To measure the quality of a set of vector quantization points a means of measuring the distance between a random point and its quantization is required. Common metrics such as the {\em Hamming} and {\em Euclidean} metrics, while mathematically simple, are inappropriate for comparing natural signals such as speech or images. In this paper it is shown how an {\em environment} of functions on an input space $X$ induces a {\em canonical distortion measure} (CDM) on X. The depiction 'canonical" is justified because it is shown that optimizing the reconstruction error of X with respect to the CDM gives rise to optimal piecewise constant approximations of the functions in the environment. The CDM is calculated in closed form for several different function classes. An algorithm for training neural networks to implement the CDM is presented along with some encouraging experimental results.

We present ProxiModel, a novel event mining framework for extracting high-quality structured event knowledge from large, redundant, and noisy news data sources. The proposed model differentiates itself from other approaches by modeling both the event correlation within each individual document as well as across the corpus. To facilitate this, we introduce the concept of a proximity-network, a novel space-efficient data structure to facilitate scalable event mining. This proximity network captures the corpus-level co-occurence statistics for candidate event descriptors, event attributes, as well as their connections. We probabilistically model the proximity network as a generative process with sparsity-inducing regularization. This allows us to efficiently and effectively extract high-quality and interpretable news events. Experiments on three different news corpora demonstrate that the proposed method is effective and robust at generating high-quality event descriptors and attributes. We briefly detail many interesting applications from our proposed framework such as news summarization, event tracking and multi-dimensional analysis on news. Finally, we explore a case study on visualizing the events for a Japan Tsunami news corpus and demonstrate ProxiModel's ability to automatically summarize emerging news events.

Multi-output Gaussian processes (MOGPs) leverage the flexibility and interpretability of GPs while capturing structure across outputs, which is desirable, for example, in spatio-temporal modelling. The key problem with MOGPs is the cubic computational scaling in the number of both inputs (e.g., time points or locations), n, and outputs, p. Current methods reduce this to O(n^3 m^3), where m < p is the desired degrees of freedom. This computational cost, however, is still prohibitive in many applications. To address this limitation, we present the Orthogonal Linear Mixing Model (OLMM), an MOGP in which exact inference scales linearly in m: O(n^3 m). This advance opens up a wide range of real-world tasks and can be combined with existing GP approximations in a plug-and-play way as demonstrated in the paper. Additionally, the paper organises the existing disparate literature on MOGP models into a simple taxonomy called the Mixing Model Hierarchy (MMH).

In this paper the problem of learning appropriate bias for an environment of related tasks is examined from a Bayesian perspective. The environment of related tasks is shown to be naturally modelled by the concept of an {\em objective} prior distribution. Sampling from the objective prior corresponds to sampling different learning tasks from the environment. It is argued that for many common machine learning problems, although we don't know the true (objective) prior for the problem, we do have some idea of a set of possible priors to which the true prior belongs. It is shown that under these circumstances a learner can use Bayesian inference to learn the true prior by sampling from the objective prior. Bounds are given on the amount of information required to learn a task when it is simultaneously learnt with several other tasks. The bounds show that if the learner has little knowledge of the true prior, and the dimensionality of the true prior is small, then sampling multiple tasks is highly advantageous.

Regularized least-squares (kernel-ridge / Gaussian process) regression is a fundamental algorithm of statistics and machine learning. Because generic algorithms for the exact solution have cubic complexity in the number of datapoints, large datasets require to resort to approximations. In this work, the computation of the least-squares prediction is itself treated as a probabilistic inference problem. We propose a structured Gaussian regression model on the kernel function that uses projections of the kernel matrix to obtain a low-rank approximation of the kernel and the matrix. A central result is an enhanced way to use the method of conjugate gradients for the specific setting of least-squares regression as encountered in machine learning. Our method improves the approximation of the kernel ridge regressor / Gaussian process posterior mean over vanilla conjugate gradients and, allows computation of the posterior variance and the log marginal likelihood (evidence) without further overhead.

A BSTRACT In probabilistic classification, a discriminative model based on Gaussian mixture exhibits flexible fitting capability. Nevertheless, it is difficult to determine the number of components. We propose a sparse classifier based on a discriminative Gaussian mixture model (GMM), which is named sparse discriminative Gaussian mixture (SDGM). In the SDGM, a GMM-based discriminative model is trained by sparse Bayesian learning. This learning algorithm improves the generalization capability by obtaining a sparse solution and automatically determines the number of components by removing redundant components. The SDGM can be embedded into neural networks (NNs) such as convolutional NNs and can be trained in an end-to-end manner. Experimental results indicated that the proposed method prevented overfitting by obtaining sparsity. Furthermore, we demonstrated that the proposed method outperformed a fully connected layer with the softmax function in certain cases when it was used as the last layer of a deep NN. 1 I NTRODUCTION In supervised classification, probabilistic classification is an approach that assigns a class label c to an input sample x by estimating the posterior probability P (c x).

Many domains of science have developed complex simulations to describe phenomena of interest. While these simulations provide high-fidelity models, they are poorly suited for inference and lead to challenging inverse problems. We review the rapidly developing field of simulation-based inference and identify the forces giving new momentum to the field. Finally, we describe how the frontier is expanding so that a broad audience can appreciate the profound change these developments may have on science.

Despite ample evidence that our concepts, our cognitive architecture, and mathematics itself are all deeply compositional, few models take advantage of this structure. We therefore propose a radically compositional approach to computational neuroscience, drawing on the methods of applied category theory. We describe how these tools grant us a means to overcome complexity and improve interpretability, and supply a rigorous common language for scientific modelling, analogous to the type theories of computer science. As a case study, we sketch how to translate from compositional narrative concepts to neural circuits and back again.

Alan Turing (1950) was one of the founders of modern computers and AI. The "Turing test" was based on the fact that the intelligent behavior of a computer is the ability to achieve human level performance in cognition related tasks.[1] The 1980s and 1990s saw a surge in interest in AI. Artificial intelligent techniques such as fuzzy expert systems, Bayesian networks, artificial neural networks, and hybrid intelligent systems were used in different clinical settings in health care. In 2016, the biggest chunk of investments in AI research were in healthcare applications compared with other sectors.[2] AI in medicine can be dichotomized into two subtypes: Virtual and physical.[3]

The Mat\'ern covariance function is a popular choice for prediction in spatial statistics and uncertainty quantification literature. A key benefit of the Mat\'ern class is that it is possible to get precise control over the degree of differentiability of the process realizations. However, the Mat\'ern class possesses exponentially decaying tails, and thus may not be suitable for modeling long range dependence. This problem can be remedied using polynomial covariances; however one loses control over the degree of differentiability of the process realizations, in that the realizations using polynomial covariances are either infinitely differentiable or not differentiable at all. We construct a new family of covariance functions using a scale mixture representation of the Mat\'ern class where one obtains the benefits of both Mat\'ern and polynomial covariances. The resultant covariance contains two parameters: one controls the degree of differentiability near the origin and the other controls the tail heaviness, independently of each other. Using a spectral representation, we derive theoretical properties of this new covariance including equivalence measures and asymptotic behavior of the maximum likelihood estimators under infill asymptotics. The improved theoretical properties in predictive performance of this new covariance class are verified via extensive simulations. Application using NASA's Orbiting Carbon Observatory-2 satellite data confirms the advantage of this new covariance class over the Mat\'ern class, especially in extrapolative settings.