Enquiries concerning the underlying mechanisms and the emergent properties of a biological brain have a long history of theoretical postulates and experimental findings. Today, the scientific community tends to converge to a single interpretation of the brain's cognitive underpinnings -- that it is a Bayesian inference machine. This contemporary view has naturally been a strong driving force in recent developments around computational and cognitive neurosciences. Of particular interest is the brain's ability to process the passage of time -- one of the fundamental dimensions of our experience. How can we explain empirical data on human time perception using the Bayesian brain hypothesis? Can we replicate human estimation biases using Bayesian models? What insights can the agent-based machine learning models provide for the study of this subject? In this chapter, we review some of the recent advancements in the field of time perception and discuss the role of Bayesian processing in the construction of temporal models.

In order to develop complex relationships between their inputs and outputs, deep neural networks train and adjust large number of parameters. To make these networks work at high accuracy, vast amounts of data are needed. Sometimes, however, the quantity of data needed is not present or obtainable for training. Neuron-specific dropout (NSDropout) is a tool to address this problem. NSDropout looks at both the training pass, and validation pass, of a layer in a model. By comparing the average values produced by each neuron for each class in a data set, the network is able to drop targeted units. The layer is able to predict what features, or noise, the model is looking at during testing that isn't present when looking at samples from validation. Unlike dropout, the "thinned" networks cannot be "unthinned" for testing. Neuron-specific dropout has proved to achieve similar, if not better, testing accuracy with far less data than traditional methods including dropout and other regularization methods. Experimentation has shown that neuron-specific dropout reduces the chance of a network overfitting and reduces the need for large training samples on supervised learning tasks in image recognition, all while producing best-in-class results.

Multi-fidelity modeling and calibration are data fusion tasks that ubiquitously arise in engineering design. In this paper, we introduce a novel approach based on latent-map Gaussian processes (LMGPs) that enables efficient and accurate data fusion. In our approach, we convert data fusion into a latent space learning problem where the relations among different data sources are automatically learned. This conversion endows our approach with attractive advantages such as increased accuracy, reduced costs, flexibility to jointly fuse any number of data sources, and ability to visualize correlations between data sources. This visualization allows the user to detect model form errors or determine the optimum strategy for high-fidelity emulation by fitting LMGP only to the subset of the data sources that are well-correlated. We also develop a new kernel function that enables LMGPs to not only build a probabilistic multi-fidelity surrogate but also estimate calibration parameters with high accuracy and consistency. The implementation and use of our approach are considerably simpler and less prone to numerical issues compared to existing technologies. We demonstrate the benefits of LMGP-based data fusion by comparing its performance against competing methods on a wide range of examples.

Welcome to the online version Bayesian Modeling and Computation in Python. If you'd like a physical copy it can purchased from the publisher here or on Amazon. This site contains an online version of the book and all the code used to produce the book. This includes the visible code, and all code used to generate figures, tables, etc. To run the code you will need to install the correct packages in a computational environment.

The Cloud paradigm is at a critical point in which the existing energy-efficiency techniques are reaching a plateau, while the computing resources demand at Data Center facilities continues to increase exponentially. The main challenge in achieving a global energy efficiency strategy based on Artificial Intelligence is that we need massive amounts of data to feed the algorithms. Nowadays, any optimization strategy must begin with data. However, companies with access to these large amounts of data decide not to share them because it could compromise their security. This paper proposes a time-series data augmentation methodology based on synthetic scenario forecasting within the Data Center. For this purpose, we will implement a powerful generative algorithm: Generative Adversarial Networks (GANs). The use of GANs will allow us to handle multivariate data and data from different natures (e.g., categorical). On the other hand, adapting Data Centers' operational management to the occurrence of sporadic anomalies is complicated due to the reduced frequency of failures in the system. Therefore, we also propose a methodology to increase the generated data variability by introducing on-demand anomalies. We validated our approach using real data collected from an operating Data Center, successfully obtaining forecasts of random scenarios with several hours of prediction. Our research will help to optimize the energy consumed in Data Centers, although the proposed methodology can be employed in any similar time-series-like problem.

Motivated by the tremendous progress we witnessed in recent years, this paper presents a survey of the scientific literature on the topic of Collaborative Simultaneous Localization and Mapping (C-SLAM), also known as multi-robot SLAM. With fleets of self-driving cars on the horizon and the rise of multi-robot systems in industrial applications, we believe that Collaborative SLAM will soon become a cornerstone of future robotic applications. In this survey, we introduce the basic concepts of C-SLAM and present a thorough literature review. We also outline the major challenges and limitations of C-SLAM in terms of robustness, communication, and resource management. We conclude by exploring the area's current trends and promising research avenues.

Active inference is an account of cognition and behavior in complex systems which brings together action, perception, and learning under the theoretical mantle of Bayesian inference. Active inference has seen growing applications in academic research, especially in fields that seek to model human or animal behavior. While in recent years, some of the code arising from the active inference literature has been written in open source languages like Python and Julia, to-date, the most popular software for simulating active inference agents is the DEM toolbox of SPM, a MATLAB library originally developed for the statistical analysis and modelling of neuroimaging data. Increasing interest in active inference, manifested both in terms of sheer number as well as diversifying applications across scientific disciplines, has thus created a need for generic, widely-available, and user-friendly code for simulating active inference in open-source scientific computing languages like Python. The Python package we present here, pymdp (see https://github.com/infer-actively/pymdp), represents a significant step in this direction: namely, we provide the first open-source package for simulating active inference with partially-observable Markov Decision Processes or POMDPs. We review the package's structure and explain its advantages like modular design and customizability, while providing in-text code blocks along the way to demonstrate how it can be used to build and run active inference processes with ease. We developed pymdp to increase the accessibility and exposure of the active inference framework to researchers, engineers, and developers with diverse disciplinary backgrounds. In the spirit of open-source software, we also hope that it spurs new innovation, development, and collaboration in the growing active inference community.

Community detection is one of the most important methodological fields of network science, and one which has attracted a significant amount of attention over the past decades. This area deals with the automated division of a network into fundamental building blocks, with the objective of providing a summary of its large-scale structure. Despite its importance and widespread adoption, there is a noticeable gap between what is considered the state-of-the-art and the methods that are actually used in practice in a variety of fields. Here we attempt to address this discrepancy by dividing existing methods according to whether they have a "descriptive" or an "inferential" goal. While descriptive methods find patterns in networks based on intuitive notions of community structure, inferential methods articulate a precise generative model, and attempt to fit it to data. In this way, they are able to provide insights into the mechanisms of network formation, and separate structure from randomness in a manner supported by statistical evidence. We review how employing descriptive methods with inferential aims is riddled with pitfalls and misleading answers, and thus should be in general avoided. We argue that inferential methods are more typically aligned with clearer scientific questions, yield more robust results, and should be in many cases preferred. We attempt to dispel some myths and half-truths often believed when community detection is employed in practice, in an effort to improve both the use of such methods as well as the interpretation of their results.

In this paper we present AIDA, which is an active inference-based agent that iteratively designs a personalized audio processing algorithm through situated interactions with a human client. The target application of AIDA is to propose on-the-spot the most interesting alternative values for the tuning parameters of a hearing aid (HA) algorithm, whenever a HA client is not satisfied with their HA performance. AIDA interprets searching for the "most interesting alternative" as an issue of optimal (acoustic) context-aware Bayesian trial design. In computational terms, AIDA is realized as an active inference-based agent with an Expected Free Energy criterion for trial design. This type of architecture is inspired by neuro-economic models on efficient (Bayesian) trial design in brains and implies that AIDA comprises generative probabilistic models for acoustic signals and user responses. We propose a novel generative model for acoustic signals as a sum of time-varying auto-regressive filters and a user response model based on a Gaussian Process Classifier. The full AIDA agent has been implemented in a factor graph for the generative model and all tasks (parameter learning, acoustic context classification, trial design, etc.) are realized by variational message passing on the factor graph. All verification and validation experiments and demonstrations are freely accessible at our GitHub repository.

Approximate Bayesian inference methods provide a powerful suite of tools for finding approximations to intractable posterior distributions. However, machine learning applications typically involve selecting actions, which -- in a Bayesian setting -- depend on the posterior distribution only via its contribution to expected utility. A growing body of work on loss-calibrated approximate inference methods has therefore sought to develop posterior approximations sensitive to the influence of the utility function. Here we introduce loss-calibrated expectation propagation (Loss-EP), a loss-calibrated variant of expectation propagation. This method resembles standard EP with an additional factor that "tilts" the posterior towards higher-utility decisions. We show applications to Gaussian process classification under binary utility functions with asymmetric penalties on False Negative and False Positive errors, and show how this asymmetry can have dramatic consequences on what information is "useful" to capture in an approximation.