick data from multiple cryptocurrency trading platforms, focusing on inter-transaction times, transaction volumes, and volatility.
result Inter-transaction times exhibit multifractality, indicating periods of increased market activity are more complex than quiet periods.
Sharp bounds found on expert error in binary advice aggregation.
problem Aggregating binary advice from conditionally independent experts.
method Sharp upper and lower bounds on optimal error probability in asymmetric case.
result Sharp bounds recover and sharpen known results in symmetric case.
Maximal Rate of Stepwise Uncertainty Reduction selects simulations to reduce uncertainty efficiently.
problem Efficiently estimating quantities of interest from multi-fidelity simulations.
method Bayesian sequential strategy that maximizes the ratio of expected uncertainty reduction to simulation cost.
result MR-SUR strategy unifies and provides principled approaches to develop new methods.
GO-OED maximizes predictive information gain on nonlinear QoIs.
problem Maximizing information gain on nonlinear predictive quantities.
method Nested Monte Carlo estimator, Markov chain Monte Carlo, kernel density estimation, Bayesian optimization.
result GO-OED outperforms conventional OED in nonlinear settings.
GINNs: Graph-Informed Neural Networks for Multiscale Physicsphysics.comp-ph
GINNs combine deep learning with PGMs for physics-based multiscale systems.
problem Intrinsic computational bottlenecks and lack of sufficient data for QoI estimation.
method Hybrid approach combining deep learning with probabilistic graphical models, informed by structured priors for CVs.
result GINNs produce tight confidence intervals for non-Gaussian QoIs.
Quantifying model form uncertainty in Reynolds-averaged turbulence models with Bayesian deep neural networksphysics.flu-dyn
Data-driven methods for improving turbulence modeling in Reynolds-Averaged Navier-Stokes (RANS) simulations have gained significant interest in the computational fluid dynamics community. Modern machine learning algorithms have opened up a new area of black-box turbulence models allowing for the tuning of RANS simulati…
Computes a new metric quantity Y(M) for Riemannian 2d-manifolds.
problem No simple metric quantity exists for Riemannian manifolds.
method Defines Y(M) and Y_disc(M) involving sectional curvatures and computes them for specific manifolds.
result Y(M) and Y_disc(M) differ from the Euler characteristic and can be positive or negative.
The Polynomial Chaos Expansion (PCE) technique recovers a finite second order random variable exploiting suitable linear combinations of orthogonal polynomials which are functions of a given stochas- tic quantity ξ, hence acting as a kind of random basis. The PCE methodology has been developed as a mathematically rigor…