A Hilbert space embedding of a distribution---in short, a kernel mean embedding---has recently emerged as a powerful tool for machine learning and inference. The basic idea behind this framework is to map distributions into a reproducing kernel Hilbert space (RKHS) in which the whole arsenal of kernel methods can be extended to probability measures. It can be viewed as a generalization of the original "feature map" common to support vector machines (SVMs) and other kernel methods. While initially closely associated with the latter, it has meanwhile found application in fields ranging from kernel machines and probabilistic modeling to statistical inference, causal discovery, and deep learning. The goal of this survey is to give a comprehensive review of existing work and recent advances in this research area, and to discuss the most challenging issues and open problems that could lead to new research directions. The survey begins with a brief introduction to the RKHS and positive definite kernels which forms the backbone of this survey, followed by a thorough discussion of the Hilbert space embedding of marginal distributions, theoretical guarantees, and a review of its applications. The embedding of distributions enables us to apply RKHS methods to probability measures which prompts a wide range of applications such as kernel two-sample testing, independent testing, and learning on distributional data. Next, we discuss the Hilbert space embedding for conditional distributions, give theoretical insights, and review some applications. The conditional mean embedding enables us to perform sum, product, and Bayes' rules---which are ubiquitous in graphical model, probabilistic inference, and reinforcement learning---in a non-parametric way. We then discuss relationships between this framework and other related areas. Lastly, we give some suggestions on future research directions.

Non-stationary continuous time Bayesian networks are introduced. They allow the parents set of each node to change over continuous time. Three settings are developed for learning non-stationary continuous time Bayesian networks from data: known transition times, known number of epochs and unknown number of epochs. A score function for each setting is derived and the corresponding learning algorithm is developed. A set of numerical experiments on synthetic data is used to compare the effectiveness of non-stationary continuous time Bayesian networks to that of non-stationary dynamic Bayesian networks.

In this paper, a methodology is investigated for signal recovery in the presence of non-Gaussian noise. In contrast with regularized minimization approaches often adopted in the literature, in our algorithm the regularization parameter is reliably estimated from the observations. As the posterior density of the unknown parameters is analytically intractable, the estimation problem is derived in a variational Bayesian framework where the goal is to provide a good approximation to the posterior distribution in order to compute posterior mean estimates. Moreover, a majorization technique is employed to circumvent the difficulties raised by the intricate forms of the non-Gaussian likelihood and of the prior density. We demonstrate the potential of the proposed approach through comparisons with state-of-the-art techniques that are specifically tailored to signal recovery in the presence of mixed Poisson-Gaussian noise. Results show that the proposed approach is efficient and achieves performance comparable with other methods where the regularization parameter is manually tuned from the ground truth.

All the regression theory developed by statisticians over the last 200 years (related to the general linear model) is useless. Regression can be performed as accurately without statistical models, including the computation of confidence intervals (for estimates, predicted values or regression parameters). The non-statistical approach is also more robust than theory described in all statistics textbooks and taught in all statistical courses. It does not require Map-Reduce when data is really big, nor any matrix inversion, maximum likelihood estimation, or mathematical optimization (Newton algorithm). It is indeed incredibly simple, robust, easy to interpret, and easy to code (no statistical libraries required).

A few months ago, Autonomy founder and CEO Mike Lynch sold his company to HP for £7.1 billion. Back in 2000, when he had just become Britain's first software billionaire, Lynch gave an interview in which he talked about perception and explained how he built his company. It was based, he said, on the ideas of a little-known 18th-century clergyman called Thomas Bayes. That was my introduction to Thomas Bayes, whose ideas have been used to solve many intractable problems, a number of which Sharon Bertsch McGrayne studies in depth in The Theory That Would Not Die. In the last ten years, Bayes has become famous, and few working in the field of probability theory, computer intelligence or mathematics can have failed to have come into contact with his rule.

We introduce a new dynamical system for sequentially observed multivariate count data. This model is based on the gamma--Poisson construction---a natural choice for count data---and relies on a novel Bayesian nonparametric prior that ties and shrinks the model parameters, thus avoiding overfitting. We present an efficient MCMC inference algorithm that advances recent work on augmentation schemes for inference in negative binomial models. Finally, we demonstrate the model's inductive bias using a variety of real-world data sets, showing that it exhibits superior predictive performance over other models and infers highly interpretable latent structure.

Here is an excellent ILP reference, somewhat older but publicly available. The most recent issue of SIGKDD Explorations is a special issue devoted to multi-relational data mining.

Many and long were the conversations between Lord Byron and Shelley to which I was a devout and silent listener. During one of these, various philosophical doctrines were discussed, and among others the nature of the principle of life, and whether there was any probability of its ever being discovered and communicated. They talked of the experiments of Dr. Darwin (I speak not of what the doctor really did or said that he did, but, as more to my purpose, of what was then spoken of as having been done by him), who preserved a piece of vermicelli in a glass case till by some extraordinary means it began to move with a voluntary motion. Not thus, after all, would life be given. Perhaps a corpse would be reanimated; galvanism had given token of such things: perhaps the component parts of a creature might be manufactured, brought together, and endued with vital warmth (Butler 1998).

This page contains some information on research by David Poole and students on probabilistic reasoning and decision making. It is not intended to be an introduction to the vast literature on these topics, but only the incremental work done by me. For more different perspectives, see the pointers from the Uncertainty in AI (UAI) home page. Maybe someday I will write an online introduction. Probabilistic Horn abduction is a pragmatic combination of logic and probability.

You may skip most of these readings if you have prior programming experience in Java.