Bayesian Networks may be appealing for clinical decision-making due to their inclusion of causal knowledge, but their practical adoption remains limited as a result of their inability to deal with unstructured data. While neural networks do not have this limitation, they are not interpretable and are inherently unable to deal with causal structure in the input space. Our goal is to build neural networks that combine the advantages of both approaches. Motivated by the perspective to inject causal knowledge while training such neural networks, this work presents initial steps in that direction. We demonstrate how a neural network can be trained to output conditional probabilities, providing approximately the same functionality as a Bayesian Network. Additionally, we propose two training strategies that allow encoding the independence relations inferred from a given causal structure into the neural network.

In any computer vision task involving color images, a necessary step is classifying pixels according to color and segmenting the respective areas. However, the development of methods able to successfully complete this task has proven challenging, mainly due to the gap between human color perception, linguistic color terms, and digital representation. In this paper, we propose a novel method combining geometric analysis of color theory, fuzzy color spaces, and multi-label systems for the automatic classification of pixels according to 12 standard color categories (Green, Yellow, Light Orange, Deep Orange, Red, Pink, Purple, Ultramarine, Blue, Teal, Brown, and Neutral). Moreover, we present a robust, unsupervised, unbiased strategy for color naming based on statistics and color theory. ABANICCO was tested against the state of the art in color classification and with the standarized ISCC-NBS color system, providing accurate classification and a standard, easily understandable alternative for hue naming recognizable by humans and machines. We expect this solution to become the base to successfully tackle a myriad of problems in all fields of computer vision, such as region characterization, histopathology analysis, fire detection, product quality prediction, object description, and hyperspectral imaging.

Direct Loss Minimization (DLM) has been proposed as a pseudo-Bayesian method motivated as regularized loss minimization. Compared to variational inference, it replaces the loss term in the evidence lower bound (ELBO) with the predictive log loss, which is the same loss function used in evaluation. A number of theoretical and empirical results in prior work suggest that DLM can significantly improve over ELBO optimization for some models. However, as we point out in this paper, this is not the case for Bayesian neural networks (BNNs). The paper explores the practical performance of DLM for BNN, the reasons for its failure and its relationship to optimizing the ELBO, uncovering some interesting facts about both algorithms.

Often the data that a model needs to be trained on is distributed among multiple computing agents and it cannot be accrued in a single server location because of logistical constraints such as memory, efficient data sharing means, or confidentiality requirements due to sensitive nature of the data. However, the need arises to train the same model with the entire distributed data. Isolated training individually by the agents with their local data may lead to overfitted models as the training data is limited. Besides, training such isolated models on different agents is redundant as more parameter updates have to be performed by the isolated models to reach a certain level of accuracy as compared to what can be achieved by sharing information. Distributed learning aims to leverage the full distributed data by a coordinated training among all the agents where the agents are allowed to share partial information (usually the learned model parameters or their gradients) without sharing any raw data.

Discussions on causal relations in real life often consider variables for which the definition of causality is unclear since the notion of interventions on the respective variables is obscure. Asking 'what qualifies an action for being an intervention on the variable X' raises the question whether the action impacted all other variables only through X or directly, which implicitly refers to a causal model. To avoid this known circularity, we instead suggest a notion of 'phenomenological causality' whose basic concept is a set of elementary actions. Then the causal structure is defined such that elementary actions change only the causal mechanism at one node (e.g. one of the causal conditionals in the Markov factorization). This way, the Principle of Independent Mechanisms becomes the defining property of causal structure in domains where causality is a more abstract phenomenon rather than being an objective fact relying on hard-wired causal links between tangible objects. We describe this phenomenological approach to causality for toy and hypothetical real-world examples and argue that it is consistent with the causal Markov condition when the system under consideration interacts with other variables that control the elementary actions.

Paleoclimatology -- the study of past climate -- is relevant beyond climate science itself, such as in archaeology and anthropology for understanding past human dispersal. Information about the Earth's paleoclimate comes from simulations of physical and biogeochemical processes and from proxy records found in naturally occurring archives. Climate-field reconstructions (CFRs) combine these data into a statistical spatial or spatiotemporal model. To date, there exists no consensus spatiotemporal paleoclimate model that is continuous in space and time, produces predictions with uncertainty, and can include data from various sources. A Gaussian process (GP) model would have these desired properties; however, GPs scale unfavorably with data of the magnitude typical for building CFRs. We propose to build on recent advances in sparse spatiotemporal GPs that reduce the computational burden by combining variational methods based on inducing variables with the state-space formulation of GPs. We successfully employ such a doubly sparse GP to construct a probabilistic model of European paleoclimate from the Last Glacial Maximum (LGM) to the mid-Holocene (MH) that synthesizes paleoclimate simulations and fossilized pollen proxy data.

Interpretable machine learning (IML) is concerned with the behavior and the properties of machine learning models. Scientists, however, are only interested in models as a gateway to understanding phenomena. Our work aligns these two perspectives and shows how to design IML property descriptors. These descriptors are IML methods that provide insight not just into the model, but also into the properties of the phenomenon the model is designed to represent. We argue that IML is necessary for scientific inference with ML models because their elements do not individually represent phenomenon properties; instead, the model in its entirety does. However, current IML research often conflates two goals of model analysis -- model audit and scientific inference -- making it unclear which model interpretations can be used to learn about phenomena. Building on statistical decision theory, we show that IML property descriptors applied on a model provide access to relevant aspects of the joint probability distribution of the data. We identify what questions such descriptors can address, provide a guide to building appropriate descriptors and quantify their epistemic uncertainty.

In brain-computer interfaces (BCI), most of the approaches based on event-related potential (ERP) focus on the detection of P300, aiming for single trial classification for a speller task. While this is an important objective, existing P300 BCI still require several repetitions to achieve a correct classification accuracy. Signal processing and machine learning advances in P300 BCI mostly revolve around the P300 detection part, leaving the character classification out of the scope. To reduce the number of repetitions while maintaining a good character classification, it is critical to embrace the full classification problem. We introduce an end-to-end pipeline, starting from feature extraction, and is composed of an ERP-level classification using probabilistic Riemannian MDM which feeds a character-level classification using Bayesian accumulation of confidence across trials. Whereas existing approaches only increase the confidence of a character when it is flashed, our new pipeline, called Bayesian accumulation of Riemannian probabilities (ASAP), update the confidence of each character after each flash. We provide the proper derivation and theoretical reformulation of this Bayesian approach for a seamless processing of information from signal to BCI characters. We demonstrate that our approach performs significantly better than standard methods on public P300 datasets.

This course is about the discussion of sampling and exploring data, as well as basic probability theory and Bayes' rule. A variety of exploratory data analysis techniques will be covered, including numeric summary statistics and basic data visualization. The concepts and techniques you will find in this course will serve as building blocks for the inference and modeling courses in the Specialization.

Equipping artificial agents with useful exploration mechanisms remains a challenge to this day. Humans, on the other hand, seem to manage the trade-off between exploration and exploitation effortlessly. In the present article, we put forward the hypothesis that they accomplish this by making optimal use of limited computational resources. We study this hypothesis by meta-learning reinforcement learning algorithms that sacrifice performance for a shorter description length (defined as the number of bits required to implement the given algorithm). The emerging class of models captures human exploration behavior better than previously considered approaches, such as Boltzmann exploration, upper confidence bound algorithms, and Thompson sampling. We additionally demonstrate that changing the description length in our class of models produces the intended effects: reducing description length captures the behavior of brain-lesioned patients while increasing it mirrors cognitive development during adolescence.