اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدA Nonparametric Adaptive Nonlinear Statistical Filter
57
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We use statistical learning methods to construct an adaptive state estimator for nonlinear stochastic systems. Optimal state estimation, in the form of a Kalman filter, requires knowledge of the systems process and measurement uncertainty. We propose that these uncertainties can be estimated from (conditioned on) past observed data, and without making any assumptions of the systems prior distribution. The systems prior distribution at each time step is constructed from an ensemble of least-squares estimates on sub-sampled sets of the data via jackknife sampling. As new data is acquired, the state estimates, process uncertainty, and measurement uncertainty are updated accordingly, as described in this manuscript.
قيم البحث
اقرأ أيضاً
We develop a data driven approach to perform clustering and end-to-end feature learning simultaneously for streaming data that can adaptively detect novel clusters in emerging data. Our approach, Adaptive Nonparametric Variational Autoencoder (AdapVA
E), learns the cluster membership through a Bayesian Nonparametric (BNP) modeling framework with Deep Neural Networks (DNNs) for feature learning. We develop a joint online variational inference algorithm to learn feature representations and clustering assignments simultaneously via iteratively optimizing the Evidence Lower Bound (ELBO). We resolve the catastrophic forgetting citep{kirkpatrick2017overcoming} challenges with streaming data by adopting generative samples from the trained AdapVAE using previous data, which avoids the need of storing and reusing past data. We demonstrate the advantages of our model including adaptive novel cluster detection without discarding useful information learned from past data, high quality sample generation and comparable clustering performance as end-to-end batch mode clustering methods on both image and text corpora benchmark datasets.
In this paper, we propose a compositional nonparametric method in which a model is expressed as a labeled binary tree of $2k+1$ nodes, where each node is either a summation, a multiplication, or the application of one of the $q$ basis functions to on
e of the $p$ covariates. We show that in order to recover a labeled binary tree from a given dataset, the sufficient number of samples is $O(klog(pq)+log(k!))$, and the necessary number of samples is $Omega(klog (pq)-log(k!))$. We further propose a greedy algorithm for regression in order to validate our theoretical findings through synthetic experiments.
Factor analysis aims to determine latent factors, or traits, which summarize a given data set. Inter-battery factor analysis extends this notion to multiple views of the data. In this paper we show how a nonlinear, nonparametric version of these mode
ls can be recovered through the Gaussian process latent variable model. This gives us a flexible formalism for multi-view learning where the latent variables can be used both for exploratory purposes and for learning representations that enable efficient inference for ambiguous estimation tasks. Learning is performed in a Bayesian manner through the formulation of a variational compression scheme which gives a rigorous lower bound on the log likelihood. Our Bayesian framework provides strong regularization during training, allowing the structure of the latent space to be determined efficiently and automatically. We demonstrate this by producing the first (to our knowledge) published results of learning from dozens of views, even when data is scarce. We further show experimental results on several different types of multi-view data sets and for different kinds of tasks, including exploratory data analysis, generation, ambiguity modelling through latent priors and classification.
The Kalman filter (KF) is used in a variety of applications for computing the posterior distribution of latent states in a state space model. The model requires a linear relationship between states and observations. Extensions to the Kalman filter ha
ve been proposed that incorporate linear approximations to nonlinear models, such as the extended Kalman filter (EKF) and the unscented Kalman filter (UKF). However, we argue that in cases where the dimensionality of observed variables greatly exceeds the dimensionality of state variables, a model for $p(text{state}|text{observation})$ proves both easier to learn and more accurate for latent space estimation. We derive and validate what we call the discriminative Kalman filter (DKF): a closed-form discriminative version of Bayesian filtering that readily incorporates off-the-shelf discriminative learning techniques. Further, we demonstrate that given mild assumptions, highly non-linear models for $p(text{state}|text{observation})$ can be specified. We motivate and validate on synthetic datasets and in neural decoding from non-human primates, showing substantial increases in decoding performance versus the standard Kalman filter.
Variational Inference (VI) combined with Bayesian nonlinear filtering produces the state-of-the-art results for latent trajectory inference. A body of recent works focused on Sequential Monte Carlo (SMC) and its expansion, e.g., Forward Filtering Bac
kward Simulation (FFBSi). These studies achieved a great success, however, remain a serious problem for particle degeneracy. In this paper, we propose Ensemble Kalman Objectives (EnKOs), the hybrid method of VI and Ensemble Kalman Filter (EnKF), to infer the State Space Models (SSMs). Unlike the SMC based methods, the our proposed method can identify the latent dynamics given fewer particles because of its rich particle diversity. We demonstrate that EnKOs outperform the SMC based methods in terms of predictive ability for three benchmark nonlinear dynamics systems tasks.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
