Bayesian Markov Logic Networks

Real-world datasets are heavily skewed where some classes are significantly outnumbered by the other classes. In these situations, machine learning algorithms fail to achieve substantial efficacy while predicting these underrepresented instances. To solve this problem, many variations of synthetic minority oversampling methods (SMOTE) have been proposed to balance datasets which deal with continuous features. However, for datasets with both nominal and continuous features, SMOTE-NC is the only SMOTE-based oversampling technique to balance the data. In this paper, we present a novel minority oversampling method, SMOTE-ENC (SMOTE—Encoded Nominal and Continuous), in which nominal features are encoded as numeric values and the difference between two such numeric values reflects the amount of change of association with the minority class. Our experiments show that classification models using the SMOTE-ENC method offer better prediction than models using SMOTE-NC when the dataset has a substantial number of nominal features and also when there is some association between the categorical features and the target class. Additionally, our proposed method addressed one of the major limitations of the SMOTE-NC algorithm. SMOTE-NC can be applied only on mixed datasets that have features consisting of both continuous and nominal features and cannot function if all the features of the dataset are nominal. Our novel method has been generalized to be applied to both mixed datasets and nominal-only datasets.

This chapter begins with a review of variational inference (VI) as a fast approximation alternative to Markov Chain Monte Carlo (MCMC) methods, solving an optimization problem for approximating the posterior. VI is scaled to stochastic variational inference and generalized to black-box variational inference (BBVI). Amortized VI leads to the variational auto-encoder (VAE) framework which is introduced using deep neural networks and graphical models and used for learning representations and generative modeling. Finally, we explore generative flows, the latent space manifold, and Riemannian geometry of generative models.

Introduction As mentioned earlier in this text, we take for granted that the Navier–Stokes equations (NSE), together with the associated boundary and initial conditions, embody all the macroscopic physics of fluid flows. In particular, the evolution of any measured property of a turbulent flow must be relatable to the solutions of those equations. In turbulent flow regimes, the physical properties are universally recognized as randomly varying and characterized by some suitable probability distribution functions. In this and the following chapter, we discuss how those probability distribution functions (also called probability distributions or measures, or Borel measures, in the mathematical terminology; see Appendix A.1) are determined by the underlying Navier–Stokes equations. Although in many cases such distributions may not be known explicitly, their existence and many useful properties may be readily established. For many practical purposes, such partial knowledge may be all that is needed. Thus we note that the issue of an explicit form of the distribution function – in particular, whether this measure is unique or depends on the initial data – is still an incompletely solved mathematical problem. But there are enough firm results available assuring that many of the widely accepted experimental results are meaningful and in consonance with the theory of the Navier–Stokes equations. For instance, measurements of various aspects of turbulent flows (e.g., the turbulent boundary layer) are actually measurements of time-averaged quantities.

We propose a tuning-free Bayesian approach to learn a set of sparse graphical models, in which adjacent graphs share similar structures. This model can be applied to estimating dynamic networks that evolve smoothly with regard to a covariate (e.g., time). Specifically, a novel structured spike and slab prior is constructed. This prior allows time-varying sparsity pattern by smoothing the spike probabilities across time using a Gauss-Markov chain. An efficient variational Bayes (VB) algorithm is then derived to learn the model, and is compared to related frequentist methods in the literature. We further extend the proposed mechanism to learn graphical models for multivariate time series in frequency domain. As an example, we analyze scalp electroencephalograms (EEG) recordings of patients at early stages of Alzheimer disease (AD), and quantify the loss of synchrony in comparison with control subjects.

In the research, we present a novel nonlinear state estimation method to solve the problems of multi-sensor fusion application in navigation systems. In a full Bayesian framework, the muti-sensor fusion is performed by estimating the maximum a posterior over the joint probability distribution function (PDF) of all state variables. In order to exploit the full sparsity of the system, the joint PDF is represented by a factor graph model. Since the outliers which represent corrupted observations could affect the accuracy of state estimation, a variational approximation scheme is applied for robust multi-sensor fusion. The proposed method is experimentally verified using the multi-sensor data that recoded by an integrated navigation system. The simulation results demonstrate that the proposed method provides a comparable performance to the traditional muti-sensor fusion method.

Robots had a great impact on the manufacturing industry ever since the early seventies when companies such as KUKA and ABB started deploying their first industrial robots. These robots merely performed very specific tasks in specific ways within well-defined environments. Still, they proved to be very useful as they could exceed human performance at these tasks. However, in order to enable robots to enter our daily life, they need to become more versatile and need to operate in much less structured environments. This thesis is partly devoted to stretching these limitations by means of learning, namely imitation learning (IL) and inverse reinforcement learning (IRL). Reinforcement learning (RL) is a powerful approach to enable robots to solve a task in an unknown environment. The practitioner describes a desired behavior by specifying a reward function and the robot autonomously interacts with the environment in order to find a control policy that generates high accumulated reward. However, RL is not suitable for teaching new tasks by non-experts because specifying appropriate reward functions can be difficult. Demonstrating the desired behavior is often easier for non-experts. Imitation learning can be used in order to enable the robot to reproduce the demonstrations. However, without explicitly inferring and modeling the intentions of the demonstrations, it can become difficult to solve the task for unseen situations. Inverse reinforcement learning (IRL) therefore aims to infer a reward function from the demonstrations, such that optimizing this reward function yields the desired behavior even for different situations. This thesis introduces a unifying approach to solve the inverse reinforcement learning problem in the same way as the reinforcement learning problem. This is achieved by framing both problems as information projection problems, i.e., we strive to minimize the relative entropy between a probabilistic model of the robot behavior and a given desired distribution. Furthermore, a trust region on the robot behavior is used to stabilize the optimization. For inverse reinforcement learning, the desired distribution is implicitly given by the expert demonstrations. The resulting optimization can be efficiently solved using state-of-the-art reinforcement learning methods. For reinforcement learning, the log-likelihood of the desired distribution is given by the reward function. The resulting optimization problem corresponds to a standard reinforcement learning formulation, except for an additional objective of maximizing the entropy of the robot behavior. This entropy objective adds little overhead to the optimization, but can lead to better exploration and more diversified policies. Trust-region I-projections are not only useful for training robots, but can also be applied to other machine learning problems. I-projections are typically used for variational inference, in order to approximate an intractable distribution by a simpler model. However, the resulting optimization problems are usually optimized based on stochastic gradient descent which often suffers from high variance in the gradient estimates. As trust-region I-projections where shown to be effective for reinforcement learning and inverse reinforcement learning, this thesis also explores their use for variational inference. More specifically, trust-region I-projections are investigated for the problem of approximating an intractable distribution by a Gaussian mixture model (GMM) with an adaptive number of components. GMMs are highly desirable for variational inference because they can yield arbitrary accurate approximations while inference from GMMs is still relatively cheap. In order to make learning the GMM feasible, we derive a lower bound that enables us to decompose the objective function. The optimization can then be performed by iteratively updating individual components using a technique from reinforcement learning. The resulting method is capable of learning approximations of significantly higher quality than existing variational inference methods. Due to the similarity of the underlying optimization problems, the insights gained from our variational inference method are also useful for IL and IRL. Namely, a similar lower bound can be applied also for the I-projection formulation of imitation learning. However, whereas for variational inference the lower bound serves to decompose the objective function, for imitation learning it allows us to provide a reward signal to the robot that does not depend on its behavior. Compared to reward functions that are relative to the current behavior of the robot---which are typical for popular adversarial methods---behavior-independent reward functions have the advantages that we can show convergence even for greedy optimization. Furthermore, behavior-independent reward functions solve the inverse reinforcement learning problem, thereby closing the gap between imitation learning and IRL. However, algorithms derived from our non-adversarial formulation are actually very similar to existing AIL methods, and we can even show that adversarial inverse reinforcement learning (AIRL) is indeed an instance of our formulation. AIRL was derived from an adversarial formulation, and we point out several problems of that derivation. In contrast, we show that AIRL can be straightforwardly derived from out non-adversarial formulation. Furthermore, we demonstrate that the non-adversarial formulation can be also used to derive novel algorithms by presenting a non-adversarial method for offline imitation learning.

1 Introduction Program schemata (also called schemes, or abstract programs) are widely known as devices for treating properties of computer programs which are invariant across a range of interpretatio ns. Since the intent of schemata is to formalize a specific aspect of effective computation, the properties studied are usually those which have been prescribed in other models of computation: e.g., totality, equivalence, decision power. It is perhaps for this reason that the methodology for dealing with schemata has evolved around constructive mathematics and direct demonstration rather than continuous mathematics, transfinite mathematics and indirect proof. Recently, however, it has been pointed out (Kfoury [3], DeMillo [2]) that useful properties of schemata can be established using arguments which rest on nonconstructi ve foundations; in this case the model theory of first order logic. The outcome of this activity has been to recast some deep questions regarding, for instance, what can and cannot be proved about computer programs into a form which is similar to the corresponding logical questions, where some of the answers are known. In this note,* we present three such applications of model theory. We allow a free wheeling notion of schemata (allowing, for example, first order oracles of any sort desired) and show that direct limitations exist in the ability to draw inferences about schemata by examining finite entailment and axiomatizability. The third application shows that even the expansive concept of effectiveness allowed here does not admit more relative decision power than the standard models of computation. 2 Notation Logical notation follows such standard sources as Bell and Slomson [1]. In particular, such notions as first order language, similarity type, relational structure, and interpretation are assumed in this presentation. A given first order language always talks about

Probabilistic graphical models are a fundamental tool in probabilistic modeling, machine learning and artificial intelligence. They allow us to integrate in a natural way expert knowledge, physical modeling, heterogeneous and correlated data and quantities of interest. For exactly this reason, multiple sources of model uncertainty are inherent within the modular structure of the graphical model. In this paper we develop information-theoretic, robust uncertainty quantification methods and non-parametric stress tests for directed graphical models to assess the effect and the propagation through the graph of multi-sourced model uncertainties to quantities of interest. These methods allow us to rank the different sources of uncertainty and correct the graphical model by targeting its most impactful components with respect to the quantities of interest. Thus, from a machine learning perspective, we provide a mathematically rigorous approach to correctability that guarantees a systematic selection for improvement of components of a graphical model while controlling potential new errors created in the process in other parts of the model. We demonstrate our methods in two physico-chemical examples, namely quantum scale-informed chemical kinetics and materials screening to improve the efficiency of fuel cells.

Accurate forecasting of insurance claims is of the utmost importance for insurance activity as the evolution of claims determines cash outflows and the pricing, and thus the profitability, of the underlying insurance coverage. These are used as inputs when the insurance company drafts its business plan and determines its risk appetite, and the respective solvency capital required (by the regulators) to absorb the assumed risks. The conventional claim forecasting methods attempt to fit (each of) the claims frequency and severity with a known probability distribution function and use it to project future claims. This study offers a fresh approach in insurance claims forecasting. First, we introduce two novel sets of variables, i.e., weather conditions and car sales, and second, we employ a battery of Machine Learning (ML) algorithms (Support Vector Machines—SVM, Decision Trees, Random Forests, and Boosting) to forecast the average (mean) insurance claim per insured car per quarter. Finally, we identify the variables that are the most influential in forecasting insurance claims. Our dataset comes from the motor portfolio of an insurance company operating in Athens, Greece and spans a period from 2008 to 2020. We found evidence that the three most informative variables pertain to the new car sales with a 3-quarter and 1-quarter lag and the minimum temperature of Elefsina (one of the weather stations in Athens) with a 3-quarter lag. Among the models tested, Random Forest with limited depth and XGboost run on the 15 most informative variables, and these exhibited the best performance. These findings can be useful in the hands of insurers as they can consider the weather conditions and the new car sales among the parameters that are considered to perform claims forecasting.

The scarcity of chart images public datasets and its generators makes difficult the comparative studies between works in areas such as information visualization, usability, computer vision, and machine learning. Therefore, this paper presents a Web tool for generating data chart images called Synthetic Chart Image Generator (SCIG). The tool uses VEGA declarative language, and the chart features are fully parameterizable for every eleven different classes, as well as image quantity and its resolution. Additionally, the charts are constructed from synthetic data, randomly generated by probability distributions functions, and rendered in PNG format. Finally, this paper presents a performance test of the chart images generation.

Machine learning (ML) has emerged as a transformative tool in material science, enabling accelerated discovery and design of novel molecules while reducing experimental costs. Uncertainty quantification (UQ) is crucial for enhancing the reliability of ML predictions, particularly in high-stakes applications, such as functional polymer discovery. In this study, we present a comprehensive evaluation of nine UQ methods in ML─ensemble, Gaussian Process Regression (GPR), Monte Carlo Dropout (MCD), mean-variance estimation (MVE), Bayesian Neural Network based on Variational Inference (BNN-VI) and Markov Chain Monte Carlo (BNN-MCMC), evidential deep learning (EDL), quantile regression (QR), natural gradient boosting (NGBoost)─for predicting key polymer properties, including glass transition temperature (Tg), band gap (Eg), melting temperature (Tm) and decomposition temperature (Td). The models are assessed using three independent metrics, including prediction accuracy (R2), Spearman's rank correlation coefficient and calibration area, offering a robust framework for evaluating both mean predictions and uncertainty estimates. Our analysis spans data sets of four properties, out-of-distribution (OOD) experimental and molecular dynamics (MD)-derived data, high-Tg polymers and diverse polymer types, providing a holistic perspective on model performance. Our findings reveal that optimal UQ method selection is highly context-dependent. Ensemble method consistently excelled for general in-distribution predictions across four properties. For challenging OOD scenarios, BNN-MCMC offered a strong balance of predictive accuracy and reliable UQ. NGBoost emerged as the top-performing method for high-Tg polymers, effectively balancing accuracy and uncertainty characterization, with Ensemble method also providing excellent accuracy in this case. Furthermore, BNN-VI demonstrated superior and consistent performance across the nine distinct polymer classes evaluated. This comprehensive benchmark underscores the critical importance of selecting tailored UQ strategies to enhance the trustworthiness of ML predictions, optimize experimental validation efforts, and ultimately accelerate the discovery of advanced functional polymers.

We present ANNz2, a new implementation of the public software for photometric redshift (photo-z) estimation of Collister & Lahav, which now includes generation of full probability distribution functions (PDFs). ANNz2 utilizes multiple machine learning methods, such as artificial neural networks and boosted decision/regression trees. The objective of the algorithm is to optimize the performance of the photo-z estimation, to properly derive the associated uncertainties, and to produce both single-value solutions and PDFs. In addition, estimators are made available, which mitigate possible problems of non-representative or incomplete spectroscopic training samples. ANNz2 has already been used as part of the first weak lensing analysis of the Dark Energy Survey, and is included in the experiment's first public data release. Here we illustrate the functionality of the code using data from the tenth data release of the Sloan Digital Sky Survey and the Baryon Oscillation Spectroscopic Survey. The code is available for download at http://github.com/IftachSadeh/ANNZ.

During the past decade, it has been quite successful to observe how computational topology has incorporated some of the fundamental concepts and ideas from algebraic and differential topology into applications. This fusion of theories gave birth to a new field named Topological Data Analysis (TDA), which has a significant value in various fields, ranging from computational biology to personalized medicine and dynamic data analysis. Going beyond its foundational applications, TDA has enriched and complemented classical machine and deep learning frameworks in establishing what is now known as “topological machine learning.” In this paper, we review the present landscape of this emerging field, emphasizing how it merges with machine learning algorithms such as deep neural networks. Each method confers special advantages, targeting areas like machine learning integration, network reconstruction, classification of network regimes, or reduction of noisy data. We described common methodologies, discussed current implementations, and anticipate future challenges in topological machine learning.

Many modern unsupervised or semi-supervised machine learning algorithms rely on Bayesian probabilistic models. These models are usually intractable and thus require approximate inference. Variational inference (VI) lets us approximate a high-dimensional Bayesian posterior with a simpler variational distribution by solving an optimization problem. This approach has been successfully applied to various models and large-scale applications. In this review, we give an overview of recent trends in variational inference. We first introduce standard mean field variational inference, then review recent advances focusing on the following aspects: (a) scalable VI, which includes stochastic approximations, (b) generic VI, which extends the applicability of VI to a large class of otherwise intractable models, such as non-conjugate models, (c) accurate VI, which includes variational models beyond the mean field approximation or with atypical divergences, and (d) amortized VI, which implements the inference over local latent variables with inference networks. Finally, we provide a summary of promising future research directions.

Graphical model, diffusion equation network dynamics, and manifold learning are different subareas in machine learning and network science. In this paper, combining the ideas from these subareas, we propose and implement graphical model and diffusion equation based manifold learning techniques for sensor data processing. We show that the graphical model and diffusion equation combined manifold learning can be used to perform data processing for one, two, and three-dimensional sensors. Experiments show that this manifold learning approach can solve many sensor data processing problems including radio frequency signal processing, image processing (computer vision), and three-dimensional lighting detection and ranging (LIDAR) processing problems better than some traditional methods.