We present Sequential Neural Likelihood (SNL), a new method for Bayesian inference in simulator models, where the likelihood is intractable but simulating data from the model is possible. SNL trains an autoregressive flow on simulated data in order to learn a model of the likelihood in the region of high posterior density. A sequential training procedure guides simulations and reduces simulation cost by orders of magnitude. We show that SNL is more robust, more accurate and requires less tuning than related state-of-the-art methods which target the posterior, and discuss diagnostics for assessing calibration, convergence and goodness-of-fit.

We propose to learn a stochastic recurrent model to solve the problem of simultaneous localisation and mapping (SLAM). Our model is a deep variational Bayes filter augmented with a latent global variable---similar to an external memory component---representing the spatially structured environment. Reasoning about the pose of an agent and the map of the environment is then naturally expressed as posterior inference in the resulting generative model. We evaluate the method on a set of randomly generated mazes which are traversed by an agent equipped with laser range finders. Path integration based on an accurate motion model is consistently outperformed, and most importantly, drift practically eliminated. Our approach inherits favourable properties from neural networks, such as differentiability, flexibility and the ability to train components either in isolation or end-to-end.

In this article, we propose a new class of priors for Bayesian inference with multiple Gaussian graphical models. We introduce fully Bayesian treatments of two popular procedures, the group graphical lasso and the fused graphical lasso, and extend them to a continuous spike-and-slab framework to allow self-adaptive shrinkage and model selection simultaneously. We develop an EM algorithm that performs fast and dynamic explorations of posterior modes. Our approach selects sparse models efficiently with substantially smaller bias than would be induced by alternative regularization procedures. The performance of the proposed methods are demonstrated through simulation and two real data examples.

A reliable modeling of uncertain evidence in Bayesian networks based on a set-valued quantification is proposed. Both soft and virtual evidences are considered. We show that evidence propagation in this setup can be reduced to standard updating in an augmented credal network, equivalent to a set of consistent Bayesian networks. A characterization of the computational complexity for this task is derived together with an efficient exact procedure for a subclass of instances. In the case of multiple uncertain evidences over the same variable, the proposed procedure can provide a set-valued version of the geometric approach to opinion pooling.

Causal inference from observation data often assumes "strong ignorability," that all confounders are observed. This assumption is standard yet untestable. However, many scientific studies involve multiple causes, different variables whose effects are simultaneously of interest. We propose the deconfounder, an algorithm that combines unsupervised machine learning and predictive model checking to perform causal inference in multiple-cause settings. The deconfounder infers a latent variable as a substitute for unobserved confounders and then uses that substitute to perform causal inference. We develop theory for when the deconfounder leads to unbiased causal estimates, and show that it requires weaker assumptions than classical causal inference. We analyze its performance in three types of studies: semi-simulated data around smoking and lung cancer, semi-simulated data around genomewide association studies, and a real dataset about actors and movie revenue. The deconfounder provides a checkable approach to estimating close-to-truth causal effects.

Recent approaches to human concept learning have successfully combined the power of symbolic, infinitely productive, rule systems and statistical learning. The aim of most of these studies is to reveal the underlying language structuring these representations and providing a general substrate for thought. Here, we ask about the plasticity of symbolic descriptive languages. We perform two concept learning experiments, that consistently demonstrate that humans can change very rapidly the repertoire of symbols they use to identify concepts, by compiling expressions which are frequently used into new symbols of the language. The pattern of concept learning times is accurately described by a Bayesian agent that rationally updates the probability of compiling a new expression according to how useful it has been to compress concepts so far. By portraying the Language of Thought as a flexible system of rules, we also highlight the intrinsic difficulties to pin it down empirically. Keywords: Language of Thought, Concept Learning, Probabilistic Inference 1. Introduction How can children acquire a vast universe of concepts with seemingly very little exposure? Preprint submitted to Cognitive Psychology. Combinatorial languages can describe a vast set of concepts from a small set of primitives. This can be understood in a relatively simple example in the domain of shapes. A combinatorial and symbolic language similar to Logo [5] can combine operations such as "move", "pen up", "pen down" or "rotate" to generate an infinite set of expressions (or programs) which, when evaluated, can convey all sort of shapes.

About this course: This course describes Bayesian statistics, in which one's inferences about parameters or hypotheses are updated as evidence accumulates. You will learn to use Bayes' rule to transform prior probabilities into posterior probabilities, and be introduced to the underlying theory and perspective of the Bayesian paradigm. The course will apply Bayesian methods to several practical problems, to show end-to-end Bayesian analyses that move from framing the question to building models to eliciting prior probabilities to implementing in R (free statistical software) the final posterior distribution. Additionally, the course will introduce credible regions, Bayesian comparisons of means and proportions, Bayesian regression and inference using multiple models, and discussion of Bayesian prediction. We assume learners in this course have background knowledge equivalent to what is covered in the earlier three courses in this specialization: "Introduction to Probability and Data," "Inferential Statistics," and "Linear Regression and Modeling."

One of the largest growing demographics in the EU is individuals aged 65 and over, and two thirds of this group are in situation of multimorbidity, i.e., perons who suffer from two or more chronic diseases. The ineffective treatment of multimorbidity has been pointed out as an urgent problem to address by the Academy of Medical Sciences in a recently released report. As part of an EU H2020 funded project called ProACT, our team at IBM Research – Ireland is working with partners in academia and industry to find new ways to use IoT, AI and cloud technologies to advance self-management capabilities and home-based integrated care for Persons with Multimorbidity (PwM). The ProACT project is investigating ways wearable, home sensors and tablet applications can be used to help persons with multimorbidity, as well as their support actors, which include informal caregivers (e.g. The project includes proof-of-concept trials in Ireland and Belgium, involving national health services, with a number of patients equipped with wearable and home sensors, and their support actors.

Pricing is a common problem faced by businesses, and one that can be addressed effectively by Bayesian statistical methods. We'll step through a simple example and build the background necessary to extend get involved with this approach. Let's start with some hypothetical data. A small company has tried a few different price points (say, one week each) and recorded the demand at each price. We'll abstract away some economic issues in order to focus on the statistical approach.

Artificial intelligence owes a lot of its smarts to Judea Pearl. In the 1980s he led efforts that allowed machines to reason probabilistically. In his latest book, "The Book of Why: The New Science of Cause and Effect," he argues that artificial intelligence has been handicapped by an incomplete understanding of what intelligence really is. Three decades ago, a prime challenge in artificial intelligence research was to program machines to associate a potential cause to a set of observable conditions. Pearl figured out how to do that using a scheme called Bayesian networks.