Recent years have witnessed the unprecedented rising of time series from almost all kindes of academic and industrial fields. Various types of deep neural network models have been introduced to time series analysis, but the important frequency information is yet lack of effective modeling. In light of this, in this pap…
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48 results for “multilevel time series”
In the past decade, Bitcoin as an emerging asset class has gained widespread public attention because of their extraordinary returns in phases of extreme price growth and their unpredictable massive crashes. We apply the log-periodic power law singularity (LPPLS) confidence indicator as a diagnostic tool for identifyin…
Dynamic functional time-series methods improve forecast accuracy for foreign exchange implied volatility surfaces.
problem Forecasting implied volatility surfaces in foreign exchange markets.
method Dynamic functional principal component analysis and multivariate functional time-series methods.
result Dynamic univariate functional time-series method shows the greatest improvement in forecast accuracy.
Framework detects covert financial market manipulation using LOB representations.
problem Detecting covert financial market manipulation (spoofing) from complex anomaly patterns in multilevel prices.
method Cascaded contrastive representation learning of LOB data.
result Transformer-based architectures achieve state-of-the-art results in detection performance.
A new multilevel framework speeds up ResNet training.
problem Training deep residual networks (ResNets) is time-consuming.
method Formulates ResNets as dynamical systems and uses time-dependent optimal control problems.
result Enhanced training of ResNets with multilevel auxiliary networks achieves significant speedup.
We investigate the extension of the multilevel Monte Carlo path simulation method to jump-diffusion SDEs. We consider models with finite rate activity, using a jump-adapted discretisation in which the jump times are computed and added to the standard uniform dis- cretisation times. The key component in multilevel analy…
Develops a fast algorithm for fitting multilevel factor models.
problem Fitting multilevel factor models with covariance structure.
method Novel expectation-maximization algorithm tailored for multilevel factor models.
result Shows efficient computation of inverse of positive definite MLR matrix.
We develop a multilevel approach to compute approximate solutions to backward differential equations (BSDEs). The fully implementable algorithm of our multilevel scheme constructs sequential martingale control variates along a sequence of refining time-grids to reduce statistical approximation errors in an adaptive and…
The paper introduces a multilevel initialization method for deep neural networks.
problem Training very deep neural networks with layer-parallel methods.
method Continuous interpretation of training as optimal control, using time-dependent ODEs for neural network discretization, and a refinement strategy across the time domain.
result The method creates deep networks with good initializations from coarser networks, reducing training time and providing regularization.
Paper proposes a new algorithm to reduce derivative pricing computation time.
problem Derivative pricing computational inefficiency.
method Combines multilevel Richardson-Romberg and importance sampling.
result Reduces computational time while maintaining accuracy.
A method learns to solve multilevel combinatorial problems with two players.
problem Multilevel combinatorial optimization problems with multiple players.
method Value-based multi-agent reinforcement learning in a graph neural network framework.
result Close to optimal solutions on graphs up to 100 nodes, with a significant speedup.
It becomes increasingly popular to perform mediation analysis for complex data from sophisticated experimental studies. In this paper, we present Granger Mediation Analysis (GMA), a new framework for causal mediation analysis of multiple time series. This framework is motivated by a functional magnetic resonance imagin…
This paper proposes and analyses a new multilevel Monte Carlo method for the estimation of mean exit times for multi-dimensional Brownian diffusions, and associated functionals which correspond to solutions to high-dimensional parabolic PDEs through the Feynman-Kac formula. In particular, it is proved that the complexi…
Detects anomalies in vector fields without distributional assumptions.
problem Detecting anomalies in high-dimensional, non-stationary vector fields.
method Optimal Karhunen-Loeve expansion, multilevel orthogonal subspaces, hypothesis tests.
result Reliable anomaly detection without distributional assumptions.
A new training method uses multilevel minimization for machine learning.
problem Training machine learning models with high variance and low efficiency.
method Constructs a multilevel hierarchy by reducing sample size and internally trains surrogate models with fewer samples.
result The multilevel method enhances model training efficiency compared to subsampled Newton's and variance reduction methods.
The time complexity of support vector machines (SVMs) prohibits training on huge data sets with millions of data points. Recently, multilevel approaches to train SVMs have been developed to allow for time-efficient training on huge data sets. While regular SVMs perform the entire training in one -- time consuming -- op…
Flexible framework assesses multilevel data group heterogeneity.
problem Multilevel data structure complicates model selection.
method Flexible framework for assessing differences between levels of grouping variables.
result Framework reliably identifies relevant multilevel components.
New neural network models speed up Bayesian multilevel modeling.
problem Complex computational challenges in Bayesian multilevel modeling.
method Probabilistic neural network architectures that leverage multilevel model factorization.
result Efficient posterior inference on unseen datasets with near-instant results.
Automates kernel discovery for longitudinal data analysis.
problem Handling irregularly sampled, sparse longitudinal data with multilevel correlation.
method Combines deep neural networks and non-parametric kernel methods to discover complex multilevel correlation structure.
result Significantly outperforms state-of-the-art methods on benchmark data sets.
Monte Carlo is a simple and flexible tool that is widely used in computational finance. In this context, it is common for the quantity of interest to be the expected value of a random variable defined via a stochastic differential equation. In 2008, Giles proposed a remarkable improvement to the approach of discretizin…
Estimates log marginal likelihood using multilevel Monte Carlo.
problem Estimating log marginal likelihood accurately.
method Unbiased multilevel Monte Carlo estimator.
result Validates application in variational Bayes.
Improved multilevel scheme for value-at-risk computation.
problem Discontinuity in Heaviside function affects value-at-risk computation.
method Adaptive multilevel stochastic approximation to mitigate discontinuity.
result Best complexity improved to O().
New method reduces CVA-VaR computation complexity.
problem Efficiently estimating CVA-VaR for financial risk management.
method Multilevel nested simulation for probabilities.
result 3 orders of magnitude reduction in computational complexity.
Solving different types of optimization models (including parameters fitting) for support vector machines on large-scale training data is often an expensive computational task. This paper proposes a multilevel algorithmic framework that scales efficiently to very large data sets. Instead of solving the whole training s…
A multilevel optimization method for constrained problems.
problem Regularized constrained linear inverse problems with box constraints.
method Geometric multilevel optimization with varying discretization levels.
result Preserves feasibility of updates while speeding up computations.
With the advent of massive data sets much of the computational science and engineering community has moved toward data-intensive approaches in regression and classification. However, these present significant challenges due to increasing size, complexity and dimensionality of the problems. In particular, covariance mat…
Since Giles introduced the multilevel Monte Carlo path simulation method [18], there has been rapid development of the technique for a variety of applications in computational finance. This paper surveys the progress so far, highlights the key features in achieving a high rate of multilevel variance convergence, and su…
Novel weak MLMC scheme for Lévy-driven SDEs, applied to financial derivatives pricing.
problem Approximating solutions to Lévy-driven SDEs for financial derivatives pricing.
method Weak multilevel Monte-Carlo scheme with state space discretization of Lévy processes.
result Efficient approximation of financial derivatives pricing models.
Accelerates MCMC sampling for large-scale problems using machine learning.
problem Efficiently sampling large-scale Bayesian inference problems with high computational cost.
method Integrates low-fidelity machine learning models into a multilevel MCMC framework.
result Significantly accelerates multilevel sampling by a factor of two with similar accuracy.
Study reveals 2020 stock crashes were mostly endogenous, not exogenous.
problem Identifying the cause of the 2020 global stock market crash.
method Applied log-periodic power law singularity (LPPLS) methodology to analyze stock market indexes.
result The 2020 stock market crashes were mostly endogenous, driven by systemic instability.
Optimizes learning Hilbert-Schmidt operators between Sobolev spaces.
problem Statistical limits of learning mappings between infinite-dimensional function spaces.
method Minimax optimal regularization and multilevel training.
result Multilevel kernel operator learning achieves optimal learning rate.
We derive generalization and excess risk bounds for neural nets using a family of complexity measures based on a multilevel relative entropy. The bounds are obtained by introducing the notion of generated hierarchical coverings of neural nets and by using the technique of chaining mutual information introduced in Asadi…
ETF Risk Modelsq-fin.RM
The paper discusses building ETF risk models using a multilevel classification taxonomy.
problem Building accurate risk models for ETFs.
method First, build a multilevel classification taxonomy for ETFs. Then, use this taxonomy to define risk factors and build risk models.
result The approach can accurately classify and model ETF risks.
In this paper, we are interested in the strong convergence properties of the Ninomiya-Victoir scheme which is known to exhibit weak convergence with order 2. We prove strong convergence with order . This study is aimed at analysing the use of this scheme either at each level or only at the finest level of a multil…
In this paper we discuss the possibility of using multilevel Monte Carlo (MLMC) methods for weak approximation schemes. It turns out that by means of a simple coupling between consecutive time discretisation levels, one can achieve the same complexity gain as under the presence of a strong convergence. We exemplify thi…
Improved Bayesian regression for large datasets using multilevel Gibbs sampling.
problem Efficiently handling large-scale Bayesian regression with complex posterior distributions.
method Developed a multilevel Gibbs sampler for linear mixed models, incorporating data clustering and correlated samples for variance reduction.
result Significant speed-up achieved for Bayesian regression without sacrificing predictive performance.
Efficiently price VIX options using multilevel Monte Carlo in rough Bergomi model.
problem Pricing VIX options in a rough Bergomi model with high computational complexity.
method Combining rectangle discretization, Cholesky sampling, and multilevel Monte Carlo.
result Reduced computational complexity to and asymptotically optimal .
Deep learning models exhibit state-of-the-art performance for many predictive healthcare tasks using electronic health records (EHR) data, but these models typically require training data volume that exceeds the capacity of most healthcare systems. External resources such as medical ontologies are used to bridge the da…
Enhances SBI accuracy with multilevel Monte Carlo for expensive simulators.
problem Limited accuracy in SBI due to expensive simulators.
method Multilevel Monte Carlo techniques for cost-effective SBI.
result Significant enhancement in SBI accuracy with fixed computational budget.
We describe general multilevel Monte Carlo methods that estimate the price of an Asian option monitored at fixed dates. Our approach yields unbiased estimators with standard deviation in expected time for a variety of processes including the Black-Scholes model, Merton's jump-diffusion mod…
The multilevel Monte Carlo path simulation method introduced by Giles ({\it Operations Research}, 56(3):607-617, 2008) exploits strong convergence properties to improve the computational complexity by combining simulations with different levels of resolution. In this paper we analyse its efficiency when using the Milst…
We propose a novel probabilistic approach to multilevel clustering problems based on composite transportation distance, which is a variant of transportation distance where the underlying metric is Kullback-Leibler divergence. Our method involves solving a joint optimization problem over spaces of probability measures t…
Multilevel Weighted Support Vector Machine for Classification on Healthcare Data with Missing Valuesstat.ML
This work is motivated by the needs of predictive analytics on healthcare data as represented by Electronic Medical Records. Such data is invariably problematic: noisy, with missing entries, with imbalance in classes of interests, leading to serious bias in predictive modeling. Since standard data mining methods often …
Proposes a method for multilevel explanations of black-box models.
problem Need for explanations at intermediate or group levels, especially for GDPR compliance.
method Meta-method that builds a multilevel explanation tree using local explainability methods.
result Effective multilevel explanations for groups of data points, including novel test points.
We apply multilevel Monte Carlo for option pricing problems using exponential Lévy models with a uniform timestep discretisation to monitor the running maximum required for lookback and barrier options. The numerical results demonstrate the computational efficiency of this approach. We derive estimates of the convergen…
Model trains passing events on a bridge using multilevel Gaussian process.
problem Represent aggregate train-passing events from a bridge monitoring system.
method Formulate a combined model with low-rank approximation hierarchical Gaussian process, incorporating domain expertise as constraints.
result Allow for simulation of previously unobserved train types.
We study the use of the multilevel Monte Carlo technique in the context of the calculation of Greeks. The pathwise sensitivity analysis differentiates the path evolution and reduces the payoff's smoothness. This leads to new challenges: the inapplicability of pathwise sensitivities to non-Lipschitz payoffs often makes …
Antithetic multilevel Monte Carlo estimation for multi-dimensional SDEs without Lévy area simulationq-fin.CP
In this paper we introduce a new multilevel Monte Carlo (MLMC) estimator for multi-dimensional SDEs driven by Brownian motions. Giles has previously shown that if we combine a numerical approximation with strong order of convergence with MLMC we can reduce the computational complexity to estimate expected value…