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54 results for “Gaussian Processes”
Data from: Avoiding tipping points in fisheries management through Gaussian process dynamic programming
Model uncertainty and limited data are fundamental challenges to robust management of human intervention in a natural system. These challenges are acutely highlighted by concerns that many ecological systems may contain tipping points, such as Allee population sizes. Before a collapse, we do not know where the tipping points lie, if they exist at all. Hence, we know neither a complete model of the system dynamics nor do we have access to data in some large region of state space where such a tipping point might exist. We illustrate how a Bayesian non-parametric approach using a Gaussian process (GP) prior provides a flexible representation of this inherent uncertainty. We embed GPs in a stochastic dynamic programming framework in order to make robust management predictions with both model uncertainty and limited data. We use simulations to evaluate this approach as compared with the standard approach of using model selection to choose from a set of candidate models. We find that model selection erroneously favours models without tipping points, leading to harvest policies that guarantee extinction. The Gaussian process dynamic programming (GPDP) performs nearly as well as the true model and significantly outperforms standard approaches. We illustrate this using examples of simulated single-species dynamics, where the standard model selection approach should be most effective and find that it still fails to account for uncertainty appropriately and leads to population crashes, while management based on the GPDP does not, as it does not underestimate the uncertainty outside of the observed data.
Gaussian processes - a gentle introduction
<p>Recording of the presentation given at the Summer School</p>
Data from: Avoiding tipping points in fisheries management through Gaussian process dynamic programming
Open the record for dataset details and reuse information.
SCALABLE TIME SERIES CHANGE DETECTION FOR BIOMASS MONITORING USING GAUSSIAN PROCESS
SCALABLE TIME SERIES CHANGE DETECTION FOR BIOMASS MONITORING USING GAUSSIAN PROCESS VARUN CHANDOLA* AND RANGA RAJU VATSAVAI* Abstract. Biomass monitoring, specifically, detecting changes in the biomass or vegetation of a geographical region, is vital for studying the carbon cycle of the system and has significant implications in the context of understanding climate change and its impacts. Recently, several time series change detection methods have been proposed to identify land cover changes in temporal profiles (time series) of vegetation collected using remote sensing instruments. In this paper, we adapt Gaussian process regression to detect changes in such time series in an online fashion. While Gaussian process (GP) has been widely used as a kernel based learning method for regression and classification, their applicability to massive spatio-temporal data sets, such as remote sensing data, has been limited owing to the high computational costs involved. In our previous work we proposed an efficient Toeplitz matrix based solution for scalable GP parameter estimation. In this paper we apply these solutions to a GP based change detection algorithm. The proposed change detection algorithm requires a memory footprint which is linear in the length of the input time series and runs in time which is quadratic to the length of the input time series. Experimental results show that both serial and parallel implementations of our proposed method achieve significant speedups over the serial implementation. Finally, we demonstrate the effectiveness of the proposed change detection method in identifying changes in Normalized Difference Vegetation Index (NDVI) data.
Distributed Prognostic Health Management with Gaussian Process Regression
Distributed prognostics architecture design is an enabling step for efficient implementation of health management systems. A major challenge encountered in such design is formulation of optimal distributed prognostics algorithms. In this paper, we present a distributed GPR based prognostics algorithm whose target platform is a wireless sensor network. In addition to challenges encountered in a distributed implementation, a wireless network poses constraints on communication patterns, thereby making the problem more challenging. The prognostics application that was used to demonstrate our new algorithms is battery prognostics. In order to present trade-offs within different prognostic approaches, we present comparison with the distributed implementation of a particle filter based prognostics for the same battery data.
Sparse Inverse Gaussian Process Regression with Application to Climate Network Discovery
Regression problems on massive data sets are ubiquitous in many application domains including the Internet, earth and space sciences, and finances. Gaussian Process regression is a popular technique for modeling the input-output relations of a set of variables under the assumption that the weight vector has a Gaussian prior. However, it is challenging to apply Gaussian Process regression to large data sets since prediction based on the learned model requires inversion of an order n kernel matrix. Approximate solutions for sparse Gaussian Processes have been proposed for sparse problems. However, in almost all cases, these solution techniques are agnostic to the input domain and do not preserve the similarity structure in the data. As a result, although these solutions sometimes provide excellent accuracy, the models do not have interpretability. Such interpretable sparsity patterns are very important for many applications. We propose a new technique for sparse Gaussian Process regression that allows us to compute a parsimonious model while preserving the interpretability of the sparsity structure in the data. We discuss how the inverse kernel matrix used in Gaussian Process prediction gives valuable domain information and then adapt the inverse covariance estimation from Gaussian graphical models to estimate the Gaussian kernel. We solve the optimization problem using the alternating direction method of multipliers that is amenable to parallel computation. We demonstrate the performance of our method in terms of accuracy, scalability and interpretability on a climate data set.
Stable and Efficient Gaussian Process Calculations
The use of Gaussian processes can be an effective approach to prediction in a supervised learning environment. For large data sets, the standard Gaussian process approach requires solving very large systems of linear equations and approximations are required for the calculations to be practical. We will focus on the subset of regressors approximation technique. We will demonstrate that there can be numerical instabilities in a well known implementation of the technique. We discuss alternate implementations that have better numerical stability properties and can lead to better predictions. Our results will be illustrated by looking at an application involving prediction of galaxy redshift from broadband spectrum data.
SPATIALLY ADAPTIVE SEMI-SUPERVISED LEARNING WITH GAUSSIAN PROCESSES FOR HYPERSPECTRAL DATA ANALYSIS
SPATIALLY ADAPTIVE SEMI-SUPERVISED LEARNING WITH GAUSSIAN PROCESSES FOR HYPERSPECTRAL DATA ANALYSIS GOO JUN * AND JOYDEEP GHOSH* Abstract. A semi-supervised learning algorithm for the classification of hyperspectral data, Gaussian process expectation maximization (GP-EM), is proposed. Model parameters for each land cover class is first estimated by a supervised algorithm using Gaussian process regressions to find spatially adaptive parameters, and the estimated parameters are then used to initialize a spatially adaptive mixture-of-Gaussians model. The mixture model is updated by expectationmaximization iterations using the unlabeled data, and the spatially adaptive parameters for unlabeled instances are obtained by Gaussian process regressions with soft assignments. Two sets of hyperspectral data taken from the Botswana area by the NASA EO-1 satellite are used for experiments. Empirical evaluations show that the proposed framework performs significantly better than baseline algorithms that do not use spatial information, and the results are also better than any previously reported results by other algorithms on the same data.
ARC Code TI: Block-GP: Scalable Gaussian Process Regression
Block GP is a Gaussian Process regression framework for multimodal data, that can be an order of magnitude more scalable than existing state-of-the-art nonlinear regression algorithms. The framework builds local Gaussian Processes on semantically meaningful partitions of the data and provides higher prediction accuracy than a single global model with very high confidence.
Block-GP: Scalable Gaussian Process Regression for Multimodal Data
Regression problems on massive data sets are ubiquitous in many application domains including the Internet, earth and space sciences, and finances. In many cases, regression algorithms such as linear regression or neural networks attempt to fit the target variable as a function of the input variables without regard to the underlying joint distribution of the variables. As a result, these global models are not sensitive to variations in the local structure of the input space. Several algorithms, including the mixture of experts model, classification and regression trees (CART), and others have been developed, motivated by the fact that a variability in the local distribution of inputs may be reflective of a significant change in the target variable. While these methods can handle the non-stationarity in the relationships to varying degrees, they are often not scalable and, therefore, not used in large scale data mining applications. In this paper we develop Block-GP, a Gaussian Process regression framework for multimodal data, that can be an order of magnitude more scalable than existing state-of-the-art nonlinear regression algorithms. The framework builds local Gaussian Processes on semantically meaningful partitions of the data and provides higher prediction accuracy than a single global model with very high confidence. The method relies on approximating the covariance matrix of the entire input space by smaller covariance matrices that can be modeled independently, and can therefore be parallelized for faster execution. Theoretical analysis and empirical studies on various synthetic and real data sets show high accuracy and scalability of Block-GP compared to existing nonlinear regression techniques.
A Gaussian processes approach facilitates the identification of robust biomarkers for exposure to complex pesticide mixtures 5
GEO Series GSE224230. Folsomia candida. 168 samples. Type: Expression profiling by high throughput sequencing.
Modeling non-Gaussian time-varying vector autoregressive process
We present a novel and general methodology for modeling time-varying vector autoregressive processes which are widely used in many areas such as modeling of chemical processes, mobile communication channels and biomedical signals. In the literature, most work utilize multivariate Gaussian models for the mentioned applications, mainly due to the lack of efficient analytical tools for modeling with non-Gaussian distributions. In this paper, we propose a particle filtering approach which can model non-Gaussian autoregressive processes having cross-correlations among them. Moreover, time-varying parameters of the process can be modeled as the most general case by using this sequential Bayesian estimation method. Simulation results justify the performance of the proposed technique, which potentially can model also Gaussian processes as a sub-case.
Making Predictions using Large Scale Gaussian Processes
One of the key problems that arises in many areas is to estimate a potentially nonlinear function [tex] G(x, \theta)[/tex] given input and output samples [tex] ( X,y ) [/tex] so that [tex]y approx G(x, \theta)[/tex]. There are many approaches to addressing this regression problem. Neural networks, regression trees, and many other methods have been developed to estimate [tex]$G$[/tex] given the input output pair [tex] ( X,y ) [/tex]. One method that I have worked with is called Gaussian process regression. There many good texts and papers on the subject. For more technical information on the method and its applications see: http://www.gaussianprocess.org/ A key problem that arises in developing these models on very large data sets is that it ends up requiring an [tex]O(N^3)[/tex] computation where N is the number of data points and the training sample. Obviously this becomes very problematic when N is large. I discussed this problem with Leslie Foster, a mathematics professor at San Jose State University. He, along with some of his students, developed a method to address this problem based on Cholesky decomposition and pivoting. He also shows that this leads to a numerically stable result. If ou're interested in some light reading, I’d suggest you take a look at his [recent paper]( ) (which was accepted in the Journal of Machine Learning Research) posted on dashlink. We've also posted code for you to try it out. Let us know how it goes. If you are interested in applications of this method in the area of prognostics, check out our [new paper](/dashlink/resources/51/) on the subject which was published in IEEE Transactions on Systems, Man, and Cybernetics.
A multi-objective Bayesian optimization framework for the synthesis of methanol from syngas using interpretable Gaussian process models
<p>The data sets are synthesized with two reactors (1) Recycle reactor (2) Once through reactor. These reactors have a typical fixed bed of catalysts. The inlet parameter values are varied, and output parameter readings are recorded.</p> <p> </p>
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Understand access before you commit
These curated guides explain access requirements, typical timelines, costs, and reuse considerations for widely used research datasets.
Allen Brain Atlas
Allen Brain Atlas is an Allen Institute collection of brain map atlases, datasets, APIs, and analysis tools covering mouse, human, and non-human primate brain resources.
Annotated Behaviour and Observability Dataset (ABODe)
ABODe is a University of Edinburgh DataShare dataset for behavior classification in group-housed mice using home-cage video, identities, bounding boxes, ground-plate positions, and annotator labels.
DANDI Archive for NWB datasets
DANDI is a BRAIN Initiative archive for publishing and sharing neurophysiology data, including electrophysiology, optophysiology, and behavioral data packaged as NWB and related standards.
International Brain Laboratory public data
The International Brain Laboratory public data releases expose standardized mouse decision-making experiments, including Neuropixels recordings, widefield calcium imaging, behavior, and session metadata accessed through the ONE API.
OpenNeuro
OpenNeuro is a free, open platform for sharing neuroimaging datasets, with public search, dataset pages, and download paths for web, S3, DataLad, and the OpenNeuro CLI.