We consider the problem of learning causal models from observational data generated by linear non-Gaussian acyclic causal models with latent variables. Without considering the effect of latent variables, one usually infers wrong causal relationships among the observed variables. Under faithfulness assumption, we propose a method to check whether there exists a causal path between any two observed variables. From this information, we can obtain the causal order among them. The next question is then whether or not the causal effects can be uniquely identified as well. It can be shown that causal effects among observed variables cannot be identified uniquely even under the assumptions of faithfulness and non-Gaussianity of exogenous noises. However, we will propose an efficient method to identify the set of all possible causal effects that are compatible with the observational data. Furthermore, we present some structural conditions on the causal graph under which we can learn causal effects among observed variables uniquely. We also provide necessary and sufficient graphical conditions for unique identification of the number of variables in the system. Experiments on synthetic data and real-world data show the effectiveness of our proposed algorithm on learning causal models.

Motivated by the need of the linking records across various databases, we propose a novel graphical model based classifier that uses a mixture of Poisson distributions with latent variables. The idea is to derive insight into each pair of hypothesis records that match by inferring its underlying latent rate of error using Bayesian Modeling techniques. The novel approach of using gamma priors for learning the latent variables along with supervised labels is unique and allows for active learning. The naive assumption is made deliberately as to the independence of the fields to propose a generalized theory for this class of problems and not to undermine the hierarchical dependencies that could be present in different scenarios. This classifier is able to work with sparse and streaming data. The application to record linkage is able to meet several challenges of sparsity, data streams and varying nature of the data-sets.

Variational inference is becoming more and more popular for approximating intractable posterior distributions in Bayesian statistics and machine learning. Meanwhile, a few recent works have provided theoretical justification and new insights on deep neural networks for estimating smooth functions in usual settings such as nonparametric regression. In this paper, we show that variational inference for sparse deep learning retains the same generalization properties than exact Bayesian inference. In particular, we highlight the connection between estimation and approximation theories via the classical bias-variance trade-off and show that it leads to near-minimax rates of convergence for H\"older smooth functions. Additionally, we show that the model selection framework over the neural network architecture via ELBO maximization does not overfit and adaptively achieves the optimal rate of convergence.

High entropy alloys (HEAs) have been increasingly attractive as promising next-generation materials due to their various excellent properties. It's necessary to essentially characterize the degree of chemical ordering and identify order-disorder transitions through efficient simulation and modeling of thermodynamics. In this study, a robust data-driven framework based on Bayesian approaches is proposed and demonstrated on the accurate and efficient prediction of configurational energy of high entropy alloys. The proposed effective pair interaction (EPI) model with ensemble sampling is used to map the configuration and its corresponding energy. The US Government retains and the publisher, by accepting the article for publication, acknowledges that the US government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for US government purposes. Compared with the arbitrary determination of model complexity, we further conduct a physical feature selection to identify the truncation of coordination shells in EPI model using Bayesian information criterion. The results achieve efficient and robust performance in predicting the configurational energy, particularly given small data. The developed methodology is applied to study a series of refractory HEAs, i.e. NbMoTaW, NbMoTaWV and NbMoTaWTi where it is demonstrated how dataset size affects the confidence we can place in statistical estimates of configurational energy when data are sparse. Introduction As one of the typical multicomponent alloys, high entropy alloys (HEAs) consisting of four or more principal elements have been widely studied due to their exceptional mechanical properties [1, 2, 3, 4].

Bayesian inference promises to ground and improve the performance of deep neural networks. It promises to be robust to overfitting, to simplify the training procedure and the space of hyperparameters, and to provide a calibrated measure of uncertainty that can enhance decision making, agent exploration and prediction fairness. Markov Chain Monte Carlo (MCMC) methods enable Bayesian inference by generating samples from the posterior distribution over model parameters. Despite the theoretical advantages of Bayesian inference and the similarity between MCMC and optimization methods, the performance of sampling methods has so far lagged behind optimization methods for large scale deep learning tasks. We aim to fill this gap and introduce ATMC, an adaptive noise MCMC algorithm that estimates and is able to sample from the posterior of a neural network. ATMC dynamically adjusts the amount of momentum and noise applied to each parameter update in order to compensate for the use of stochastic gradients. We use a ResNet architecture without batch normalization to test ATMC on the Cifar10 benchmark and the large scale ImageNet benchmark and show that, despite the absence of batch normalization, ATMC outperforms a strong optimization baseline in terms of both classification accuracy and test log-likelihood. We show that ATMC is intrinsically robust to overfitting on the training data and that ATMC provides a better calibrated measure of uncertainty compared to the optimization baseline.

Recent advances in statistical inference have significantly expanded the toolbox of probabilistic modeling. Historically, probabilistic modeling has been constrained to (i) very restricted model classes where exact or approximate probabilistic inference were feasible, and (ii) small or medium-sized data sets which fit within the main memory of the computer. However, developments in variational inference, a general form of approximate probabilistic inference originated in statistical physics, are allowing probabilistic modeling to overcome these restrictions: (i) Approximate probabilistic inference is now possible over a broad class of probabilistic models containing a large number of parameters, and (ii) scalable inference methods based on stochastic gradient descent and distributed computation engines allow to apply probabilistic modeling over massive data sets. One important practical consequence of these advances is the possibility to include deep neural networks within a probabilistic model to capture complex non-linear stochastic relationships between random variables. These advances in conjunction with the release of novel probabilistic modeling toolboxes have greatly expanded the scope of application of probabilistic models, and allow these models to take advantage of the recent strides made by the deep learning community. In this paper we review the main concepts, methods and tools needed to use deep neural networks within a probabilistic modeling framework.

Variational Bayes (VB) has become a versatile tool for Bayesian inference in statistics. Nonetheless, the development of the existing VB algorithms is so far generally restricted to the case where the variational parameter space is Euclidean, which hinders the potential broad application of VB methods. This paper extends the scope of VB to the case where the variational parameter space is a Riemannian manifold. We develop, for the first time in the literature, an efficient manifold-based VB algorithm that exploits both the geometric structure of the constraint parameter space and the information geometry of the manifold of VB approximating probability distributions. Our algorithm is provably convergent and achieves a convergence rate of order $\mathcal O(1/\sqrt{T})$ and $\mathcal O(1/T^{2-2\epsilon})$ for a non-convex evidence lower bound function and a strongly retraction-convex evidence lower bound function, respectively. We develop in particular two manifold VB algorithms, Manifold Gaussian VB and Manifold Neural Net VB, and demonstrate through numerical experiments that the proposed algorithms are stable, less sensitive to initialization and compares favourably to existing VB methods.

Developing a reliable parametric cost model at the conceptual stage of the project is crucial for projects managers and decision-makers. Existing methods, such as probabilistic and statistical algorithms have been developed for project cost prediction. However, these methods are unable to produce accurate results for conceptual cost prediction due to small and unstable data samples. Artificial intelligence (AI) and machine learning (ML) algorithms include numerous models and algorithms for supervised regression applications. Therefore, a comparison analysis for AI models is required to guide practitioners to the appropriate model. The study focuses on investigating twenty artificial intelligence (AI) techniques which are conducted for cost modeling such as fuzzy logic (FL) model, artificial neural networks (ANNs), multiple regression analysis (MRA), case-based reasoning (CBR), hybrid models, and ensemble methods such as scalable boosting trees (XGBoost). Field canals improvement projects (FCIPs) are used as an actual case study to analyze the performance of the applied ML models. Out of 20 AI techniques, the results showed that the most accurate and suitable method is XGBoost with 9.091% and 0.929 based on Mean Absolute Percentage Error (MAPE) and adjusted R2. Nonlinear adaptability, handling missing values and outliers, model interpretation and uncertainty have been discussed for the twenty developed AI models. Keywords: Artificial intelligence, Machine learning, ensemble methods, XGBoost, evolutionary fuzzy rules generation, Conceptual cost, and parametric cost model.

This paper develops several average-case reduction techniques to show new hardness results for three central high-dimensional statistics problems, implying a statistical-computational gap induced by robustness, a detection-recovery gap and a universality principle for these gaps. A main feature of our approach is to map to these problems via a common intermediate problem that we introduce, which we call Imbalanced Sparse Gaussian Mixtures. We assume the planted clique conjecture for a version of the planted clique problem where the position of the planted clique is mildly constrained, and from this obtain the following computational lower bounds: (1) a $k$-to-$k^2$ statistical-computational gap for robust sparse mean estimation, providing the first average-case evidence for a conjecture of Li (2017) and Balakrishnan et al. (2017); (2) a tight lower bound for semirandom planted dense subgraph, which shows that a semirandom adversary shifts the detection threshold in planted dense subgraph to the conjectured recovery threshold; and (3) a universality principle for $k$-to-$k^2$ gaps in a broad class of sparse mixture problems that includes many natural formulations such as the spiked covariance model. Our main approach is to introduce several average-case techniques to produce structured and Gaussianized versions of an input graph problem, and then to rotate these high-dimensional Gaussians by matrices carefully constructed from hyperplanes in $\mathbb{F}_r^t$. For our universality result, we introduce a new method to perform an algorithmic change of measure tailored to sparse mixtures. We also provide evidence that the mild promise in our variant of planted clique does not change the complexity of the problem.

Tractable yet expressive density estimators are a key building block of probabilistic machine learning. While sum-product networks (SPNs) offer attractive inference capabilities, obtaining structures large enough to fit complex, high-dimensional data has proven challenging. In this paper, we present random sum-product forests (RSPFs), an ensemble approach for mixing multiple randomly generated SPNs. We also introduce residual links, which reference specialized substructures of other component SPNs in order to leverage the context-specific knowledge encoded within them. Our empirical evidence demonstrates that RSPFs provide better performance than their individual components. Adding residual links improves the models further, allowing the resulting ResSPNs to be competitive with commonly used structure learning methods.