An empirical study of the sample size variability of optimal active learning using Gaussian process regression

This paper presents an active learning approach for recognizing human actions in videos based on multiple kernel combined method. We design the classifier based on Multiple Kernel Learning (MKL) through Gaussian Processes (GP) regression. This classifier is then trained in an active learning approach. In each iteration, one optimal sample is selected to be interactively annotated and incorporated into training set. The selection of the sample is based on the heuristic feedback of the GP classifier. To our knowledge, GP regression MKL based active learning methods have not been applied to address the human action recognition yet. We test this approach on standard benchmarks. This approach outperforms the state-of-the-art techniques in accuracy while requires significantly less training samples.

The aim of this article is to present a novel parallelization method for temporal Gaussian process (GP) regression problems. The method allows for solving GP regression problems in logarithmic <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$O(\log N)$</tex> time, where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$N$</tex> stands for the number of observations and test points. Our approach uses the state-space representation of GPs which, in its original form, allows for linear <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$O(N)$</tex> time GP regression by leveraging Kalman filtering and smoothing methods. By using a recently proposed parallelization method for Bayesian filters and smoothers, we are able to reduce the linear computational complexity of the temporal GP regression problems into logarithmic span complexity. This ensures logarithmic time complexity when parallel hardware such as a graphics processing unit (GPU) are employed. We experimentally show the computational benefits of our approach on simulated and real datasets via our open-source implementation leveraging the GPflow framework.

The current exponential increase of spatiotemporally explicit data streams from satellitebased Earth observation missions offers promising opportunities for global vegetation monitoring. Intelligent sampling through active learning (AL) heuristics provides a pathway for fast inference of essential vegetation variables by means of hybrid retrieval approaches, i.e., machine learning regression algorithms trained by radiative transfer model (RTM) simulations. In this study we summarize AL theory and perform a brief systematic literature survey about AL heuristics used in the context of Earth observation regression problems over terrestrial targets. Across all relevant studies it appeared that: (i) retrieval accuracy of AL-optimized training data sets outperformed models trained over large randomly sampled data sets, and (ii) Euclidean distance-based (EBD) diversity method tends to be the most efficient AL technique in terms of accuracy and computational demand. Additionally, a case study is presented based on experimental data employing both uncertainty and diversity AL criteria. Hereby, a a simulated training data base by the PROSAIL-PRO canopy RTM is used to demonstrate the benefit of AL techniques for the estimation of total leaf carotenoid content (Cxc) and leaf water content (Cw). Gaussian process regression (GPR) was incorporated to minimize and optimize the training data set with AL. Training the GPR algorithm on optimally AL-based sampled data sets led to improved variable retrievals compared to training on full data pools, which is further demonstrated on a mapping example. From these findings we can recommend the use of AL-based sub-sampling procedures to select the most informative samples out of large training data pools. This will not only optimize regression accuracy due to exclusion of redundant information, but also speed up processing time and reduce final model size of kernel-based machine learning regression algorithms, such as GPR. With this study we want to encourage further testing and implementation of AL sampling methods for hybrid retrieval workflows. AL can contribute to the solution of regression problems within the framework of operational vegetation monitoring using satellite imaging spectroscopy data, and may strongly facilitate data processing for cloud-computing platforms.

Earth observation from satellite sensory data pose challenging problems, where machine learning is currently a key player. In recent years, Gaussian Process (GP) regression and other kernel methods have excelled in biophysical parameter estimation tasks from space. GP regression is based on solid Bayesian statistics, and generally yield efficient and accurate parameter estimates. However, GPs are typically used for inverse modeling based on concurrent observations and in situ measurements only. Very often a forward model encoding the well-understood physical relations is available though. In this work, we review three GP models that respect and learn the physics of the underlying processes in the context of inverse modeling. First, we will introduce a Joint GP (JGP) model that combines in situ measurements and simulated data in a single GP model. Second, we present a latent force model (LFM) for GP modeling that encodes ordinary differential equations to blend data-driven modeling and physical models of the system. The LFM performs multi-output regression, adapts to the signal characteristics, is able to cope with missing data in the time series, and provides explicit latent functions that allow system analysis and evaluation. Finally, we present an Automatic Gaussian Process Emulator (AGAPE) that approximates the forward physical model via interpolation, reducing the number of necessary nodes. Empirical evidence of the performance of these models will be presented through illustrative examples of vegetation monitoring and atmospheric modeling.

Active Learning (AL) is a methodology from machine learning in which the learner interacts with the data source. In this paper, we investigate application of AL techniques to a new domain: regression problems in performance analysis. For computational systems with many factors, each of which can take on many levels, fixed experiment designs can require many experiments, and can explore the problem space inefficiently. We address these problems with a dynamic, adaptive experiment design, using AL in conjunction with Gaussian Process Regression (GPR). The performance analysis process is seeded with a small number of initial experiments, then GPR provides estimates of regression confidence across the full input space. AL is used to suggest follow-up experiments to run, in general, it will suggest experiments in areas where the GRP model indicates low confidence, and through repeated experiments, the process eventually achieves high confidence throughout the input space. We apply this approach to the problem of estimating performance and energy usage of HPGMG-FE, and create good-quality predictive models for the quantities of interest, with low error and reduced cost, using only a modest number of experiments. Our analysis shows that the error reduction achieved from replacing the basic AL algorithm with a cost-aware algorithm can be significant, reaching up to 38% for the same computational cost of experiments.

Mechanical property prediction plays a crucial role in the steel industry, enabling better materials selection and enhancing production efficiency. In this study, we propose a novel framework that facilitates optimal materials selection for steel’s alloying elements, based on accurate predictions of the Jominy hardness curve. Leveraging Gaussian Process (GP) regression, we provide probabilistic predictions of steel hardenability characteristics from alloy element composition. Taking it a step further, our framework incorporates these accurate predictions into a constrained optimization process, yielding optimal compositions that reduce overall spending while meeting performance specifications. Through data obtained from 1080 steel samples, our GP regression model exhibits high accuracy, achieving an RMSE of 1.37 and showcasing significant improvements in the field. Moreover, our constrained optimization utilizing the GP model and historical market data reveals an average cost reduction of 18% on alloying element expenses, highlighting the tangible cost-saving potential of this approach. By leveraging Gaussian Process (GP) regression, we not only achieve accurate predictions of the Jominy hardness curve based on alloy element composition, but we also introduce a crucial element of uncertainty quantification. This empowers us to place trust in the results of our optimization process, ensuring robust and reliable materials selection. The integration of GP regression and optimization provides a powerful tool for achieving cost-effective materials selection and marks a significant advancement compared to existing studies. This research underscores the promise of machine learning in the steel industry, demonstrating its ability to yield substantial cost savings and enhance decision-making in materials selection.

Understanding the interaction between polymers and proteins is of interest for researchers in medicine, biology, food science, and water treatment, among other fields. The goal may be to create strong interactions with enzymes to improve their catalytic stability, while in nanomedicine and biomedical engineering, the focus is often on reducing protein adsorption on polymer surfaces. Researchers have developed libraries of polymers with various monomer combinations and tested their binding to different proteins to better understand these interactions. In this work, we aimed to identify the polymer with the highest or lowest binding affinity to all proteins, respectively, using Gaussian Process Regression (GPR). However, incorporating categorical features such as the type of monomer has not been widely applied in GPR. Here we compare a range of process models, which were coined Multiplicative kernel, Additive kernel, Easy to interpret Gaussian Process model (EzGP), Latent Variable Gaussian Processes (LVGP), and the Latent Map Gaussian Processes (LMGP) by their developers. The LVGP model was found to perform best on the polymer-protein data set, where the output for binding strength was given by Förster resonance energy transfer (FRET), which can be used to help generate large data sets for machine learning (ML). The polymer that had the highest affinity to glucose oxidase (GOx), uricase (Uri), casein (Cas), trypsin (Trp), carbonic anhydrase (CAn) and bovine serum albumin (BSA) carried positive charges as well as hydrophobic benzyl groups. Negatively charged monomers dominated the polymer that rejected the most proteins intermixed with some cationic units, reminiscent of zwitterionic polymers.

This paper describes a real-time data collection framework and an adaptive machining learning method for constructing a real-time energy prediction model for a machine tool. To effectively establish the energy consumption pattern of a machine tool over time, the energy prediction model is continuously updated with new measurement data to account for time-varying effects of the machine tool, such as tool wear and machine tool deterioration. In this work, a real-time data collection and processing framework is developed to retrieve raw data from a milling machine tool and its sensors and convert them into relevant input features. The extracted input features are then used to construct the energy prediction model using Gaussian Process (GP) regression. To update the GP regression model with real-time streaming data, we investigate the use of sparse representation of the covariance matrix to reduce the computational and storage demands of the GP regression. We compare computational efficiency of sparse GP to that of full GP regression model and show the effectiveness of the sparse GP regression model for tracking the variation in the energy consumption pattern of the target machine.

We introduce an exploratory active learning (AL) algorithm using Gaussian process regression and marginalized graph kernel (GPR-MGK) to sample chemical compound space (CCS) at minimal cost. Targeting 251,728 enumerated alkane molecules with 4-19 carbon atoms, we applied the AL algorithm to select a diverse and representative set of molecules and then conducted high-throughput molecular simulations on these selected molecules. To demonstrate the power of the AL algorithm, we built directed message-passing neural networks (D-MPNN) using simulation data as the training set to predict liquid densities, heat capacities, and vaporization enthalpies of the CCS. Validations show that D-MPNN models built on the smallest training set considered in this work, which consists of 313 molecules or 0.124% of the original CCS, predict the properties with R2 > 0.99 against the computational data and R2 > 0.94 against the experimental data. The advantage of the presented AL algorithm is that the predicted uncertainty of GPR depends on only the molecular structures, which renders it compatible with high-throughput data generation.

This paper proposes a simulation-based active policy learning algorithm for finite-horizon, partially-observed sequential decision processes. The algorithm is tested in the domain of robot navigation and exploration under uncertainty, where the expected cost is a function of the belief state (filtering distribution). This filtering distribution is in turn nonlinear and subject to discontinuities, which arise because constraints in the robot motion and control models. As a result, the expected cost is non-differentiable and very expensive to simulate. The new algorithm overcomes the first difficulty and reduces the number of simulations as follows. First, it assumes that we have carried out previous evaluations of the expected cost for different corresponding policy parameters. Second, it fits a Gaussian process (GP) regression model to these values, so as to approximate the expected cost as a function of the policy parameters. Third, it uses the GP predicted mean and variance to construct a statistical measure that determines which policy parameters should be used in the next simulation. The process is iterated using the new parameters and the newly gathered expected cost observation. Since the objective is to find the policy parameters that minimize the expected cost, this active learning approach effectively trades-off between exploration (where the GP variance is large) and exploitation (where the GP mean is low). In our experiments, a robot uses the proposed method to plan an optimal path for accomplishing a set of tasks, while maximizing the information about its pose and map estimates. These estimates are obtained with a standard filter for SLAM. Upon gathering new observations, the robot updates the state estimates and is able to replan a new path in the spirit of openloop feedback control.

BackgroundThe analysis of gene expression from time series underpins many biological studies. Two basic forms of analysis recur for data of this type: removing inactive (quiet) genes from the study and determining which genes are differentially expressed. Often these analysis stages are applied disregarding the fact that the data is drawn from a time series. In this paper we propose a simple model for accounting for the underlying temporal nature of the data based on a Gaussian process.ResultsWe review Gaussian process (GP) regression for estimating the continuous trajectories underlying in gene expression time-series. We present a simple approach which can be used to filter quiet genes, or for the case of time series in the form of expression ratios, quantify differential expression. We assess via ROC curves the rankings produced by our regression framework and compare them to a recently proposed hierarchical Bayesian model for the analysis of gene expression time-series (BATS). We compare on both simulated and experimental data showing that the proposed approach considerably outperforms the current state of the art.ConclusionsGaussian processes offer an attractive trade-off between efficiency and usability for the analysis of microarray time series. The Gaussian process framework offers a natural way of handling biological replicates and missing values and provides confidence intervals along the estimated curves of gene expression. Therefore, we believe Gaussian processes should be a standard tool in the analysis of gene expression time series.

Human motion intent learning based motion assistance control for a wearable exoskeleton

Kepler-78b is a transiting planet that is 1.2 times the radius of Earth and orbits a young, active K dwarf every 8 hours. The mass of Kepler-78b has been independently reported by two teams based on radial velocity measurements using the HIRES and HARPS-N spectrographs. Due to the active nature of the host star, a stellar activity model is required to distinguish and isolate the planetary signal in radial velocity data. Whereas previous studies tested parametric stellar activity models, we modeled this system using nonparametric Gaussian process (GP) regression. We produced a GP regression of relevant Kepler photometry. We then use the posterior parameter distribution for our photometric fit as a prior for our simultaneous GP + Keplerian orbit models of the radial velocity datasets. We tested three simple kernel functions for our GP regressions. Based on a Bayesian likelihood analysis, we selected a quasi-periodic kernel model with GP hyperparameters coupled between the two RV datasets, giving a Doppler amplitude of 1.86 $\pm$ 0.25 m s$^{-1}$ and supporting our belief that the correlated noise we are modeling is astrophysical. The corresponding mass of 1.87 $^{+0.27}_{-0.26}$ M$_{\oplus}$ is consistent with that measured in previous studies, and more robust due to our nonparametric signal estimation. Based on our mass and the radius measurement from transit photometry, Kepler-78b has a bulk density of 6.0$^{+1.9}_{-1.4}$ g cm$^{-3}$. We estimate that Kepler-78b is 32$\pm$26% iron using a two-component rock-iron model. This is consistent with an Earth-like composition, with uncertainty spanning Moon-like to Mercury-like compositions.

This article investigates optimization of wind farms using a modifier adaptation scheme based on Gaussian processes. In this scheme measurements are used to identify plant-model mismatch using Gaussian process regression, which are then used to find the optimal plant control inputs. However, for systems with many agents and a large control input space, the identification of the input-output map of the plant is challenging. Therefore, the paper proposes a distributed learning approach, in which sub-parts of the plant are identified with individual GP regression models. Afterwards, all of these are used to build a model of the overall plant-model mismatch, which is then used in the optimization. In the wind farm case the sub-parts are the individual turbines. The distributed learning approach clearly outperforms the original central learning approach in numerical illustrations of wind farm test cases.

Gaussian process (GP) regression is a nonparametric regression method that can be used to predict continuous quantities. Here, we show that the same technique can be applied to a class of phase imaging techniques based on measurements of intensity at multiple propagation distances, i.e. the transport of intensity equation (TIE). In this paper, we demonstrate how to apply GP regression to estimate the first intensity derivative along the direction of propagation and incorporate non-uniform propagation distance sampling. The low-frequency artifacts that often occur in phase recovery using traditional methods can be significantly suppressed by the proposed GP TIE method. The method is shown to be stable with moderate amounts of Gaussian noise. We validate the method experimentally by recovering the phase of human cheek cells in a bright field microscope and show better performance as compared to other TIE reconstruction methods.