Noisy-OR Bayesian Networks (BNs) are a family of probabilistic graphical models which express rich statistical dependencies in binary data. Variational inference (VI) has been the main method proposed to learn noisy-OR BNs with complex latent structures (Jaakkola & Jordan, 1999; Ji et al., 2020; Buhai et al., 2020). However, the proposed VI approaches either (a) use a recognition network with standard amortized inference that cannot induce ``explaining-away''; or (b) assume a simple mean-field (MF) posterior which is vulnerable to bad local optima. Existing MF VI methods also update the MF parameters sequentially which makes them inherently slow. In this paper, we propose parallel max-product as an alternative algorithm for learning noisy-OR BNs with complex latent structures and we derive a fast stochastic training scheme that scales to large datasets. We evaluate both approaches on several benchmarks where VI is the state-of-the-art and show that our method (a) achieves better test performance than Ji et al. (2020) for learning noisy-OR BNs with hierarchical latent structures on large sparse real datasets; (b) recovers a higher number of ground truth parameters than Buhai et al. (2020) from cluttered synthetic scenes; and (c) solves the 2D blind deconvolution problem from Lazaro-Gredilla et al. (2021) and variant - including binary matrix factorization - while VI catastrophically fails and is up to two orders of magnitude slower.

The last decade witnessed a growing interest in Bayesian learning. Yet, the technicality of the topic and the multitude of ingredients involved therein, besides the complexity of turning theory into practical implementations, limit the use of the Bayesian learning paradigm, preventing its widespread adoption across different fields and applications. This self-contained survey engages and introduces readers to the principles and algorithms of Bayesian Learning for Neural Networks. It provides an introduction to the topic from an accessible, practical-algorithmic perspective. Upon providing a general introduction to Bayesian Neural Networks, we discuss and present both standard and recent approaches for Bayesian inference, with an emphasis on solutions relying on Variational Inference and the use of Natural gradients. We also discuss the use of manifold optimization as a state-of-the-art approach to Bayesian learning. We examine the characteristic properties of all the discussed methods, and provide pseudo-codes for their implementation, paying attention to practical aspects, such as the computation of the gradients.

In Markov Decision Processes (MDPs), an agent interacts with the environment and learns to optimally behave in it [28]. However, the MDP solution may be very sensitive to little changes in the model parameters [23]. Hence we should be cautious applying the solution of the MDP, when the model is changing or when there is uncertainty in the model parameters. Robust MDPs provide a way to address this issue, where an agent can learn to optimally behave even when the model parameters are uncertain [15, 29, 18]. Another motivation to study robust MDPs is that they can lead to better generalization [33, 34, 25] compared to non-robust solutions.

Trustworthy machine learning aims at combating distributional uncertainties in training data distributions compared to population distributions. Typical treatment frameworks include the Bayesian approach, (min-max) distributionally robust optimization (DRO), and regularization. However, two issues have to be raised: 1) All these methods are biased estimators of the true optimal cost; 2) the prior distribution in the Bayesian method, the radius of the distributional ball in the DRO method, and the regularizer in the regularization method are difficult to specify. This paper studies a new framework that unifies the three approaches and that addresses the two challenges mentioned above. The asymptotic properties (e.g., consistency and asymptotic normalities), non-asymptotic properties (e.g., unbiasedness and generalization error bound), and a Monte--Carlo-based solution method of the proposed model are studied. The new model reveals the trade-off between the robustness to the unseen data and the specificity to the training data.

Recommender systems are a class of online reinforcement learning algorithms that interact sequentially with an environment suggesting relevant items to a user. During the last decade, there has been an increasing interest in online recommendation techniques due to the importance of advertisement recommendation for e-commerce websites or the rise of movies and music streaming platforms [1, 2]. Among different settings for recommender systems, in this work, we focus on the contextual bandit framework applied to the recommendation of quantum data. The contextual bandit problem is a variant of the multi-armed bandit problem where a learner at each round receives a context and given a set of actions (also called actions) has to decide the best action using the context information. After selecting an action the learner will receive a reward and for the next rounds, they will use the previous information of contexts and rewards in order to make their future choices.

Root Cause Analysis (RCA) plays an indispensable role in distributed data system maintenance and operations, as it bridges the gap between fault detection and system recovery. Existing works mainly study multidimensional localization or graph-based root cause localization. This paper opens up the possibilities of exploiting the recently developed framework of explainable AI (XAI) for the purpose of RCA. In particular, we propose BALANCE (BAyesian Linear AttributioN for root CausE localization), which formulates the problem of RCA through the lens of attribution in XAI and seeks to explain the anomalies in the target KPIs by the behavior of the candidate root causes. BALANCE consists of three innovative components. First, we propose a Bayesian multicollinear feature selection (BMFS) model to predict the target KPIs given the candidate root causes in a forward manner while promoting sparsity and concurrently paying attention to the correlation between the candidate root causes. Second, we introduce attribution analysis to compute the attribution score for each candidate in a backward manner. Third, we merge the estimated root causes related to each KPI if there are multiple KPIs. We extensively evaluate the proposed BALANCE method on one synthesis dataset as well as three real-world RCA tasks, that is, bad SQL localization, container fault localization, and fault type diagnosis for Exathlon. Results show that BALANCE outperforms the state-of-the-art (SOTA) methods in terms of accuracy with the least amount of running time, and achieves at least $6\%$ notably higher accuracy than SOTA methods for real tasks. BALANCE has been deployed to production to tackle real-world RCA problems, and the online results further advocate its usage for real-time diagnosis in distributed data systems.

Deep learning is a topic of considerable current interest. The availability of massive data collections and powerful software resources has led to an impressive amount of results in many application areas that reveal essential but hidden properties of the observations. System identification learns mathematical descriptions of dynamic systems from input-output data and can thus benefit from the advances of deep neural networks to enrich the possible range of models to choose from. For this reason, we provide a survey of deep learning from a system identification perspective. We cover a wide spectrum of topics to enable researchers to understand the methods, providing rigorous practical and theoretical insights into the benefits and challenges of using them. The main aim of the identified model is to predict new data from previous observations. This can be achieved with different deep learning based modelling techniques and we discuss architectures commonly adopted in the literature, like feedforward, convolutional, and recurrent networks. Their parameters have to be estimated from past data trying to optimize the prediction performance. For this purpose, we discuss a specific set of first-order optimization tools that is emerged as efficient. The survey then draws connections to the well-studied area of kernel-based methods. They control the data fit by regularization terms that penalize models not in line with prior assumptions. We illustrate how to cast them in deep architectures to obtain deep kernel-based methods. The success of deep learning also resulted in surprising empirical observations, like the counter-intuitive behaviour of models with many parameters. We discuss the role of overparameterized models, including their connection to kernels, as well as implicit regularization mechanisms which affect generalization, specifically the interesting phenomena of benign overfitting ...

Probabilistic graphical models (PGMs) provide a compact and flexible framework to model very complex real-life phenomena. They combine the probability theory which deals with uncertainty and logical structure represented by a graph which allows one to cope with the computational complexity and also interpret and communicate the obtained knowledge. In the thesis, we consider two different types of PGMs: Bayesian networks (BNs) which are static, and continuous time Bayesian networks which, as the name suggests, have a temporal component. We are interested in recovering their true structure, which is the first step in learning any PGM. This is a challenging task, which is interesting in itself from the causal point of view, for the purposes of interpretation of the model and the decision-making process. All approaches for structure learning in the thesis are united by the same idea of maximum likelihood estimation with the LASSO penalty. The problem of structure learning is reduced to the problem of finding non-zero coefficients in the LASSO estimator for a generalized linear model. In the case of CTBNs, we consider the problem both for complete and incomplete data. We support the theoretical results with experiments.

Anomaly detection is critical for finding suspicious behavior in innumerable systems. We need to detect anomalies in real-time, i.e. determine if an incoming entity is anomalous or not, as soon as we receive it, to minimize the effects of malicious activities and start recovery as soon as possible. Therefore, online algorithms that can detect anomalies in a streaming manner are essential. We first propose MIDAS which uses a count-min sketch to detect anomalous edges in dynamic graphs in an online manner, using constant time and memory. We then propose two variants, MIDAS-R which incorporates temporal and spatial relations, and MIDAS-F which aims to filter away anomalous edges to prevent them from negatively affecting the internal data structures. We then extend the count-min sketch to a Higher-Order sketch to capture complex relations in graph data, and to reduce detecting suspicious dense subgraph problem to finding a dense submatrix in constant time. Using this sketch, we propose four streaming methods to detect edge and subgraph anomalies. Next, we broaden the graph setting to multi-aspect data. We propose MStream which detects explainable anomalies in multi-aspect data streams. We further propose MStream-PCA, MStream-IB, and MStream-AE to incorporate correlation between features. Finally, we consider multi-dimensional data streams with concept drift and propose MemStream. MemStream leverages the power of a denoising autoencoder to learn representations and a memory module to learn the dynamically changing trend in data without the need for labels. We prove a theoretical bound on the size of memory for effective drift handling. In addition, we allow quick retraining when the arriving stream becomes sufficiently different from the training data. Furthermore, MemStream makes use of two architecture design choices to be robust to memory poisoning.

In many applications in engineering and sciences analysts have simultaneous access to multiple data sources. In such cases, the overall cost of acquiring information can be reduced via data fusion or multi-fidelity (MF) modeling where one leverages inexpensive low-fidelity (LF) sources to reduce the reliance on expensive high-fidelity (HF) data. In this paper, we employ neural networks (NNs) for data fusion in scenarios where data is very scarce and obtained from an arbitrary number of sources with varying levels of fidelity and cost. We introduce a unique NN architecture that converts MF modeling into a nonlinear manifold learning problem. Our NN architecture inversely learns non-trivial (e.g., non-additive and non-hierarchical) biases of the LF sources in an interpretable and visualizable manifold where each data source is encoded via a low-dimensional distribution. This probabilistic manifold quantifies model form uncertainties such that LF sources with small bias are encoded close to the HF source. Additionally, we endow the output of our NN with a parametric distribution not only to quantify aleatoric uncertainties, but also to reformulate the network's loss function based on strictly proper scoring rules which improve robustness and accuracy on unseen HF data. Through a set of analytic and engineering examples, we demonstrate that our approach provides a high predictive power while quantifying various sources uncertainties.