The notions of disintegration and Bayesian inversion are fundamental in conditional probability theory. They produce channels, as conditional probabilities, from a joint state, or from an already given channel (in opposite direction). These notions exist in the literature, in concrete situations, but are presented here in abstract graphical formulations. The resulting abstract descriptions are used for proving basic results in conditional probability theory. The existence of disintegration and Bayesian inversion is discussed for discrete probability, and also for measure-theoretic probability --- via standard Borel spaces and via likelihoods. Finally, the usefulness of disintegration and Bayesian inversion is illustrated in several examples.

Formal Verification (Fv) and Machine Learning (Ml) can seem incompatible due to their opposite mathematical foundations and their use in real-life problems: Fv mostly relies on discrete mathematics and aims at ensuring correctness; Ml often relies on probabilistic models and consists of learning patterns from training data. In this paper, we postulate that they are complementary in practice, and explore how Ml helps Fv in its classical approaches: static analysis, model-checking, theorem-proving, and Sat solving. We draw a landscape of the current practice and catalog some of the most prominent uses of Ml inside Fv tools, thus offering a new perspective on Fv techniques that can help researchers and practitioners to better locate the possible synergies. We discuss lessons learned from our work, point to possible improvements and offer visions for the future of the domain in the light of the science of software and systems modeling.

These models are computer algorithms, or smart apps, that seek to give computers the ability to learn like children for a variety of tasks. Here, we highlight how an author's work may solve a particular set of real-world tasks or problems. By doing this, we aim to foster more and more machine, learning works, to be done by more and more Jamaican people. Today, we'll highlight the machine-learning work, a paper/algorithm called'Modelling Sensorineural Hearing-impaired Listeners' Perception of Speaker Intelligibility in Noise", by UWI lecturers Dr Lindon W. Falconer, Dr AndrÈ Coy, and their overseas colleague, Professor Jon Barker. Jordan: How would you describe your work? Dr Coy, et al: Disabling hearing loss is a major challenge faced by many individuals in societies throughout the world. The World Health Organization (WHO) has reported that approximately 6.1 per cent of the world's population has disabling hearing loss, and about 93 per cent of these people are adults.

Predicting structured outputs can be computationally onerous due to the combinatorially large output spaces. In this paper, we focus on reducing the prediction time of a trained black-box structured classifier without losing accuracy. To do so, we train a speedup classifier that learns to mimic a black-box classifier under the learning-to-search approach. As the structured classifier predicts more examples, the speedup classifier will operate as a learned heuristic to guide search to favorable regions of the output space. We present a mistake bound for the speedup classifier and identify inference situations where it can independently make correct judgments without input features. We evaluate our method on the task of entity and relation extraction and show that the speedup classifier outperforms even greedy search in terms of speed without loss of accuracy.

Our goal is for AI systems to correctly identify and act according to their human user's objectives. Cooperative Inverse Reinforcement Learning (CIRL) formalizes this value alignment problem as a two-player game between a human and robot, in which only the human knows the parameters of the reward function: the robot needs to learn them as the interaction unfolds. Previous work showed that CIRL can be solved as a POMDP, but with an action space size exponential in the size of the reward parameter space. In this work, we exploit a specific property of CIRL---the human is a full information agent---to derive an optimality-preserving modification to the standard Bellman update; this reduces the complexity of the problem by an exponential factor and allows us to relax CIRL's assumption of human rationality. We apply this update to a variety of POMDP solvers and find that it enables us to scale CIRL to non-trivial problems, with larger reward parameter spaces, and larger action spaces for both robot and human. In solutions to these larger problems, the human exhibits pedagogic (teaching) behavior, while the robot interprets it as such and attains higher value for the human.

A staggering amount of data is created everyday; analyzing and organizing this enormous amount of data can be quite a complex task. Haskell is a powerful and well-designed functional programming language that is designed to work with complex data. It is trending in the field of data science as it provides a powerful platform for robust data science practices. This course will introduce the basic concepts of Haskell and move on to discuss how Haskell can be used to solve the issues by using the real-world data. The course will guide you through the installation procedure, after you have all the tools that you require in place, you will explore the basic concepts of Haskell including the functions, and the data structures.

We present an application of deep generative models in the context of partial-differential equation (PDE) constrained inverse problems. We combine a generative adversarial network (GAN) representing an a priori model that creates subsurface geological structures and their petrophysical properties, with the numerical solution of the PDE governing the propagation of acoustic waves within the earth's interior. We perform Bayesian inversion using an approximate Metropolis-adjusted Langevin algorithm (MALA) to sample from the posterior given seismic observations. Gradients with respect to the model parameters governing the forward problem are obtained by solving the adjoint of the acoustic wave equation. Gradients of the mismatch with respect to the latent variables are obtained by leveraging the differentiable nature of the deep neural network used to represent the generative model. We show that approximate MALA sampling allows efficient Bayesian inversion of model parameters obtained from a prior represented by a deep generative model, obtaining a diverse set of realizations that reflect the observed seismic response.

We introduce a method for embedding words as probability densities in a low-dimensional space. Rather than assuming that a word embedding is fixed across the entire text collection, as in standard word embedding methods, in our Bayesian model we generate it from a word-specific prior density for each occurrence of a given word. Intuitively, for each word, the prior density encodes the distribution of its potential 'meanings'. These prior densities are conceptually similar to Gaussian embeddings. Interestingly, unlike the Gaussian embeddings, we can also obtain context-specific densities: they encode uncertainty about the sense of a word given its context and correspond to posterior distributions within our model. The context-dependent densities have many potential applications: for example, we show that they can be directly used in the lexical substitution task. We describe an effective estimation method based on the variational autoencoding framework. We also demonstrate that our embeddings achieve competitive results on standard benchmarks.

While off-policy temporal difference (TD) methods have widely been used in reinforcement learning due to their efficiency and simple implementation, their Bayesian counterparts have not been utilized as frequently. One reason is that the non-linear max operation in the Bellman optimality equation makes it difficult to define conjugate distributions over the value functions. In this paper, we introduce a novel Bayesian approach to off-policy TD methods using Assumed Density Filtering (ADFQ), which updates beliefs on state-action values (Q) through an online Bayesian inference method. Uncertainty measures in the beliefs provide a natural regularization for learning, and we show how ADFQ reduces in a limiting case to the traditional Q-learning algorithm. Our empirical results demonstrate that the proposed ADFQ algorithms outperform comparable algorithms on several task domains. Moreover, our algorithms are computationally more efficient than other existing approaches to Bayesian reinforcement learning.

Machine learning is a major component in the race towards artificial intelligence. Whether you're seeking true artificial intelligence or simply trying to gain insight from all the data you've been collecting, machine learning is a major step forward. But where to get started? If you're a beginner, machine learning can feel overwhelming – how to choose which algorithms to use, from the seemingly infinite options, and how to know just which one will provide the right predictions (data outputs). These top 5 machine learning algorithms for beginners offer a fine balance of ease, lower computational power, and immediate, accurate results.