A recently-introduced class of probabilistic (uncertainty-aware) solvers for ordinary differential equations (ODEs) applies Gaussian (Kalman) filtering to initial value problems. These methods model the true solution $x$ and its first $q$ derivatives a priori as a Gauss--Markov process $\boldsymbol{X}$, which is then iteratively conditioned on information about $\dot{x}$. We prove worst-case local convergence rates of order $h^{q+1}$ for a wide range of versions of this Gaussian ODE filter, as well as global convergence rates of order $h^q$ in the case of $q=1$ and an integrated Brownian motion prior, and analyze how inaccurate information on $\dot{x}$ coming from approximate evaluations of $f$ affects these rates. Moreover, we present explicit formulas for the steady states and show that the posterior confidence intervals are well calibrated in all considered cases that exhibit global convergence---in the sense that they globally contract at the same rate as the truncation error.

We study the problem of synthesizing a number of likely future frames from a single input image. In contrast to traditional methods that have tackled this problem in a deterministic or non-parametric way, we propose to model future frames in a probabilistic manner. Our probabilistic model makes it possible for us to sample and synthesize many possible future frames from a single input image. To synthesize realistic movement of objects, we propose a novel network structure, namely a Cross Convolutional Network; this network encodes image and motion information as feature maps and convolutional kernels, respectively. In experiments, our model performs well on synthetic data, such as 2D shapes and animated game sprites, and on real-world video frames. We present analyses of the learned network representations, showing it is implicitly learning a compact encoding of object appearance and motion. We also demonstrate a few of its applications, including visual analogy-making and video extrapolation.

Probabilistic representations, such as Bayesian and Markov networks, are fundamental to much of statistical machine learning. Thus, learning probabilistic representations directly from data is a deep challenge, the main computational bottleneck being inference that is intractable. Tractable learning is a powerful new paradigm that attempts to learn distributions that support efficient probabilistic querying. By leveraging local structure, representations such as sum-product networks (SPNs) can capture high tree-width models with many hidden layers, essentially a deep architecture, while still admitting a range of probabilistic queries to be computable in time polynomial in the network size. The leaf nodes in SPNs, from which more intricate mixtures are formed, are tractable univariate distributions, and so the literature has focused on Bernoulli and Gaussian random variables. This is clearly a restriction for handling mixed discrete-continuous data, especially if the continuous features are generated from non-parametric and non-Gaussian distribution families. In this work, we present a framework that systematically integrates SPN structure learning with weighted model integration, a recently introduced computational abstraction for performing inference in hybrid domains, by means of piecewise polynomial approximations of density functions of arbitrary shape. Our framework is instantiated by exploiting the notion of propositional abstractions, thus minimally interfering with the SPN structure learning module, and supports a powerful query interface for conditioning on interval constraints. Our empirical results show that our approach is effective, and allows a study of the trade off between the granularity of the learned model and its predictive power.

Germany Market Analysis Table 35: German Recent Past, Current & Future Analysis for Artificial Intelligence Analyzed with Annual Revenue Figures in US$ Million for Years 2015 through 2024 (includes corresponding Graph/Chart) 9.4.3 Italy Market Analysis Table 36: Italian Recent Past, Current & Future Analysis for Artificial Intelligence Analyzed with Annual Revenue Figures in US$ Million for Years 2015 through 2024 (includes corresponding Graph/Chart) 9.4.4

Agriculture uses 70 percent of the water in the world, and this appears to be an upward trend regarding water needs. As the demand in other industry sectors is also increasing, and the effects of climate change exacerbate water shortages, water saving measures have become an unavoidable challenge for maintaining the sector and preserving life. Agronomy researcher Rafael González has developed a model to predict in advance the water that users will need each day. This tool came about from a drive to ally with water resource sustainability. The model applies artificial intelligence techniques including fuzzy logic, a system used to explain the behavior of decision making.

Agriculture uses 70% of the water in the world and this appears to be an upward trend regarding water needs. In this context in which the demand in other industry sectors is increasing as well and the effects of climate change influence ever-increasing water shortages, water saving measures have become an unavoidable challenge if we want to maintain the sector and preserve life. This is the challenge taken on by Agronomy Department researcher Rafael González when developing a model able to predict in advance the water that each water user will need each day. Therefore, this tool came about from a drive to ally with water resource sustainability. What is innovative about this model lies in the application of artificial intelligence techniques such as fuzzy logic, a system used to explain the behavior of decision making.

The article focuses on determining the predictive uncertainty of a model on the example of atrial fibrillation detection problem by a single-lead ECG signal. To this end, the model predicts parameters of the beta distribution over class probabilities instead of these probabilities themselves. It was shown that the described approach allows to detect atypical recordings and significantly improve the quality of the algorithm on confident predictions.

Agriculture uses 70% of the water in the world and this appears to be an upward trend regarding water needs. In this context in which the demand in other industry sectors is increasing as well and the effects of climate change influence ever-increasing water shortages, water saving measures have become an unavoidable challenge if we want to maintain the sector and preserve life. This is the challenge taken on by Agronomy Department researcher Rafael González when developing a model able to predict in advance the water that each water user will need each day. Therefore, this tool came about from a drive to ally with water resource sustainability. What is innovative about this model lies in the application of artificial intelligence techniques such as fuzzy logic, a system used to explain the behavior of decision making.

We propose a Multi-vAlue Rule Set (MRS) model for in-hospital predicting patient mortality. Compared to rule sets built from single-valued rules, MRS adopts a more generalized form of association rules that allows multiple values in a condition. Rules of this form are more concise than classical single-valued rules in capturing and describing patterns in data. Our formulation also pursues a higher efficiency of feature utilization, which reduces possible cost in data collection and storage. We propose a Bayesian framework for formulating a MRS model and propose an efficient inference method for learning a maximum \emph{a posteriori}, incorporating theoretically grounded bounds to iteratively reduce the search space and improve the search efficiency. Experiments show that our model was able to achieve better performance than baseline method including the current system used by the hospital.

Following the recent successful examples of large technology companies, many modern enterprises seek to build knowledge graphs to provide a unified view of corporate knowledge and to draw deep insights using machine learning and logical reasoning. There is currently a perceived disconnect between the traditional approaches for data science, typically based on machine learning and statistical modelling, and systems for reasoning with domain knowledge. In this paper we present a state-of-the-art Knowledge Graph Management System, Vadalog, which delivers highly expressive and efficient logical reasoning and provides seamless integration with modern data science toolkits, such as the Jupyter platform. We demonstrate how to use Vadalog to perform traditional data wrangling tasks, as well as complex logical and probabilistic reasoning. We argue that this is a significant step forward towards combining machine learning and reasoning in data science.