Mathematical Theory of Evidence (MTE) is known as a foundation for reasoning when knowledge is expressed at various levels of detail. Though much research effort has been committed to this theory since its foundation, many questions remain open. One of the most important open questions seems to be the relationship between frequencies and the Mathematical Theory of Evidence. The theory is blamed to leave frequencies outside (or aside of) its framework. The seriousness of this accusation is obvious: no experiment may be run to compare the performance of MTE-based models of real world processes against real world data. In this paper we develop a frequentist model of the MTE bringing to fall the above argument against MTE. We describe, how to interpret data in terms of MTE belief functions, how to reason from data about conditional belief functions, how to generate a random sample out of a MTE model, how to derive MTE model from data and how to compare results of reasoning in MTE model and reasoning from data. It is claimed in this paper that MTE is suitable to model some types of destructive processes

The benefits of automating design cycles for Bayesian inference-based algorithms are becoming increasingly recognized by the machine learning community. As a result, interest in probabilistic programming frameworks has much increased over the past few years. This paper explores a specific probabilistic programming paradigm, namely message passing in Forney-style factor graphs (FFGs), in the context of automated design of efficient Bayesian signal processing algorithms. To this end, we developed "ForneyLab" (https://github.com/biaslab/ForneyLab.jl) as a Julia toolbox for message passing-based inference in FFGs. We show by example how ForneyLab enables automatic derivation of Bayesian signal processing algorithms, including algorithms for parameter estimation and model comparison. Crucially, due to the modular makeup of the FFG framework, both the model specification and inference methods are readily extensible in ForneyLab. In order to test this framework, we compared variational message passing as implemented by ForneyLab with automatic differentiation variational inference (ADVI) and Monte Carlo methods as implemented by state-of-the-art tools "Edward" and "Stan". In terms of performance, extensibility and stability issues, ForneyLab appears to enjoy an edge relative to its competitors for automated inference in state-space models.

Annotating the right data for training deep neural networks is an important challenge. Active learning using uncertainty estimates from Bayesian Neural Networks (BNNs) could provide an effective solution to this. Despite being theoretically principled, BNNs require approximations to be applied to large-scale problems, and have not been used widely by practitioners. In this paper, we introduce Deep Probabilistic Ensembles (DPEs), a scalable technique that uses a regularized ensemble to approximate a deep BNN. We conduct a series of active learning experiments to evaluate DPEs on classification with the CIFAR-10, CIFAR-100 and ImageNet datasets, and semantic segmentation with the BDD100k dataset. Our models consistently outperform baselines and previously published methods, requiring significantly less training data to achieve competitive performances.

We introduce a novel framework for the estimation of the posterior distribution of the weights of a neural network, based on a new probabilistic interpretation of adaptive subgradient algorithms such as AdaGrad and Adam. Having a confidence measure of the weights allows several shortcomings of neural networks to be addressed. In particular, the robustness of the network can be improved by performing weight pruning based on signal-to-noise ratios from the weight posterior distribution. Using the MNIST dataset, we demonstrate that the empirical performance of Badam, a particular instance of our framework based on Adam, is competitive in comparison to related Bayesian approaches such as Bayes By Backprop.

Uncertainty estimation in deep neural networks is essential for designing reliable and robust AI systems. Applications such as video surveillance for identifying suspicious activities are designed with deep neural networks (DNNs), but DNNs do not provide uncertainty estimates. Capturing reliable uncertainty estimates in safety and security critical applications will help to establish trust in the AI system. Our contribution is to apply Bayesian deep learning framework to visual activity recognition application and quantify model uncertainty along with principled confidence. We utilize the variational inference technique while training the Bayesian DNNs to infer the approximate posterior distribution around model parameters and perform Monte Carlo sampling on the posterior of model parameters to obtain the predictive distribution. We show that the Bayesian inference applied to DNNs provides reliable confidence measures for visual activity recognition task as compared to the conventional DNNs. We also show that our method improves the visual activity recognition precision-recall score by 6% compared to non-Bayesian baseline. We evaluate our models on Moments-In-Time (MiT) activity recognition dataset by selecting a subset of in- and out-of-distribution video samples.

We describe algorithms for use by prediction markets in forming a crowd consensus joint probability distribution over thousands of related events. Equivalently, we describe market mechanisms to efficiently crowdsource both structure and parameters of a Bayesian network. Prediction markets are among the most accurate methods to combine forecasts; forecasters form a consensus probability distribution by trading contingent securities. A combinatorial prediction market forms a consensus joint distribution over many related events by allowing conditional trades or trades on Boolean combinations of events. Explicitly representing the joint distribution is infeasible, but standard inference algorithms for graphical probability models render it tractable for large numbers of base events. We show how to adapt these algorithms to compute expected assets conditional on a prospective trade, and to find the conditional state where a trader has minimum assets, allowing full asset reuse. We compare the performance of three algorithms: the straightforward algorithm from the DAGGRE (Decomposition-Based Aggregation) prediction market for geopolitical events, the simple block-merge model from the SciCast market for science and technology forecasting, and a more sophisticated algorithm we developed for future markets.

Understanding and interpreting how machine learning (ML) models make decisions have been a big challenge. While recent research has proposed various technical approaches to provide some clues as to how an ML model makes individual predictions, they cannot provide users with an ability to inspect a model as a complete entity. In this work, we propose a novel technical approach that augments a Bayesian non-parametric regression mixture model with multiple elastic nets. Using the enhanced mixture model, we can extract generalizable insights for a target model through a global approximation. To demonstrate the utility of our approach, we evaluate it on different ML models in the context of image recognition. The empirical results indicate that our proposed approach not only outperforms the state-of-the-art techniques in explaining individual decisions but also provides users with an ability to discover the vulnerabilities of the target ML models.

This paper addresses the mapping problem. Using a conjugate prior form, we derive the exact theoretical batch multi-object posterior density of the map given a set of measurements. The landmarks in the map are modeled as extended objects, and the measurements are described as a Poisson process, conditioned on the map. We use a Poisson process prior on the map and prove that the posterior distribution is a hybrid Poisson, multi-Bernoulli mixture distribution. We devise a Gibbs sampling algorithm to sample from the batch multi-object posterior. The proposed method can handle uncertainties in the data associations and the cardinality of the set of landmarks, and is parallelizable, making it suitable for large-scale problems. The performance of the proposed method is evaluated on synthetic data and is shown to outperform a state-of-the-art method.

In this paper, we propose an effective TH resholding method based on ORder S tatistic, called THORS, to convert an arbitrary scoring-type classifier, which can induce a continuous cumulative distribution function of the score, into a cost-sensitive one. The procedure, uses order statistic to find an optimal threshold for classification, requiring almost no knowledge of classifiers itself. Unlike common data-driven methods, we analytically show that THORS has theoretical guaranteed performance, theoretical bounds for the costs and lower time complexity. Coupled with empirical results on several real-world data sets, we argue that THORS is the preferred cost-sensitive technique. Key words: Classification; Cost-sensitive learning; Imbalanced data set; Statistical learning; Threshold adjusting.

An intelligent agent performs actions in order to achieve its goals. Such actions can either be externally directed, such as opening a door, or internally directed, such as writing data to a memory location or strengthening a synaptic connection. Some internal actions, to which we refer as computations, potentially help the agent choose better actions. Considering that (external) actions and computations might draw upon the same resources, such as time and energy, deciding when to act or compute, as well as what to compute, are detrimental to the performance of an agent. In an environment that provides rewards depending on an agent's behavior, an action's value is typically defined as the sum of expected long-term rewards succeeding the action (itself a complex quantity that depends on what the agent goes on to do after the action in question). However, defining the value of a computation is not as straightforward, as computations are only valuable in a higher order way, through the alteration of actions. This thesis offers a principled way of computing the value of a computation in a planning setting formalized as a Markov decision process. We present two different definitions of computation values: static and dynamic. They address two extreme cases of the computation budget: affording calculation of zero or infinitely many steps in the future. We show that these values have desirable properties, such as temporal consistency and asymptotic convergence. Furthermore, we propose methods for efficiently computing and approximating the static and dynamic computation values. We describe a sense in which the policies that greedily maximize these values can be optimal. We utilize these principles to construct Monte Carlo tree search algorithms that outperform most of the state-of-the-art in terms of finding higher quality actions given the same simulation resources.