A lot of relevant works have been completed to provided different kinds of method to properly handle information offered which promotes the development of information industry. The representatives of the corresponding theories are soft theory [1-5], Z-numbers [6-9], D-numbers [10-14], fuzzy theory [15-18], Dempster-Shafer evidence theory [19-23] and some other mixed theories [24-26]. And the effectiveness of these theories are verified in many practical applications, like risk evaluation [27-29], pattern classification [30], optimization [31-34] and decision making [35-38]. Moreover, due to the rapid progress of quantum computing, some researchers come up with the idea that traditional information management can be transferred to the level of quantum. Some meaningful works about the topic are complex mass function [39-43] and quantum information theory [44-47]. In this paper, the proposed method is based on the quantum model of mass function [47]. In order to avoid the deviation which may caused by the original quantum evidences, a dual check system is designed to ensure the authenticity of the original judgments which utilizes the concept of Z-number [9]. Besides, because of the introduction of the time interval, a specially devised rule is proposed to appropriately decide the importance of different relationships of incidents, which is a kind of expert system under some restrictions. The contributions of the proposed method can be listed as: (1) The second dual check system can help avoid the deviation produced by the original evidences to help provide more effective results.

Ensembles of machine learning models yield improved system performance as well as robust and interpretable uncertainty estimates; however, their inference costs may often be prohibitively high. Ensemble Distribution Distillation is an approach that allows a single model to efficiently capture both the predictive performance and uncertainty estimates of an ensemble. For classification, this is achieved by training a Dirichlet distribution over the ensemble members' output distributions via the maximum likelihood criterion. Although theoretically principled, this criterion exhibits poor convergence when applied to large-scale tasks where the number of classes is very high. In our work, we analyze this effect and show that for the Dirichlet log-likelihood criterion classes with low probability induce larger gradients than high-probability classes. This forces the model to focus on the distribution of the ensemble tail-class probabilities. We propose a new training objective which minimizes the reverse KL-divergence to a Proxy-Dirichlet target derived from the ensemble. This loss resolves the gradient issues of Ensemble Distribution Distillation, as we demonstrate both theoretically and empirically on the ImageNet and WMT17 En-De datasets containing 1000 and 40,000 classes, respectively.

Algorithmic Information Theory has inspired intractable constructions of general intelligence (AGI), and undiscovered tractable approximations are likely feasible. Reinforcement Learning (RL), the dominant paradigm by which an agent might learn to solve arbitrary solvable problems, gives an agent a dangerous incentive: to gain arbitrary "power" in order to intervene in the provision of their own reward. We review the arguments that generally intelligent algorithmic-information-theoretic reinforcement learners such as Hutter's (2005) AIXI would seek arbitrary power, including over us. Then, using an information-theoretic exploration schedule, and a setup inspired by causal influence theory, we present a variant of AIXI which learns to not seek arbitrary power; we call it "unambitious". We show that our agent learns to accrue reward at least as well as a human mentor, while relying on that mentor with diminishing probability. And given a formal assumption that we probe empirically, we show that eventually, the agent's world-model incorporates the following true fact: intervening in the "outside world" will have no effect on reward acquisition; hence, it has no incentive to shape the outside world.

Biopharmaceutical manufacturing is a rapidly growing industry with impact in virtually all branches of medicine. Biomanufacturing processes require close monitoring and control, in the presence of complex bioprocess dynamics with many interdependent factors, as well as extremely limited data due to the high cost and long duration of experiments. We develop a novel model-based reinforcement learning framework that can achieve human-level control in low-data environments. The model uses a probabilistic knowledge graph to capture causal interdependencies between factors in the underlying stochastic decision process, leveraging information from existing kinetic models from different unit operations while incorporating real-world experimental data. We then present a computationally efficient, provably convergent stochastic gradient method for policy optimization. Validation is conducted on a realistic application with a multi-dimensional, continuous state variable.

Recently, denoising diffusion probabilistic models and generative score matching have shown high potential in modelling complex data distributions while stochastic calculus has provided a unified point of view on these techniques allowing for flexible inference schemes. In this paper we introduce Grad-TTS, a novel text-to-speech model with score-based decoder producing mel-spectrograms by gradually transforming noise predicted by encoder and aligned with text input by means of Monotonic Alignment Search. The framework of stochastic differential equations helps us to generalize conventional diffusion probabilistic models to the case of reconstructing data from noise with different parameters and allows to make this reconstruction flexible by explicitly controlling trade-off between sound quality and inference speed. Subjective human evaluation shows that Grad-TTS is competitive with state-of-the-art text-to-speech approaches in terms of Mean Opinion Score. We will make the code publicly available shortly.

We develop simple methods for constructing likelihoods and parameter priors for learning about the parameters and structure of a Bayesian network. In particular, we introduce several assumptions that permit the construction of likelihoods and parameter priors for a large number of Bayesian-network structures from a small set of assessments. The most notable assumption is that of likelihood equivalence, which says that data can not help to discriminate network structures that encode the same assertions of conditional independence. We describe the constructions that follow from these assumptions, and also present a method for directly computing the marginal likelihood of a random sample with no missing observations. Also, we show how these assumptions lead to a general framework for characterizing parameter priors of multivariate distributions.

This note is meant to provide an introduction to linear models and the theories behind them. Our goal is to give a rigorous introduction to the readers with prior exposure to ordinary least squares. In machine learning, the output is usually a nonlinear function of the input. Deep learning even aims to find a nonlinear dependence with many layers which require a large amount of computation. However, most of these algorithms build upon simple linear models. We then describe linear models from different views and find the properties and theories behind the models. The linear model is the main technique in regression problems and the primary tool for it is the least squares approximation which minimizes a sum of squared errors. This is a natural choice when we're interested in finding the regression function which minimizes the corresponding expected squared error. We first describe ordinary least squares from three different points of view upon which we disturb the model with random noise and Gaussian noise. By Gaussian noise, the model gives rise to the likelihood so that we introduce a maximum likelihood estimator. It also develops some distribution theories for it via this Gaussian disturbance. The distribution theory of least squares will help us answer various questions and introduce related applications. We then prove least squares is the best unbiased linear model in the sense of mean squared error and most importantly, it actually approaches the theoretical limit. We end up with linear models with the Bayesian approach and beyond.

Neural networks (NNs) have shown high predictive performance, however, with shortcomings. Firstly, the reasons behind the classifications are not fully understood. Several explanation methods have been developed, but they do not provide mechanisms for users to interact with the explanations. Explanations are social, meaning they are a transfer of knowledge through interactions. Nonetheless, current explanation methods contribute only to one-way communication. Secondly, NNs tend to be overconfident, providing unreasonable uncertainty estimates on out-of-distribution observations. We overcome these difficulties by training a Bayesian convolutional neural network (CNN) that uses explanation feedback. After training, the model presents explanations of training sample classifications to an annotator. Based on the provided information, the annotator can accept or reject the explanations by providing feedback. Our proposed method utilizes this feedback for fine-tuning to correct the model such that the explanations and classifications improve. We use existing CNN architectures to demonstrate the method's effectiveness on one toy dataset (decoy MNIST) and two real-world datasets (Dogs vs. Cats and ISIC skin cancer). The experiments indicate that few annotated explanations and fine-tuning epochs are needed to improve the model and predictive performance, making the model more trustworthy and understandable.

In real life, lots of information merges from time to time. To appropriately describe the actual situations, lots of theories have been proposed. Among them, Dempster-Shafer evidence theory is a very useful tool in managing uncertain information. To better adapt to complex situations of open world, a generalized evidence theory is designed. However, everything occurs in sequence and owns some underlying relationships with each other. In order to further embody the details of information and better conforms to situations of real world, a Markov model is introduced into the generalized evidence theory which helps extract complete information volume from evidence provided. Besides, some numerical examples is offered to verify the correctness and rationality of the proposed method.

Artificial neural networks will always make a prediction, even when completely uncertain and regardless of the consequences. This obliviousness of uncertainty is a major obstacle towards their adoption in practice. Techniques exist, however, to estimate the two major types of uncertainty: model uncertainty and observation noise in the data. Bayesian neural networks are theoretically well-founded models that can learn the model uncertainty of their predictions. Minor modifications to these models and their loss functions allow learning the observation noise for individual samples as well. This paper is the first to apply these techniques to predictive process monitoring. We found that they contribute towards more accurate predictions and work quickly. However, their main benefit resides with the uncertainty estimates themselves that allow the separation of higher-quality from lower-quality predictions and the building of confidence intervals. This leads to many interesting applications, enables an earlier adoption of prediction systems with smaller datasets and fosters a better cooperation with humans.