New Algorithms And Fast Implementations To Approximate Stochastic Processes

• URL: http://arxiv.org/abs/2012.01185v1
• Date: Tue, 1 Dec 2020 06:14:16 GMT
• Title: New Algorithms And Fast Implementations To Approximate Stochastic Processes
• Authors: Kipngeno Benard Kirui, Georg Ch. Pflug, Alois Pichler
• Abstract summary: We present new algorithms and fast implementations to find efficient approximations for modelling processes. The goal is always to find a finite model, which represents a given knowledge about the real data process as accurate as possible.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present new algorithms and fast implementations to find efficient approximations for modelling stochastic processes. For many numerical computations it is essential to develop finite approximations for stochastic processes. While the goal is always to find a finite model, which represents a given knowledge about the real data process as accurate as possible, the ways of estimating the discrete approximating model may be quite different: (i) if the stochastic model is known as a solution of a stochastic differential equation, e.g., one may generate the scenario tree directly from the specified model; (ii) if a simulation algorithm is available, which allows simulating trajectories from all conditional distributions, a scenario tree can be generated by stochastic approximation; (iii) if only some observed trajectories of the scenario process are available, the construction of the approximating process can be based on non-parametric conditional density estimates.

Related papers

• Iterative Methods for Full-Scale Gaussian Process Approximations for Large Spatial Data [9.913418444556486]
  We show how iterative methods can be used to reduce the computational costs for calculating likelihoods, gradients, and predictive distributions with FSAs. We also present a novel, accurate, and fast way to calculate predictive variances relying on estimations and iterative methods. All methods are implemented in a free C++ software library with high-level Python and R packages.
  arXiv  Detail & Related papers  (2024-05-23T12:25:22Z)
• Online Identification of Stochastic Continuous-Time Wiener Models Using Sampled Data [4.037738063437126]
  We develop an online estimation algorithm based on an output-error predictor for the identification of continuous-time Wiener models. The method is robust with respect to the assumptions on the spectrum of the disturbance process.
  arXiv  Detail & Related papers  (2024-03-09T12:33:09Z)
• Logistic-beta processes for dependent random probabilities with beta marginals [58.91121576998588]
  We propose a novel process called the logistic-beta process, whose logistic transformation yields a process with common beta marginals. It can model dependence on both discrete and continuous domains, such as space or time, and has a flexible dependence structure through correlation kernels. We illustrate the benefits through nonparametric binary regression and conditional density estimation examples, both in simulation studies and in a pregnancy outcome application.
  arXiv  Detail & Related papers  (2024-02-10T21:41:32Z)
• Likelihood-based inference and forecasting for trawl processes: a stochastic optimization approach [0.0]
  We develop the first likelihood-based methodology for the inference of real-valued trawl processes. We introduce novel deterministic and probabilistic forecasting methods. We release a Python library which can be used to fit a large class of trawl processes.
  arXiv  Detail & Related papers  (2023-08-30T15:37:48Z)
• Learning Unnormalized Statistical Models via Compositional Optimization [73.30514599338407]
  Noise-contrastive estimation(NCE) has been proposed by formulating the objective as the logistic loss of the real data and the artificial noise. In this paper, we study it a direct approach for optimizing the negative log-likelihood of unnormalized models.
  arXiv  Detail & Related papers  (2023-06-13T01:18:16Z)
• Distributed Bayesian Learning of Dynamic States [65.7870637855531]
  The proposed algorithm is a distributed Bayesian filtering task for finite-state hidden Markov models. It can be used for sequential state estimation, as well as for modeling opinion formation over social networks under dynamic environments.
  arXiv  Detail & Related papers  (2022-12-05T19:40:17Z)
• Reliability analysis of discrete-state performance functions via adaptive sequential sampling with detection of failure surfaces [0.0]
  The paper presents a new efficient and robust method for rare event probability estimation. The method can estimate the probabilities of multiple failure types. It can accommodate this information to increase the accuracy of the estimated probabilities.
  arXiv  Detail & Related papers  (2022-08-04T05:59:25Z)
• Sampling from Arbitrary Functions via PSD Models [55.41644538483948]
  We take a two-step approach by first modeling the probability distribution and then sampling from that model. We show that these models can approximate a large class of densities concisely using few evaluations, and present a simple algorithm to effectively sample from these models.
  arXiv  Detail & Related papers  (2021-10-20T12:25:22Z)
• MINIMALIST: Mutual INformatIon Maximization for Amortized Likelihood Inference from Sampled Trajectories [61.3299263929289]
  Simulation-based inference enables learning the parameters of a model even when its likelihood cannot be computed in practice. One class of methods uses data simulated with different parameters to infer an amortized estimator for the likelihood-to-evidence ratio. We show that this approach can be formulated in terms of mutual information between model parameters and simulated data.
  arXiv  Detail & Related papers  (2021-06-03T12:59:16Z)
• Mean-Field Approximation to Gaussian-Softmax Integral with Application to Uncertainty Estimation [23.38076756988258]
  We propose a new single-model based approach to quantify uncertainty in deep neural networks. We use a mean-field approximation formula to compute an analytically intractable integral. Empirically, the proposed approach performs competitively when compared to state-of-the-art methods.
  arXiv  Detail & Related papers  (2020-06-13T07:32:38Z)
• Instability, Computational Efficiency and Statistical Accuracy [101.32305022521024]
  We develop a framework that yields statistical accuracy based on interplay between the deterministic convergence rate of the algorithm at the population level, and its degree of (instability) when applied to an empirical object based on $n$ samples. We provide applications of our general results to several concrete classes of models, including Gaussian mixture estimation, non-linear regression models, and informative non-response models.
  arXiv  Detail & Related papers  (2020-05-22T22:30:52Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.