The interactive version of this post can be found here. Since Medium does not support Javascript and equations written in Latex, we recommend to check out our interactive post as well. When we think of Peter, his positive nature and his can-do attitude inevitably come to mind. He had an ability to inspire and carry the people around him, convincing them that almost everything is possible. Back in 2018 he came up with the idea for an interactive blog post on the subject of Energy Based Models and pitched it to us. It was almost impossible to resist his enthusiastic manner and of course we embarked on this adventure with him. Equipped with our knowledge in physics and machine learning and hardly any clue about Javascript, we started our journey. After a lot of hard work, we were finally able to complete this project. We are overjoyed with the final result and we wish he could see it.

Bayesian variable selection is a powerful tool for data analysis, as it offers a principled method for variable selection that accounts for prior information and uncertainty. However, wider adoption of Bayesian variable selection has been hampered by computational challenges, especially in difficult regimes with a large number of covariates or non-conjugate likelihoods. Generalized linear models for count data, which are prevalent in biology, ecology, economics, and beyond, represent an important special case. Here we introduce an efficient MCMC scheme for variable selection in binomial and negative binomial regression that exploits Tempered Gibbs Sampling (Zanella and Roberts, 2019) and that includes logistic regression as a special case. In experiments we demonstrate the effectiveness of our approach, including on cancer data with seventeen thousand covariates.

This work is driven by a practical question, corrections of Artificial Intelligence (AI) errors. Systematic re-training of a large AI system is hardly possible. To solve this problem, special external devices, correctors, are developed. They should provide quick and non-iterative system fix without modification of a legacy AI system. A common universal part of the AI corrector is a classifier that should separate undesired and erroneous behavior from normal operation. Training of such classifiers is a grand challenge at the heart of the one- and few-shot learning methods. Effectiveness of one- and few-short methods is based on either significant dimensionality reductions or the blessing of dimensionality effects. Stochastic separability is a blessing of dimensionality phenomenon that allows one-and few-shot error correction: in high-dimensional datasets under broad assumptions each point can be separated from the rest of the set by simple and robust linear discriminant. The hierarchical structure of data universe is introduced where each data cluster has a granular internal structure, etc. New stochastic separation theorems for the data distributions with fine-grained structure are formulated and proved. Separation theorems in infinite-dimensional limits are proven under assumptions of compact embedding of patterns into data space. New multi-correctors of AI systems are presented and illustrated with examples of predicting errors and learning new classes of objects by a deep convolutional neural network.

Gradual pattern mining allows for extraction of attribute correlations through gradual rules such as: "the more X, the more Y". Such correlations are useful in identifying and isolating relationships among the attributes that may not be obvious through quick scans on a data set. For instance, a researcher may apply gradual pattern mining to determine which attributes of a data set exhibit unfamiliar correlations in order to isolate them for deeper exploration or analysis. In this work, we propose an ant colony optimization technique which uses a popular probabilistic approach that mimics the behavior biological ants as they search for the shortest path to find food in order to solve combinatorial problems. In our second contribution, we extend an existing gradual pattern mining technique to allow for extraction of gradual patterns together with an approximated temporal lag between the affected gradual item sets. Such a pattern is referred to as a fuzzy-temporal gradual pattern and it may take the form: "the more X, the more Y, almost 3 months later". In our third contribution, we propose a data crossing model that allows for integration of mostly gradual pattern mining algorithm implementations into a Cloud platform. This contribution is motivated by the proliferation of IoT applications in almost every area of our society and this comes with provision of large-scale time-series data from different sources.

The widespread use of machine learning algorithms calls for automatic change detection algorithms to monitor their behavior over time. As a machine learning algorithm learns from a continuous, possibly evolving, stream of data, it is desirable and often critical to supplement it with a companion change detection algorithm to facilitate its monitoring and control. We present a generic score-based change detection method that can detect a change in any number of components of a machine learning model trained via empirical risk minimization. This proposed statistical hypothesis test can be readily implemented for such models designed within a differentiable programming framework. We establish the consistency of the hypothesis test and show how to calibrate it to achieve a prescribed false alarm rate. We illustrate the versatility of the approach on synthetic and real data.

The large-scale data stream problem refers to high-speed information flow which cannot be processed in scalable manner under a traditional computing platform. This problem also imposes expensive labelling cost making the deployment of fully supervised algorithms unfeasible. On the other hand, the problem of semi-supervised large-scale data streams is little explored in the literature because most works are designed in the traditional single-node computing environments while also being fully supervised approaches. This paper offers Weakly Supervised Scalable Teacher Forcing Network (WeScatterNet) to cope with the scarcity of labelled samples and the large-scale data streams simultaneously. WeScatterNet is crafted under distributed computing platform of Apache Spark with a data-free model fusion strategy for model compression after parallel computing stage. It features an open network structure to address the global and local drift problems while integrating a data augmentation, annotation and auto-correction ($DA^3$) method for handling partially labelled data streams. The performance of WeScatterNet is numerically evaluated in the six large-scale data stream problems with only $25\%$ label proportions. It shows highly competitive performance even if compared with fully supervised learners with $100\%$ label proportions.

In this paper, we propose conjugate energy-based models (CEBMs), a new class of energy-based models that define a joint density over data and latent variables. The joint density of a CEBM decomposes into an intractable distribution over data and a tractable posterior over latent variables. CEBMs have similar use cases as variational autoencoders, in the sense that they learn an unsupervised mapping from data to latent variables. However, these models omit a generator network, which allows them to learn more flexible notions of similarity between data points. Our experiments demonstrate that conjugate EBMs achieve competitive results in terms of image modelling, predictive power of latent space, and out-of-domain detection on a variety of datasets.

While multifidelity modeling provides a cost-effective way to conduct uncertainty quantification with computationally expensive models, much greater efficiency can be achieved by adaptively deciding the number of required high-fidelity (HF) simulations, depending on the type and complexity of the problem and the desired accuracy in the results. We propose a framework for active learning with multifidelity modeling emphasizing the efficient estimation of rare events. Our framework works by fusing a low-fidelity (LF) prediction with an HF-inferred correction, filtering the corrected LF prediction to decide whether to call the high-fidelity model, and for enhanced subsequent accuracy, adapting the correction for the LF prediction after every HF model call. The framework does not make any assumptions as to the LF model type or its correlations with the HF model. In addition, for improved robustness when estimating smaller failure probabilities, we propose using dynamic active learning functions that decide when to call the HF model. We demonstrate our framework using several academic case studies and two finite element (FE) model case studies: estimating Navier-Stokes velocities using the Stokes approximation and estimating stresses in a transversely isotropic model subjected to displacements via a coarsely meshed isotropic model. Across these case studies, not only did the proposed framework estimate the failure probabilities accurately, but compared with either Monte Carlo or a standard variance reduction method, it also required only a small fraction of the calls to the HF model.

This paper describes a new library for learning Bayesian networks from data containing discrete and continuous variables (mixed data). In addition to the classical learning methods on discretized data, this library proposes its algorithm that allows structural learning and parameters learning from mixed data without discretization since data discretization leads to information loss. This algorithm based on mixed MI score function for structural learning, and also linear regression and Gaussian distribution approximation for parameters learning. The library also offers two algorithms for enumerating graph structures - the greedy Hill-Climbing algorithm and the evolutionary algorithm. Thus the key capabilities of the proposed library are as follows: (1) structural and parameters learning of a Bayesian network on discretized data, (2) structural and parameters learning of a Bayesian network on mixed data using the MI mixed score function and Gaussian approximation, (3) launching learning algorithms on one of two algorithms for enumerating graph structures - Hill-Climbing and the evolutionary algorithm. Since the need for mixed data representation comes from practical necessity, the advantages of our implementations are evaluated in the context of solving approximation and gap recovery problems on synthetic data and real datasets.

This paper explores the use of factor graphs as an inference and analysis tool for Bayesian peer-to-peer decentralized data fusion. We propose a framework by which agents can each use local factor graphs to represent relevant partitions of a complex global joint probability distribution, thus allowing them to avoid reasoning over the entirety of a more complex model and saving communication as well as computation cost. This allows heterogeneous multi-robot systems to cooperate on a variety of real world, task oriented missions, where scalability and modularity are key. To develop the initial theory and analyze the limits of this approach, we focus our attention on static linear Gaussian systems in tree-structured networks and use Channel Filters (also represented by factor graphs) to explicitly track common information. We discuss how this representation can be used to describe various multi-robot applications and to design and analyze new heterogeneous data fusion algorithms. We validate our method in simulations of a multi-agent multi-target tracking and cooperative multi-agent mapping problems, and discuss the computation and communication gains of this approach.