Academic literature on the topic 'Machine Learning, Graphical Models, Kernel Methods, Optimization'

Abstract Motivation In a predictive modeling setting, if sufficient details of the system behavior are known, one can build and use a simulation for making predictions. When sufficient system details are not known, one typically turns to machine learning, which builds a black-box model of the system using a large dataset of input sample features and outputs. We consider a setting which is between these two extremes: some details of the system mechanics are known but not enough for creating simulations that can be used to make high quality predictions. In this context we propose using approximate simulations to build a kernel for use in kernelized machine learning methods, such as support vector machines. The results of multiple simulations (under various uncertainty scenarios) are used to compute similarity measures between every pair of samples: sample pairs are given a high similarity score if they behave similarly under a wide range of simulation parameters. These similarity values, rather than the original high dimensional feature data, are used to build the kernel. Results We demonstrate and explore the simulation-based kernel (SimKern) concept using four synthetic complex systems—three biologically inspired models and one network flow optimization model. We show that, when the number of training samples is small compared to the number of features, the SimKern approach dominates over no-prior-knowledge methods. This approach should be applicable in all disciplines where predictive models are sought and informative yet approximate simulations are available. Availability and implementation The Python SimKern software, the demonstration models (in MATLAB, R), and the datasets are available at https://github.com/davidcraft/SimKern. Supplementary information Supplementary data are available at Bioinformatics online.

The interplay of machine learning (ML) and optimization methods is an emerging field of artificial intelligence. Both ML and optimization are concerned with modeling of systems related to real-world problems. Parameter selection for classification models is an important task for ML algorithms. In statistical learning theory, cross-validation (CV) which is the most well-known model selection method can be very time consuming for large data sets. One of the recent model selection techniques developed for support vector machines (SVMs) is based on the observed test point margins. In this study, observed margin strategy is integrated into our novel infinite kernel learning (IKL) algorithm together with multi-local procedure (MLP) which is an optimization technique to find global solution. The experimental results show improvements in accuracy and speed when comparing with multiple kernel learning (MKL) and semi-infinite linear programming (SILP) with CV.

The paper constructed a depression classification model based on emotionally related eye-movement data and kernel extreme learn machine (ELM). In order to improve the classification ability of the model, we use particle swarm optimization (PSO) to optimize the model parameters (regularization coefficient C and the parameter σ in the kernel function). At the same time, in order to avoid to be caught in the local optimum and improve PSO's searching ability, we use improved chaotic PSO optimization algorithm and Gauss mutation strategy to increase PSO's particle diversity. The classification results show that the accuracy, sensitivity and specificity of classification models without parameter optimization and Gauss mutation strategy are 80.23%, 80.31% and 79.43%, respectively, while those results of classification model using improved chaotic projection model and Gauss mutation strategy are improved to 88.55%, 87.71% and 89.42%, respectively. Compared with other classification methods of depression, the proposed classification method has better performance on depression recognition.

Gaussian processes (GPs) are natural generalisations of multivariate Gaussian random variables to infinite (countably or continuous) index sets. GPs have been applied in a large number of fields to a diverse range of ends, and very many deep theoretical analyses of various properties are available. This paper gives an introduction to Gaussian processes on a fairly elementary level with special emphasis on characteristics relevant in machine learning. It draws explicit connections to branches such as spline smoothing models and support vector machines in which similar ideas have been investigated. Gaussian process models are routinely used to solve hard machine learning problems. They are attractive because of their flexible non-parametric nature and computational simplicity. Treated within a Bayesian framework, very powerful statistical methods can be implemented which offer valid estimates of uncertainties in our predictions and generic model selection procedures cast as nonlinear optimization problems. Their main drawback of heavy computational scaling has recently been alleviated by the introduction of generic sparse approximations.13,78,31 The mathematical literature on GPs is large and often uses deep concepts which are not required to fully understand most machine learning applications. In this tutorial paper, we aim to present characteristics of GPs relevant to machine learning and to show up precise connections to other "kernel machines" popular in the community. Our focus is on a simple presentation, but references to more detailed sources are provided.

When assessing the quality of the grain supply chain's quality, it is essential to identify and authenticate wheat types, as this is where the process begins with the examination of seeds. Manual inspection by eye is used for both grain identification and confirmation. High-speed, low-effort options became available thanks to automatic classification methods based on machine learning and computer vision. To this day, classifying at the varietal level is still challenging. Classification of wheat seeds was performed using machine learning techniques in this work. Wheat area, wheat perimeter, compactness, kernel length, kernel width, asymmetry coefficient, and kernel groove length are the 7 physical parameters used to categorize the seeds. The dataset includes 210 separate instances of wheat kernels, and was compiled from the UCI library. The 70 components of the dataset were selected randomly and included wheat kernels from three different varieties: Kama, Rosa, and Canadian. In the first stage, we use single machine learning models for classification, including multilayer neural networks, decision trees, and support vector machines. Each algorithm's output is measured against that of the machine learning ensemble method, which is optimized using the whale optimization and stochastic fractal search algorithms. In the end, the findings show that the proposed optimized ensemble is achieving promising results when compared to single machine learning models.

Sentiment analysis and classification task is used in recommender systems to analyze movie reviews, tweets, Facebook posts, online product reviews, blogs, discussion forums, and online comments in social networks. Usually, the classification is performed using supervised machine learning methods such as support vector machine (SVM) classifier, which have many distinct parameters. The selection of the values for these parameters can greatly influence the classification accuracy and can be addressed as an optimization problem. Here we analyze the use of three heuristics, nature-inspired optimization techniques, cuckoo search optimization (CSO), ant lion optimizer (ALO), and polar bear optimization (PBO), for parameter tuning of SVM models using various kernel functions. We validate our approach for the sentiment classification task of Twitter dataset. The results are compared using classification accuracy metric and the Nemenyi test.

Accurate prediction of performance indices using impeller parameters is of great importance for the initial and optimal design of centrifugal pump. In this study, a kernel-based non-parametric machine learning method named with Gaussian process regression (GPR) was proposed, with the purpose of predicting the performance of centrifugal pump with less effort based on available impeller parameters. Nine impeller parameters were defined as model inputs, and the pump performance indices, that is, the head and efficiency, were determined as model outputs. The applicability of three widely used nonlinear kernel functions of GPR including squared exponential (SE), rational quadratic (RQ) and Matern5/2 was investigated, and it was found by comparing with the experimental data that the SE kernel function is more suitable to capture the relationship between impeller parameters and performance indices because of the highest R square and the lowest values of max absolute relative error (MARE), mean absolute proportional error (MAPE), and root mean square error (RMSE). In addition, the results predicted by GPR with SE kernel function were compared with the results given by other three machine learning models. The comparison shows that the GPR with SE kernel function is more accurate and robust than other models in centrifugal pump performance prediction, and its prediction errors and uncertainties are both acceptable in terms of engineering applications. The GPR method is less costly in the performance prediction of centrifugal pump with sufficient accuracy, which can be further used to effectively assist the design and manufacture of centrifugal pump and to speed up the optimization design process of impeller coupled with stochastic optimization methods.

Fractional polytropic gas sphere problems and electrical engineering models typically simulated with interconnected circuits have numerous applications in physical, astrophysical phenomena, and thermionic currents. Generally, most of these models are singular-nonlinear, symmetric, and include time delay, which has increased attention to them among researchers. In this work, we explored deep neural networks (DNNs) with an optimization algorithm to calculate the approximate solutions for nonlinear fractional differential equations (NFDEs). The target data-driven design of the DNN-LM algorithm was further implemented on the fractional models to study the rigorous impact and symmetry of different parameters on RL, RC circuits, and polytropic gas spheres. The targeted data generated from the analytical and numerical approaches in the literature for different cases were utilized by the deep neural networks to predict the numerical solutions by minimizing the differences in mean square error using the Levenberg–Marquardt algorithm. The numerical solutions obtained by the designed technique were contrasted with the multi-step reproducing kernel Hilbert space method (MS-RKM), Laplace transformation method (LTM), and Padé approximations. The results demonstrate the accuracy of the design technique as the DNN-LM algorithm overlaps with the actual results with minimum percentage absolute errors that lie between 10−8 and 10−12. The extensive graphical and statistical analysis of the designed technique showed that the DNN-LM algorithm is dependable and facilitates the examination of higher-order nonlinear complex problems due to the flexibility of the DNN architecture and the effectiveness of the optimization procedure.

In recent years, the correntropy instead of the mean squared error has been widely taken as a powerful tool for enhancing the robustness against noise and outliers by forming the local similarity measurements. However, most correntropy-based models either have too simple descriptions of the correntropy or require too many parameters to adjust in advance, which is likely to cause poor performance since the correntropy fails to reflect the probability distributions of the signals. Therefore, in this paper, a novel correntropy-based extreme learning machine (ELM) called ECC-ELM has been proposed to provide a more robust training strategy based on the newly developed multi-kernel correntropy with the parameters that are generated using cooperative evolution. To achieve an accurate description of the correntropy, the method adopts a cooperative evolution which optimizes the bandwidths by switching delayed particle swarm optimization (SDPSO) and generates the corresponding influence coefficients that minimizes the minimum integrated error (MIE) to adaptively provide the best solution. The simulated experiments and real-world applications show that cooperative evolution can achieve the optimal solution which provides an accurate description on the probability distribution of the current error in the model. Therefore, the multi-kernel correntropy that is built with the optimal solution results in more robustness against the noise and outliers when training the model, which increases the accuracy of the predictions compared with other methods.

Driven by the development of machine learning (ML) and deep learning techniques, prognostics and health management (PHM) has become a key aspect of reliability engineering research. With the recent rise in popularity of quantum computing algorithms and public availability of first-generation quantum hardware, it is of interest to assess their potential for efficiently handling large quantities of operational data for PHM purposes. This paper addresses the application of quantum kernel classification models for fault detection in wind turbine systems (WTSs). The analyzed data correspond to low-frequency SCADA sensor measurements and recorded SCADA alarm logs, focused on the early detection of pitch fault failures. This work aims to explore potential advantages of quantum kernel methods, such as quantum support vector machines (Q-SVMs), over traditional ML approaches and compare principal component analysis (PCA) and autoencoders (AE) as feature reduction tools. Results show that the proposed quantum approach is comparable to conventional ML models in terms of performance and can outperform traditional models (random forest, k-nearest neighbors) for the selected reduced dimensionality of 19 features for both PCA and AE. The overall highest mean accuracies obtained are 0.945 for Gaussian SVM and 0.925 for Q-SVM models.

Over the past two decades graphical models have been widely used as powerful tools for compactly representing distributions. On the other hand, kernel methods have been used extensively to come up with rich representations. This thesis aims to combine graphical models with kernels to produce compact models with rich representational abilities. Graphical models are a powerful underlying formalism in machine learning. Their graph theoretic properties provide both an intuitive modular interface to model the interacting factors, and a data structure facilitating efficient learning and inference. The probabilistic nature ensures the global consistency of the whole framework, and allows convenient interface of models to data. Kernel methods, on the other hand, provide an effective means of representing rich classes of features for general objects, and at the same time allow efficient search for the optimal model. Recently, kernels have been used to characterize distributions by embedding them into high dimensional feature space. Interestingly, graphical models again decompose this characterization and lead to novel and direct ways of comparing distributions based on samples. Among the many uses of graphical models and kernels, this thesis is devoted to the following four areas: Conditional random fields for multi-agent reinforcement learning Conditional random fields (CRFs) are graphical models for modelling the probability of labels given the observations. They have traditionally been trained with using a set of observation and label pairs. Underlying all CRFs is the assumption that, conditioned on the training data, the label sequences of different training examples are independent and identically distributed (iid ). We extended the use of CRFs to a class of temporal learning algorithms, namely policy gradient reinforcement learning (RL). Now the labels are no longer iid. They are actions that update the environment and affect the next observation. From an RL point of view, CRFs provide a natural way to model joint actions in a decentralized Markov decision process. They define how agents can communicate with each other to choose the optimal joint action. We tested our framework on a synthetic network alignment problem, a distributed sensor network, and a road traffic control system. Using tree sampling by Hamze & de Freitas (2004) for inference, the RL methods employing CRFs clearly outperform those which do not model the proper joint policy. Bayesian online multi-label classification Gaussian density filtering (GDF) provides fast and effective inference for graphical models (Maybeck, 1982). Based on this natural online learner, we propose a Bayesian online multi-label classification (BOMC) framework which learns a probabilistic model of the linear classifier. The training labels are incorporated to update the posterior of the classifiers via a graphical model similar to TrueSkill (Herbrich et al., 2007), and inference is based on GDF with expectation propagation. Using samples from the posterior, we label the test data by maximizing the expected F-score. Our experiments on Reuters1-v2 dataset show that BOMC delivers significantly higher macro-averaged F-score than the state-of-the-art online maximum margin learners such as LaSVM (Bordes et al., 2005) and passive aggressive online learning (Crammer et al., 2006). The online nature of BOMC also allows us to effciently use a large amount of training data. Hilbert space embedment of distributions Graphical models are also an essential tool in kernel measures of independence for non-iid data. Traditional information theory often requires density estimation, which makes it unideal for statistical estimation. Motivated by the fact that distributions often appear in machine learning via expectations, we can characterize the distance between distributions in terms of distances between means, especially means in reproducing kernel Hilbert spaces which are called kernel embedment. Under this framework, the undirected graphical models further allow us to factorize the kernel embedment onto cliques, which yields efficient measures of independence for non-iid data (Zhang et al., 2009). We show the effectiveness of this framework for ICA and sequence segmentation, and a number of further applications and research questions are identified. Optimization in maximum margin models for structured data Maximum margin estimation for structured data, e.g. (Taskar et al., 2004), is an important task in machine learning where graphical models also play a key role. They are special cases of regularized risk minimization, for which bundle methods (BMRM, Teo et al., 2007) and the closely related SVMStruct (Tsochantaridis et al., 2005) are state-of-the-art general purpose solvers. Smola et al. (2007b) proved that BMRM requires O(1/έ) iterations to converge to an έ accurate solution, and we further show that this rate hits the lower bound. By utilizing the structure of the objective function, we devised an algorithm for the structured loss which converges to an έ accurate solution in O(1/√έ) iterations. This algorithm originates from Nesterov's optimal first order methods (Nesterov, 2003, 2005b).

This thesis is concerned with two main areas: approximate inference in discrete graphical models, and random embeddings for dimensionality reduction and approximate inference in kernel methods. Approximate inference is a fundamental problem in machine learning and statistics, with strong connections to other domains such as theoretical computer science. At the same time, there has often been a gap between the success of many algorithms in this area in practice, and what can be explained by theory; thus, an important research effort is to bridge this gap. Random embeddings for dimensionality reduction and approximate inference have led to great improvements in scalability of a wide variety of methods in machine learning. In recent years, there has been much work on how the stochasticity introduced by these approaches can be better controlled, and what further computational improvements can be made. In the first part of this thesis, we study approximate inference algorithms for discrete graphical models. Firstly, we consider linear programming methods for approximate MAP inference, and develop our understanding of conditions for exactness of these approximations. Such guarantees of exactness are typically based on either structural restrictions on the underlying graph corresponding to the model (such as low treewidth), or restrictions on the types of potential functions that may be present in the model (such as log-supermodularity). We contribute two new classes of exactness guarantees: the first of these takes the form of particular hybrid restrictions on a combination of graph structure and potential types, whilst the second is given by excluding particular substructures from the underlying graph, via graph minor theory. We also study a particular family of transformation methods of graphical models, uprooting and rerooting, and their effect on approximate MAP and marginal inference methods. We prove new theoretical results on the behaviour of particular approximate inference methods under these transformations, in particular showing that the triplet relaxation of the marginal polytope is unique in being universally rooted. We also introduce a heuristic which quickly picks a rerooting, and demonstrate benefits empirically on models over several graph topologies. In the second part of this thesis, we study Monte Carlo methods for both linear dimensionality reduction and approximate inference in kernel machines. We prove the statistical benefit of coupling Monte Carlo samples to be almost-surely orthogonal in a variety of contexts, and study fast approximate methods of inducing this coupling. A surprising result is that these approximate methods can simultaneously offer improved statistical benefits, time complexity, and space complexity over i.i.d. Monte Carlo samples. We evaluate our methods on a variety of datasets, directly studying their effects on approximate kernel evaluation, as well as on downstream tasks such as Gaussian process regression.

Over the past two decades graphical models have been widely used as a powerful tool for compactly representing distributions. On the other hand, kernel methods have also been used extensively to come up with rich representations. This thesis aims to combine graphical models with kernels to produce compact models with rich representational abilities. The following four areas are our focus. 1. Conditional random fields for multi-agent reinforcement learning. Conditional random fields (CRFs) are graphical models for modeling the probability of labels given the observations. They have traditionally assumed that, conditioned on the training data, the label sequences of different training examples are independent and identically distributed (iid). We extended the use of CRFs to a class of temporal learning algorithms, namely policy gradient reinforcement learning (RL). Now the labels are no longer iid. They are actions that update the environment and affect the next observation. From an RL point of view, CRFs provide a natural way to model joint actions in a decentralized Markov decision process. Using tree sampling for inference, our experiment shows the RL methods employing CRFs clearly outperform those which do not model the proper joint policy. 2. Bayesian online multi-label classification. Gaussian density filtering provides fast and effective inference for graphical models (Maybeck, 1982). Based on it, we propose a Bayesian online multi-label classification (BOMC) framework which learns a probabilistic model of the linear classifier. The training labels are incorporated to update the posterior of the classifiers via a graphical model similar to TrueSkill (Herbrich et al, 2007). Using samples from the posterior, we label the test data by maximizing the expected F1-score. In our experiments, BOMC delivers significantly higher macro-averaged F1-score than the state-of-the-art online maximum margin learners. 3. Hilbert space embedment of distributions. Graphical models are also an essential tool in kernel measures of independence for non-iid data. Traditional information theory often requires density estimation, which makes it unideal for statistical estimation. Motivated by the fact that distributions often appear in machine learning via expectations, we can characterize the distance between distributions in terms of distances between means, especially means in reproducing kernel Hilbert spaces which are called kernel embeddings. Under this framework, the undirected graphical models further allow us to factorize the kernel embeddings onto cliques, which yields efficient measures of independence for non-iid data (Zhang et al, 2009). 4. Optimization in maximum margin models for structured data. Maximum margin estimation for structured data is an important task where graphical models also play a key role. They are special cases of regularized risk minimization, for which bundle methods (BMRM, Teo et al, 2007) are a state-of-the-art general purpose solver. Smola et al (2007) proved that BMRM requires O(1/epsilon) iterations to converge to an epsilon accurate solution, and we further show that this rate hits the lower bound. Motivated by (Nesterov 2003, 2005), we utilized the composite structure of the objective function and devised an algorithm for the structured loss which converges to an epsilon accurate solution in O(1/sqrt{epsilon}) iterations.

AbstractAtomistic machine learning (AML) simulations are used in chemistry at an everincreasing pace. A large number of AML models has been developed, but their implementations are scattered among different packages, each with its own conventions for input and output. Thus, here we give an overview of our MLatom 2 software package, which provides an integrative platform for a wide variety of AML simulations by implementing from scratch and interfacing existing software for a range of state-of-the-art models. These include kernel method-based model types such as KREG (native implementation), sGDML, and GAP-SOAP as well as neuralnetwork- based model types such as ANI, DeepPot-SE, and PhysNet. The theoretical foundations behind these methods are overviewed too. The modular structure of MLatom allows for easy extension to more AML model types. MLatom 2 also has many other capabilities useful for AML simulations, such as the support of custom descriptors, farthest-point and structure-based sampling, hyperparameter optimization, model evaluation, and automatic learning curve generation. It can also be used for such multi-step tasks as Δ-learning, self-correction approaches, and absorption spectrum simulation within the machine-learning nuclear-ensemble approach. Several of these MLatom 2 capabilities are showcased in application examples.

Abstract Water Saturation (Sw) is a critical input to reserves estimation and reservoir modeling workflows which ultimately informs effective reservoir management and decision-making. Without laboratory analysis on expensive core data, Sw is estimated using traditional correlations—commonly Archie's equation. However, using such a correlation in routine petrophysical analysis for estimating reservoir properties on a case-by-case basis is challenging and time-consuming. This study employs a data-driven approach to model Sw in Niger Delta sandstone reservoirs using readily available geophysical well logs. We evaluate the performance of several generic and ensemble machine learning (ML) algorithms for predicting Archie's computed Sw. ML techniques such as unsupervised anomaly detection and multivariate single imputation were used for preprocessing the data and feature engineering was used to improve the predictive quality of the input well logs. The generalization ability of the ML models was assessed on the individual training wells as well as a held-out test well. Model hyperparameters were tuned using Bayesian Optimization in the cross-validation process to achieve a high rate of success. Several evaluation metrics and graphical methods such as learning curves, convergence plots, and partial dependence plots (PDPs) were then used to assess the predictive performance of the models and explain their behavior. This revealed the Tree Boosting ensembles as the top performers. The superior performance of the Tree Boosting ensembles over the benchmark linear model reveals that the relationship between the transformed logs and Sw is complex and better modeled in the nonlinear domain. Based on the results obtained in this research, we propose the Tree Boosting ensembles as potential models for rapidly estimating Sw for reservoir characterization. A broader field application of the proposed methodologies is expected to provide greater insight into subsurface fluid distribution thereby improving hydrocarbon recovery.

Abstract Scientific and engineering problems often require an inexpensive surrogate model to aid understanding and the search for promising designs. While Gaussian processes (GP) stand out as easy-to-use and interpretable learners in surrogate modeling, they have difficulties in accommodating big datasets, qualitative inputs, and multi-type responses obtained from different simulators, which has become a common challenge for a growing number of data-driven design applications. In this paper, we propose a GP model that utilizes latent variables and functions obtained through variational inference to address the aforementioned challenges simultaneously. The method is built upon the latent variable Gaussian process (LVGP) model where qualitative factors are mapped into a continuous latent space to enable GP modeling of mixed-variable datasets. By extending variational inference to LVGP models, the large training dataset is replaced by a small set of inducing points to address the scalability issue. Output response vectors are represented by a linear combination of independent latent functions, forming a flexible kernel structure to handle multi-type responses. Comparative studies demonstrate that the proposed method scales well for large datasets with over 104 data points, while outperforming state-of-the-art machine learning methods without requiring much hyperparameter tuning. In addition, an interpretable latent space is obtained to draw insights into the effect of qualitative factors, such as those associated with “building blocks” of architectures and element choices in metamaterial and materials design. Our approach is demonstrated for machine learning of ternary oxide materials and topology optimization of a multiscale compliant mechanism with aperiodic microstructures and multiple materials.